Exam 14: Introduction to Multiple Regression

In a multiple regression model, the value of the coefficient of multiple determination

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (X₁ = Age), experience in the field (X₂ = Exper), number of degrees (X₃ = Degrees), and number of previous jobs in the field (X₄ = Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-8, the analyst wants to use a t test to test for the significance of the coefficient of X₃. For a level of significance of 0.01, the critical values of the test are ________.

TABLE 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 Table 14-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate?

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-7, the department head wants to test H₀ : β₁ = β₂ = 0. The critical value of the F test for a level of significance of 0.05 is ________.

TABLE 14-15 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Note: -Referring to Table 14-15, what is the p-value of the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

If a categorical independent variable contains 4 categories, then ________ dummy variable(s) will be needed to uniquely represent these categories.

TABLE 14-15 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Note: -Referring to Table 14-15, what are the numerator and denominator degrees of freedom, respectively, for the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares (SSR/SST) and subtracting that value from 1.

When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-7, the department head wants to test H₀ : β₁ = β₂ = 0. The value of the F-test statistic is ________.

TABLE 14-4 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: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-4, which of the independent variables in the model are significant at the 2% level?

TABLE 14-3 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. SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-3, to test for the significance of the coefficient on gross domestic product, the p-value is

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: -Referring to Table 14-10, the 99% confidence interval for the change in average insurance premiums of a person who has become 1 year older (i.e., the slope coefficient for AGE) is -0.82 ± ________.

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: -Referring to Table 14-10, the residual mean squares (MSE) that are missing in the ANOVA table should be ________.

TABLE 14-14 An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is -Referring to Table 14-14, the fitted model for predicting mileages for 4-cylinder cars is ________.

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 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 EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10^-5 Model 2 Note: 2.9036E-06 = 2.9036×10^-6 -Referring to Table 14-6, 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?

TABLE 14-14 An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is -Referring to Table 14-14, the predicted mileage for a 200 horsepower, 4-cylinder car is ________.

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 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 EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10^-5 Model 2 Note: 2.9036E-06 = 2.9036×10^-6 -Referring to Table 14-6 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 β_j ≠ 0, j = 1, 2, ..., 4 using Model 1?

TABLE 14-5 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. SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-5, what is the p-value for testing whether Wages have a negative impact on corporate sales?

TABLE 14-4 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: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 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?