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Deck 13: Introduction to Multiple Regression
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Question
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate?
A) 10.90
B) 12.20
C) 24.87
D) 25.70
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate?
A) 10.90
B) 12.20
C) 24.87
D) 25.70
Question
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate?
A) 10.90
B) 12.20
C) 17.23
D) 25.11
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate?
A) 10.90
B) 12.20
C) 17.23
D) 25.11
Question
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for the number of economics courses taken, b₂?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for the number of economics courses taken, b₂?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
Question
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r² value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?
A) 98.2
B) 11.1
C) 2.8
D) 1.1
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r² value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?
A) 98.2
B) 11.1
C) 2.8
D) 1.1
Question
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b₁?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b₁?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the regression model as a whole is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the regression model as a whole is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
Question
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the value for the regression constant, b₀?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the value for the regression constant, b₀?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
Question
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?
A) 79.09
B) 60.88
C) 55.62
D) 17.98
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?
A) 79.09
B) 60.88
C) 55.62
D) 17.98
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the aggregated price index is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the aggregated price index is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for GDP is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for GDP is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
Question
Question
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for performance rating, b₁?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for performance rating, b₁?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
Question
Question
Question
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the value for the regression constant, b₀?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the value for the regression constant, b₀?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
Question
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b₂?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b₂?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
Question
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by
A) regression sum of squares.
B) error sum of squares.
C) total sum of squares.
D) regression mean squares.
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by
A) regression sum of squares.
B) error sum of squares.
C) total sum of squares.
D) regression mean squares.
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether gross domestic product has a positive impact on consumption, the p-value is ________.
A) 0.00005
B) 0.0001
C) 0.9999
D) 0.99995
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether gross domestic product has a positive impact on consumption, the p-value is ________.
A) 0.00005
B) 0.0001
C) 0.9999
D) 0.99995
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?
A) $4.39 billion
B) $0.39 billion
C) -$0.39 billion
D) -$1.33 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?
A) $4.39 billion
B) $0.39 billion
C) -$0.39 billion
D) -$1.33 billion
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what fraction of the variability in house size is explained by income, size of family, and education?
A) 27.0%
B) 33.4%
C) 74.8%
D) 86.5%
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what fraction of the variability in house size is explained by income, size of family, and education?
A) 27.0%
B) 33.4%
C) 74.8%
D) 86.5%
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?
A) 11.43
B) 15.15
C) 24.88
D) 53.87
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?
A) 11.43
B) 15.15
C) 24.88
D) 53.87
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the independent variables in the model are significant at the 5% level?
A) Income, Size, School
B) Income, Size
C) Size, School
D) Income, School
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the independent variables in the model are significant at the 5% level?
A) Income, Size, School
B) Income, Size
C) Size, School
D) Income, School
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home (House = 100)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home (House = 100)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?
A) 2.8%
B) 51.8%
C) 72.6%
D) 74.8%
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?
A) 2.8%
B) 51.8%
C) 72.6%
D) 74.8%
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $40,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet)for this data point?
A) -6.99
B) -5.35
C) 5.40
D) 16.99
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $40,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet)for this data point?
A) -6.99
B) -5.35
C) 5.40
D) 16.99
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the value of the relevant t-statistic is ________.
A) 2.365
B) 0.143
C) -0.219
D) -1.960
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the value of the relevant t-statistic is ________.
A) 2.365
B) 0.143
C) -0.219
D) -1.960
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet)for this data point?
A) 7.40
B) 2.52
C) -2.52
D) -5.40
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet)for this data point?
A) 7.40
B) 2.52
C) -2.52
D) -5.40
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?
A) $2.52 billion
B) $0.48 billion
C) -$1.33 billion
D) -$2.52 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?
A) $2.52 billion
B) $0.48 billion
C) -$1.33 billion
D) -$2.52 billion
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a positive impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.5835
D) 0.8330
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a positive impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.5835
D) 0.8330
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home (House = 50)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home (House = 50)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a negative impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.8330
D) 0.8837
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a negative impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.8330
D) 0.8837
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
A) 0.0005
B) 0.001
C) 0.01
D) 0.05
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
A) 0.0005
B) 0.001
C) 0.01
D) 0.05
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
Question
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on gross domestic product, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on gross domestic product, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Wages?
