Deck 14: Introduction to Multiple Regression

Question 1

SCENARIO 14-2
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 6 workers and collects the following information:

Referring to Scenario 14-2,for these data,what is the value for the regression constant,b₀?

A)0.616
B)1.054
C)6.932
D)9.103

Answer 1

6.932

Question 2

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.

Answer 2

It has to be positive.

Question 3

The coefficient of multiple determination r²

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.

Answer 3

measures the proportion of variation in Y that is explained by X₁ and X₂.

Question 4

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 5

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,the p-value for the aggregated price index is

A)0.05
B)0.01
C)0.001
D)None of the above.

Question 6

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 7

SCENARIO 14-2
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 6 workers and collects the following information:

Referring to Scenario 14-2,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 8

SCENARIO 14-1
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 8 employees provides the following:

Referring to Scenario 14-1,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 9

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 10

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 11

SCENARIO 14-2
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 6 workers and collects the following information:

Referring to Scenario 14-2,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 12

SCENARIO 14-1
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 8 employees provides the following:

Referring to Scenario 14-1,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 13

SCENARIO 14-2
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 6 workers and collects the following information:

Referring to Scenario 14-2,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 14

SCENARIO 14-1
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 8 employees provides the following:

Referring to Scenario 14-1,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 15

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.

Question 16

SCENARIO 14-2
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 6 workers and collects the following information:

Referring to Scenario 14-2,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 17

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.

Question 18

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 19

SCENARIO 14-1
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 8 employees provides the following:

Referring to Scenario 14-1,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 20

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,the p-value for GDP is

A)0.05
B)0.01
C)0.001
D)None of the above.

Question 21

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 22

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,what annual income (in thousands of dollars)would an individual with a family size of 9 need to attain a predicted 5,000 square foot home (House = 50)?

Question 23

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,which of the independent variables in the model are significant at the 5% level?

A)Income only
B)Size only
C)Income and Size
D)None

Question 24

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,what annual income (in thousands of dollars)would an individual with a family size of 4 need to attain a predicted 10,000 square foot home (House = 100)?

Question 25

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,when the builder used a simple linear regression model with house size (House)as the dependent variable and family size (Size)as the independent variable,he obtained an r² value of 1.25%.What additional percentage of the total variation in house size has been explained by including income in the multiple regression?

A)15.00%
B)70.64%
C)71.50%
D)73.62%

Question 26

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,which of the following values for the level of significance is the smallest for which at most one explanatory variable is significant individually?

A)0.001
B)0.010
C)0.025
D)0.050

Question 27

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 28

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,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 29

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 30

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,what fraction of the variability in house size is explained by income and size of family?

A)17.56%
B)70.69%
C)71.89%
D)84.79%

Question 31

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 32

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,which of the following values for the level of significance is the smallest for which at least one explanatory variable is significant individually?

A)0.005
B)0.010
C)0.025
D)0.050

Question 33

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,to test for the significance of the coefficient on aggregate price,the value of the relevant t-statistic is

A)2.365
B)0.143
C)- 0.219
D)- 1.960

Question 34

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 35

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,one individual in the sample had an annual income of $100,000 and a family size of 10.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?

Question 36

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 37

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000 and having a family size of 4?

Question 38

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 39

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,which of the following values for the level of significance is the smallest for which each explanatory variable is significant individually?

A)0.001
B)0.010
C)0.025
D)0.050

Question 40

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-3,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 41

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,_____% of the variation in the house size can be explained by the variation in the family income while holding the family size constant.

Question 42

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,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 43

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,the partial F test for
H₀ : Variable X₁ does not significantly improve the model after variable X₂ has been included
H₁ : Variable X₁ significantly improves the model after variable X₂ has been included has_____ and _____degrees of freedom.

Question 44

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 45

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,the partial F test for
H₀ : Variable X₂ does not significantly improve the model after variable X₁ has been included
H₁ : Variable X₂ significantly improves the model after variable X₁ has been included has _____ and _____degrees of freedom.

Question 46

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,one individual in the sample had an annual income of $40,000 and a family size of 1.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?

Question 47

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,what are the residual degrees of freedom that are missing from the output?

A)2
B)47
C)49
D)50

Question 48

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,_____% of the variation in the house size can be explained by the variation in the family size while holding the family income constant.

Question 49

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,what is the p-value for Wages?

A)0.01
B)0.05
C)0.0001
D)None of the above

Question 50

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 51

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917

-Referring to Scenario 14-4 and allowing for a 1% probability of committing a type I error,what is ^{the decision and conclusion for the test} H₀ : $\beta$ ₁ = $\beta$ ₂ $\neq$ 0 vs.H₁ : At least one $\beta$ _j $\neq$ 0,j = 1,2 ?