A) 0.01
B) 0.05
C) 0.0001
D) none of the above
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Wages?
A) 0.01
B) 0.05
C) 0.0001
D) none of the above
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the following values for α is the smallest for which the regression model as a whole is significant?
A) 0.00005
B) 0.001
C) 0.01
D) 0.05
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the following values for α is the smallest for which the regression model as a whole is significant?
A) 0.00005
B) 0.001
C) 0.01
D) 0.05
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?
A) School is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) School is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) School is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) School is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?
A) School is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) School is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) School is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) School is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a positive impact on corporate sales?
A) 0.01
B) 0.05
C) 0.0001
D) 0.00005
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a positive impact on corporate sales?
A) 0.01
B) 0.05
C) 0.0001
D) 0.00005
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a positive influence on corporate sales?
A) 0.025
B) 0.05
C) 0.2743
D) 0.5485
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a positive influence on corporate sales?
A) 0.025
B) 0.05
C) 0.2743
D) 0.5485
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r² value of 0.601. What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?
A) 60.1%
B) 31.1%
C) 22.9%
D) 8.8%
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r² value of 0.601. What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?
A) 60.1%
B) 31.1%
C) 22.9%
D) 8.8%
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model?
A) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model?
A) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the residual degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the residual degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a negative impact on corporate sales?
A) 0.05
B) 0.0001
C) 0.00005
D) 0.99995
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a negative impact on corporate sales?
A) 0.05
B) 0.0001
C) 0.00005
D) 0.99995
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?
A) 0.0001
B) 0.0299
C) 0.726
D) 45.5340
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?
A) 0.0001
B) 0.0299
C) 0.726
D) 45.5340
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $500 million on capital and $200 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $500 million on capital and $200 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a negative influence on corporate sales?
A) 0.05
B) 0.2743
C) 0.5485
D) 0.7258
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a negative influence on corporate sales?
A) 0.05
B) 0.2743
C) 0.5485
D) 0.7258
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the regression degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the regression degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what fraction of the variability in sales is explained by spending on capital and wages?
A) 27.0%
B) 50.9%
C) 68.9%
D) 83.0%
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what fraction of the variability in sales is explained by spending on capital and wages?
A) 27.0%
B) 50.9%
C) 68.9%
D) 83.0%
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, the observed value of the F-statistic is missing from the printout. What are the degrees of freedom for this F-statistic?
A) 46 for the numerator, 3 for the denominator
B) 3 for the numerator, 49 for the denominator
C) 46 for the numerator, 49 for the denominator
D) 3 for the numerator, 46 for the denominator
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, the observed value of the F-statistic is missing from the printout. What are the degrees of freedom for this F-statistic?
A) 46 for the numerator, 3 for the denominator
B) 3 for the numerator, 49 for the denominator
C) 46 for the numerator, 49 for the denominator
D) 3 for the numerator, 46 for the denominator
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Capital?
A) 0.01
B) 0.025
C) 0.05
D) none of the above
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Capital?
A) 0.01
B) 0.025
C) 0.05
D) none of the above
Question
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the independent variables in the model are significant at the 5% level?
A) Capital, Wages
B) Capital
C) Wages
D) none of the above
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the independent variables in the model are significant at the 5% level?
A) Capital, Wages
B) Capital
C) Wages
D) none of the above
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The slopes in a multiple regression model are called net regression coefficients.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The slopes in a multiple regression model are called net regression coefficients.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?
A) [6.58, 3.65]
B) [6.24, 2.78]
C) [5.94, 3.08]
D) [2.37, 15.12]
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?
A) [6.58, 3.65]
B) [6.24, 2.78]
C) [5.94, 3.08]
D) [2.37, 15.12]
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination, r², measures the proportion of variation in Y that is explained by X₁ and X₂.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination, r², measures the proportion of variation in Y that is explained by X₁ and X₂.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6 and allowing for a 1% probability of committing a Type I error, what is the decision and conclusion for the test H₀: β₁ = β₂ = β₃ = β₄ = 0 vs. H₁: At least one βⱼ ≠ 0, j = 1, 2, ..., 4 using Model 1?
A) Do not reject H₀ and conclude that the four independent variables have significant individual linear effects on heating costs.
B) Reject H₀ and conclude that the four independent variables taken as a group have significant linear effects on heating costs.
C) Do not reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
D) Reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6 and allowing for a 1% probability of committing a Type I error, what is the decision and conclusion for the test H₀: β₁ = β₂ = β₃ = β₄ = 0 vs. H₁: At least one βⱼ ≠ 0, j = 1, 2, ..., 4 using Model 1?
A) Do not reject H₀ and conclude that the four independent variables have significant individual linear effects on heating costs.
B) Reject H₀ and conclude that the four independent variables taken as a group have significant linear effects on heating costs.
C) Do not reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
D) Reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, suppose the microeconomist wants to test whether the coefficient on Capital is significantly different from 0. What is the value of the relevant t-statistic?
A) 0.609
B) 2.617
C) 4.804
D) 25.432
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, suppose the microeconomist wants to test whether the coefficient on Capital is significantly different from 0. What is the value of the relevant t-statistic?
A) 0.609
B) 2.617
C) 4.804
D) 25.432
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what can we say about Model 1?
A) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs.
B) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.
C) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs.
D) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what can we say about Model 1?
A) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs.
B) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.
C) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs.
D) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The total sum of squares (SST)in a regression model will never be greater than the regression sum of squares (SSR).
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The total sum of squares (SST)in a regression model will never be greater than the regression sum of squares (SSR).
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
In calculating the standard error of the estimate, SYX =
, there are n-k-1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
In calculating the standard error of the estimate, SYX =
, there are n-k-1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model. Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 874.55
B) 622.87
C) -790.69
D) -983.56
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 874.55
B) 622.87
C) -790.69
D) -983.56
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the coefficient of multiple determination will never decrease.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the coefficient of multiple determination will never decrease.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination measures the proportion of the total variation in the dependent variable that is explained by the set of independent variables.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination measures the proportion of the total variation in the dependent variable that is explained by the set of independent variables.
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic?
A) 25 for the numerator, 2 for the denominator
B) 2 for the numerator, 23 for the denominator
C) 23 for the numerator, 25 for the denominator
D) 2 for the numerator, 25 for the denominator
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic?
A) 25 for the numerator, 2 for the denominator
B) 2 for the numerator, 23 for the denominator
C) 23 for the numerator, 25 for the denominator
D) 2 for the numerator, 25 for the denominator
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is your decision and conclusion for the test H₀: β₂ = 0 vs. H₁: β₂ < 0 at the α = 0.01 level of significance using Model 1?
A) Do not reject H₀ and conclude that the amount of insulation has a linear effect on heating cots.
B) Reject H₀ and conclude that the amount of insulation does not have a linear effect on heating costs.
C) Reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
D) Do not reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is your decision and conclusion for the test H₀: β₂ = 0 vs. H₁: β₂ < 0 at the α = 0.01 level of significance using Model 1?
A) Do not reject H₀ and conclude that the amount of insulation has a linear effect on heating cots.
B) Reject H₀ and conclude that the amount of insulation does not have a linear effect on heating costs.
C) Reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
D) Do not reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $21.439 billion (Sales = 21,439). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 790.69
B) 648.31
C) -648.31
D) -790.69
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $21.439 billion (Sales = 21,439). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 790.69
B) 648.31
C) -648.31
D) -790.69
Question
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?
A) Capital is significant in explaining corporate sales and should be included in the model because its p-value is less than 0.01.
B) Capital is significant in explaining corporate sales and should be included in the model because its p-value is more than 0.01.
C) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is less than 0.01.
D) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01.
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?
A) Capital is significant in explaining corporate sales and should be included in the model because its p-value is less than 0.01.
B) Capital is significant in explaining corporate sales and should be included in the model because its p-value is more than 0.01.
C) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is less than 0.01.
D) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the adjusted r² can increase.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the adjusted r² can increase.
Question
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, the estimated value of the partial regression parameter β₁ in Model 1 means that
A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.