A)Do not reject H₀ and conclude that the 2 independent variables taken as a group have significant linear effects on house size.
B)Do not reject H₀ and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size.
C)Reject H₀ and conclude that the 2 independent variables taken as a group have significant linear effects on house size.
D)Reject H₀ and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size.

Question 52

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,suppose the builder wants to test whether the coefficient on Size is significantly different from 0.What is the value of the relevant t-statistic?

A)-0.7630
B)3.2708
C)10.8668
D)60.0864

Question 53

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,the value of the partial F test statistic is _____for
H₀ : Variable X₁ does not significantly improve the model after variable X₂ has been included
H₁ : Variable X₁ significantly improves the model after variable X₂ has been included

Question 54

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 55

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,at the 0.01 level of significance,what conclusion should the builder draw regarding the inclusion of Size in the regression model?

A)Size is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B)Size is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C)Size 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)Size 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 56

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,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?

Question 57

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,the observed value of the F-statistic is missing from the printout.What are the degrees of freedom for this F-statistic?

A)2 for the numerator,47 for the denominator
B)2 for the numerator,49 for the denominator
C)49 for the numerator,47 for the denominator
D)47 for the numerator,49 for the denominator

Question 58

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,what are the regression degrees of freedom that are missing from the output?

A)2
B)47
C)49
D)50

Question 59

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,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)-0.7630
B)3.2708
C)10.8668
D)60.0864

Question 60

SCENARIO 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:


Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917
Referring to Scenario 14-4,the value of the partial F test statistic is _____ for
H₀ : Variable X₂ does not significantly improve the model after variable X₁ has been included
H₁ : Variable X₂ significantly improves the model after variable X₁ has been included

Question 61

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 62

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 63

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-6,the value of the partial F test statistic is _____ for
H₀ : Variable X₂ does not significantly improve the model after variable X₁ has been included
H₁ : Variable X₂ significantly improves the model after variable X₁ has been included

Question 64

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-6,what can we say about the regression model?

A)The model explains 17.12% of the variability of heating costs;after correcting for the degrees of freedom,the model explains 27.78% of the sample variability of heating costs.
B)The model explains 19.28% of the variability of heating costs;after correcting for the degrees of freedom,the model explains 27.78% of the sample variability of heating costs.
C)The model explains 27.78% of the variability of heating costs;after correcting for the degrees of freedom,the model explains 19.28% of the sample variability of heating costs.
D)The model explains 19.28% of the variability of heating costs;after correcting for the degrees of freedom,the model explains 17.12% of the sample variability of heating costs.

Question 65

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 66

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 67

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 68

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672

-Referring to Scenario 14-6,the estimated value of the regression parameter $\beta$ ₁ in means that

A)holding the effect of the amount of insulation constant,an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 2.76 degrees.
B)holding the effect of the amount of insulation constant,a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $2.76.
C)holding the effect of the amount of insulation constant,a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $2.76.
D)holding the effect of the amount of insulation constant,a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 2.76%.

Question 69

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672

-Referring to Scenario 14-6 and allowing for a 1% probability of committing a type I error,what is the decision and conclusion for the test
H₀ : $\beta$ ₁ =0 $\beta$ ₂ = 0 vs. H₁ : At least one $\beta$ _j $\neq$ 0,j = 1,2 ^?

A)Do not reject H₀ and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs.
B)Do not reject H₀ and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs.
C)Reject H₀ and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs.
D)Reject H₀ and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs.

Question 70

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-6,the partial F test for
H₀ : Variable X₁ does not significantly improve the model after variable X₂ has been included
H₁ : Variable X₁ significantly improves the model after variable X₂ has been included has _____ and _____ degrees of freedom.

Question 71

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 72

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 73

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672

-Referring to Scenario 14-6,what is your decision and conclusion for the test H₀ : $\beta$ ₂ = 0 vs.H₁ : $\beta$ ₂ $\neq$ 0 at the $\alpha$ = 0.01 level of significance?

A)Do not reject H₀ and conclude that the amount of insulation has a linear effect on heating costs.
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 linear effect on heating costs.
D)Do not reject H₀ and conclude that the amount of insulation does not have a linear effect on heating costs.

Question 74

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,what is the p-value for Capital?

A)0.01
B)0.025
C)0.05
D)None of the above

Question 75

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-6,the value of the partial F test statistic is _____ for
H₀ : Variable X₁ does not significantly improve the model after variable X₂ has been included
H₁ : Variable X₁ significantly improves the model after variable X₂ has been included

Question 76

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,which of the following values for 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 77

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 78

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 79

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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 80

SCENARIO 14-6
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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model.



Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672
Referring to Scenario 14-5,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