B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51.
C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51.
D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, the estimated value of the partial regression parameter β₁ in Model 1 means that
A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.
B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51.
C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51.
D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%.
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Deck 13: Introduction to Multiple Regression
1
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate?
A) 10.90
B) 12.20
C) 24.87
D) 25.70
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate?
A) 10.90
B) 12.20
C) 24.87
D) 25.70
C
2
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate?
A) 10.90
B) 12.20
C) 17.23
D) 25.11
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate?
A) 10.90
B) 12.20
C) 17.23
D) 25.11
B
3
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for the number of economics courses taken, b₂?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for the number of economics courses taken, b₂?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
A
4
In a multiple regression model, the value of the coefficient of multiple determination
A) has to fall between -1 and +1.
B) has to fall between 0 and +1.
C) has to fall between -1 and 0.
D) can fall between any pair of real numbers.
A) has to fall between -1 and +1.
B) has to fall between 0 and +1.
C) has to fall between -1 and 0.
D) can fall between any pair of real numbers.
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5
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r² value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?
A) 98.2
B) 11.1
C) 2.8
D) 1.1
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r² value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?
A) 98.2
B) 11.1
C) 2.8
D) 1.1
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6
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b₁?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b₁?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
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7
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the regression model as a whole is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the regression model as a whole is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
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8
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
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9
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the value for the regression constant, b₀?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the value for the regression constant, b₀?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
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10
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?
A) 79.09
B) 60.88
C) 55.62
D) 17.98
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?
A) 79.09
B) 60.88
C) 55.62
D) 17.98
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11
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the aggregated price index is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for the aggregated price index is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
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12
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for GDP is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, the p-value for GDP is ________.
A) 0.05
B) 0.01
C) 0.001
D) none of the above
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13
The coefficient of multiple determination r²Y.₁₂
A) measures the variation around the predicted regression equation.
B) measures the proportion of variation in Y that is explained by X₁ and X₂.
C) measures the proportion of variation in Y that is explained by X₁ holding X₂ constant.
D) will have the same sign as b₁.
A) measures the variation around the predicted regression equation.
B) measures the proportion of variation in Y that is explained by X₁ and X₂.
C) measures the proportion of variation in Y that is explained by X₁ holding X₂ constant.
D) will have the same sign as b₁.
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14
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for performance rating, b₁?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the estimated coefficient for performance rating, b₁?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
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15
In a multiple regression model, which of the following is correct regarding the value of the adjusted r²?
A) It can be negative.
B) It has to be positive.
C) It has to be larger than the coefficient of multiple determination.
D) It can be larger than 1.
A) It can be negative.
B) It has to be positive.
C) It has to be larger than the coefficient of multiple determination.
D) It can be larger than 1.
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16
In a multiple regression problem involving two independent variables, if b₁ is computed to be +2.0, it means that
A) the relationship between X₁ and Y is significant.
B) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant.
C) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, without regard to X₂.
D) the estimated mean of Y is 2 when X₁ equals zero.
A) the relationship between X₁ and Y is significant.
B) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant.
C) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, without regard to X₂.
D) the estimated mean of Y is 2 when X₁ equals zero.
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17
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the value for the regression constant, b₀?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
Referring to Table 13-2, for these data, what is the value for the regression constant, b₀?
A) 0.616
B) 1.054
C) 6.932
D) 9.103
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18
TABLE 13-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b₂?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of eight employees provides the following:
Referring to Table 13-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b₂?
A) 0.998
B) 3.103
C) 4.698
D) 21.293
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19
TABLE 13-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by
A) regression sum of squares.
B) error sum of squares.
C) total sum of squares.
D) regression mean squares.
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects six workers and collects the following information:
The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by
A) regression sum of squares.
B) error sum of squares.
C) total sum of squares.
D) regression mean squares.
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20
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
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21
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether gross domestic product has a positive impact on consumption, the p-value is ________.
A) 0.00005
B) 0.0001
C) 0.9999
D) 0.99995
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether gross domestic product has a positive impact on consumption, the p-value is ________.
A) 0.00005
B) 0.0001
C) 0.9999
D) 0.99995
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22
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
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23
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?
A) $4.39 billion
B) $0.39 billion
C) -$0.39 billion
D) -$1.33 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?
A) $4.39 billion
B) $0.39 billion
C) -$0.39 billion
D) -$1.33 billion
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24
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
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25
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what fraction of the variability in house size is explained by income, size of family, and education?
A) 27.0%
B) 33.4%
C) 74.8%
D) 86.5%
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what fraction of the variability in house size is explained by income, size of family, and education?
A) 27.0%
B) 33.4%
C) 74.8%
D) 86.5%
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26
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?
A) 11.43
B) 15.15
C) 24.88
D) 53.87
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?
A) 11.43
B) 15.15
C) 24.88
D) 53.87
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27
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the independent variables in the model are significant at the 5% level?
A) Income, Size, School
B) Income, Size
C) Size, School
D) Income, School
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the independent variables in the model are significant at the 5% level?
A) Income, Size, School
B) Income, Size
C) Size, School
D) Income, School
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28
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home (House = 100)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home (House = 100)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
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29
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?
A) 2.8%
B) 51.8%
C) 72.6%
D) 74.8%
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?
A) 2.8%
B) 51.8%
C) 72.6%
D) 74.8%
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30
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $40,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet)for this data point?
A) -6.99
B) -5.35
C) 5.40
D) 16.99
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $40,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet)for this data point?
A) -6.99
B) -5.35
C) 5.40
D) 16.99
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31
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the value of the relevant t-statistic is ________.
A) 2.365
B) 0.143
C) -0.219
D) -1.960
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the value of the relevant t-statistic is ________.
A) 2.365
B) 0.143
C) -0.219
D) -1.960
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32
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet)for this data point?
A) 7.40
B) 2.52
C) -2.52
D) -5.40
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet)for this data point?
A) 7.40
B) 2.52
C) -2.52
D) -5.40
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33
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
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34
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?
A) $2.52 billion
B) $0.48 billion
C) -$1.33 billion
D) -$2.52 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?
A) $2.52 billion
B) $0.48 billion
C) -$1.33 billion
D) -$2.52 billion
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35
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a positive impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.5835
D) 0.8330
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a positive impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.5835
D) 0.8330
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36
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home (House = 50)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home (House = 50)?
A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand
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37
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a negative impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.8330
D) 0.8837
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test whether aggregate price index has a negative impact on consumption, the p-value is ________.
A) 0.0001
B) 0.4165
C) 0.8330
D) 0.8837
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38
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
A) 0.0005
B) 0.001
C) 0.01
D) 0.05
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
A) 0.0005
B) 0.001
C) 0.01
D) 0.05
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39
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, what is the estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?
A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion
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40
TABLE 13-3
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on gross domestic product, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
An economist is interested to see how consumption for an economy (in $billions) is influenced by gross domestic product ($billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
Referring to Table 13-3, to test for the significance of the coefficient on gross domestic product, the p-value is ________.
A) 0.0001
B) 0.8330
C) 0.8837
D) 0.9999
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41
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Wages?
A) 0.01
B) 0.05
C) 0.0001
D) none of the above
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Wages?
A) 0.01
B) 0.05
C) 0.0001
D) none of the above
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42
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the following values for α is the smallest for which the regression model as a whole is significant?
A) 0.00005
B) 0.001
C) 0.01
D) 0.05
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the following values for α is the smallest for which the regression model as a whole is significant?
A) 0.00005
B) 0.001
C) 0.01
D) 0.05
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43
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?
A) School is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) School is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) School is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) School is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?
A) School is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) School is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) School is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) School is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
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44
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a positive impact on corporate sales?
A) 0.01
B) 0.05
C) 0.0001
D) 0.00005
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a positive impact on corporate sales?
A) 0.01
B) 0.05
C) 0.0001
D) 0.00005
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45
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a positive influence on corporate sales?
A) 0.025
B) 0.05
C) 0.2743
D) 0.5485
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a positive influence on corporate sales?
A) 0.025
B) 0.05
C) 0.2743
D) 0.5485
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46
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
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47
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r² value of 0.601. What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?
A) 60.1%
B) 31.1%
C) 22.9%
D) 8.8%
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r² value of 0.601. What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?
A) 60.1%
B) 31.1%
C) 22.9%
D) 8.8%
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48
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model?
A) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model?
A) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
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49
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the residual degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the residual degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
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50
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a negative impact on corporate sales?
A) 0.05
B) 0.0001
C) 0.00005
D) 0.99995
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Wages have a negative impact on corporate sales?
A) 0.05
B) 0.0001
C) 0.00005
D) 0.99995
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51
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?
A) 0.0001
B) 0.0299
C) 0.726
D) 45.5340
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?
A) 0.0001
B) 0.0299
C) 0.726
D) 45.5340
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52
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $500 million on capital and $200 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what are the predicted sales (in millions of dollars)for a company spending $500 million on capital and $200 million on wages?
A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98
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53
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
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54
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a negative influence on corporate sales?
A) 0.05
B) 0.2743
C) 0.5485
D) 0.7258
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for testing whether Capital has a negative influence on corporate sales?
A) 0.05
B) 0.2743
C) 0.5485
D) 0.7258
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55
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the regression degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, what are the regression degrees of freedom that are missing from the output?
A) 3
B) 46
C) 49
D) 50
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56
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what fraction of the variability in sales is explained by spending on capital and wages?
A) 27.0%
B) 50.9%
C) 68.9%
D) 83.0%
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what fraction of the variability in sales is explained by spending on capital and wages?
A) 27.0%
B) 50.9%
C) 68.9%
D) 83.0%
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57
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, the observed value of the F-statistic is missing from the printout. What are the degrees of freedom for this F-statistic?
A) 46 for the numerator, 3 for the denominator
B) 3 for the numerator, 49 for the denominator
C) 46 for the numerator, 49 for the denominator
D) 3 for the numerator, 46 for the denominator
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, the observed value of the F-statistic is missing from the printout. What are the degrees of freedom for this F-statistic?
A) 46 for the numerator, 3 for the denominator
B) 3 for the numerator, 49 for the denominator
C) 46 for the numerator, 49 for the denominator
D) 3 for the numerator, 46 for the denominator
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58
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Capital?
A) 0.01
B) 0.025
C) 0.05
D) none of the above
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, what is the p-value for Capital?
A) 0.01
B) 0.025
C) 0.05
D) none of the above
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59
TABLE 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Referring to Table 13-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?
A) 5.286
B) 5.195
C) 3.945
D) -1.509
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60
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the independent variables in the model are significant at the 5% level?
A) Capital, Wages
B) Capital
C) Wages
D) none of the above
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, which of the independent variables in the model are significant at the 5% level?
A) Capital, Wages
B) Capital
C) Wages
D) none of the above
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61
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.
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62
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The slopes in a multiple regression model are called net regression coefficients.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The slopes in a multiple regression model are called net regression coefficients.
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63
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.
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64
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?
A) [6.58, 3.65]
B) [6.24, 2.78]
C) [5.94, 3.08]
D) [2.37, 15.12]
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?
A) [6.58, 3.65]
B) [6.24, 2.78]
C) [5.94, 3.08]
D) [2.37, 15.12]
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65
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination, r², measures the proportion of variation in Y that is explained by X₁ and X₂.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination, r², measures the proportion of variation in Y that is explained by X₁ and X₂.
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66
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6 and allowing for a 1% probability of committing a Type I error, what is the decision and conclusion for the test H₀: β₁ = β₂ = β₃ = β₄ = 0 vs. H₁: At least one βⱼ ≠ 0, j = 1, 2, ..., 4 using Model 1?
A) Do not reject H₀ and conclude that the four independent variables have significant individual linear effects on heating costs.
B) Reject H₀ and conclude that the four independent variables taken as a group have significant linear effects on heating costs.
C) Do not reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
D) Reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6 and allowing for a 1% probability of committing a Type I error, what is the decision and conclusion for the test H₀: β₁ = β₂ = β₃ = β₄ = 0 vs. H₁: At least one βⱼ ≠ 0, j = 1, 2, ..., 4 using Model 1?
A) Do not reject H₀ and conclude that the four independent variables have significant individual linear effects on heating costs.
B) Reject H₀ and conclude that the four independent variables taken as a group have significant linear effects on heating costs.
C) Do not reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
D) Reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
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67
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, suppose the microeconomist wants to test whether the coefficient on Capital is significantly different from 0. What is the value of the relevant t-statistic?
A) 0.609
B) 2.617
C) 4.804
D) 25.432
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, suppose the microeconomist wants to test whether the coefficient on Capital is significantly different from 0. What is the value of the relevant t-statistic?
A) 0.609
B) 2.617
C) 4.804
D) 25.432
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68
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what can we say about Model 1?
A) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs.
B) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.
C) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs.
D) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what can we say about Model 1?
A) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs.
B) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.
C) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs.
D) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.
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69
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The total sum of squares (SST)in a regression model will never be greater than the regression sum of squares (SSR).
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The total sum of squares (SST)in a regression model will never be greater than the regression sum of squares (SSR).
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70
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
In calculating the standard error of the estimate, SYX = , there are n-k-1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
In calculating the standard error of the estimate, SYX =
, there are n-k-1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model. Unlock Deck
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71
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 874.55
B) 622.87
C) -790.69
D) -983.56
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 874.55
B) 622.87
C) -790.69
D) -983.56
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72
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the coefficient of multiple determination will never decrease.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an additional explanatory variable is introduced into a multiple regression model, the coefficient of multiple determination will never decrease.
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73
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination measures the proportion of the total variation in the dependent variable that is explained by the set of independent variables.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The coefficient of multiple determination measures the proportion of the total variation in the dependent variable that is explained by the set of independent variables.
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74
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic?
A) 25 for the numerator, 2 for the denominator
B) 2 for the numerator, 23 for the denominator
C) 23 for the numerator, 25 for the denominator
D) 2 for the numerator, 25 for the denominator
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic?
A) 25 for the numerator, 2 for the denominator
B) 2 for the numerator, 23 for the denominator
C) 23 for the numerator, 25 for the denominator
D) 2 for the numerator, 25 for the denominator
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75
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is your decision and conclusion for the test H₀: β₂ = 0 vs. H₁: β₂ < 0 at the α = 0.01 level of significance using Model 1?
A) Do not reject H₀ and conclude that the amount of insulation has a linear effect on heating cots.
B) Reject H₀ and conclude that the amount of insulation does not have a linear effect on heating costs.
C) Reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
D) Do not reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, what is your decision and conclusion for the test H₀: β₂ = 0 vs. H₁: β₂ < 0 at the α = 0.01 level of significance using Model 1?
A) Do not reject H₀ and conclude that the amount of insulation has a linear effect on heating cots.
B) Reject H₀ and conclude that the amount of insulation does not have a linear effect on heating costs.
C) Reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
D) Do not reject H₀ and conclude that the amount of insulation has a negative linear effect on heating costs.
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76
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.
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77
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $21.439 billion (Sales = 21,439). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 790.69
B) 648.31
C) -648.31
D) -790.69
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, one company in the sample had sales of $21.439 billion (Sales = 21,439). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?
A) 790.69
B) 648.31
C) -648.31
D) -790.69
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78
TABLE 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?
A) Capital is significant in explaining corporate sales and should be included in the model because its p-value is less than 0.01.
B) Capital is significant in explaining corporate sales and should be included in the model because its p-value is more than 0.01.
C) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is less than 0.01.
D) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01.
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
Referring to Table 13-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?
A) Capital is significant in explaining corporate sales and should be included in the model because its p-value is less than 0.01.
B) Capital is significant in explaining corporate sales and should be included in the model because its p-value is more than 0.01.
C) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is less than 0.01.
D) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01.
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79
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the adjusted r² can increase.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
When an explanatory variable is dropped from a multiple regression model, the adjusted r² can increase.
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80
TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, the estimated value of the partial regression parameter β₁ in Model 1 means that
A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.
B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51.
C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51.
D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%.
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft Excel outputs of two regression models.
Referring to Table 13-6, the estimated value of the partial regression parameter β₁ in Model 1 means that
A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.
B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51.
C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51.
D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%.
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