Exam 13: Introduction to Multiple Regression

TABLE 13-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of multiple determination for the regression model using each of the 5 variables Xj as the dependent variable and all other X variables as independent variables (Rj2) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Table 13-16, what is the correct interpretation for the estimated coefficient for SUV?

TABLE 13-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of multiple determination for the regression model using each of the 5 variables Xj as the dependent variable and all other X variables as independent variables (Rj2) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.1252 seconds higher than that of an SUV.

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 ________.

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 ________.

TABLE 13-10 You worked as an intern at We Always Win Car Insurance Company last summer. You noticed 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 Microsoft Excel and obtained the following information: -Referring to Table 13-10, the estimated mean change in insurance premiums for every two additional tickets received is ________.

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?

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?

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?

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?

TABLE 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and four 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: -Referring to Table 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X₃. The value of the test statistic is ________.

TABLE 13-12 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is Yi = α + β1X1i + β2X2i + β3X3i + ε where Y is the meter price X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise X3 is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus, and the value 0 otherwise The following Microsoft Excel results are obtained. -Referring to Table 13-12, what is the correct interpretation for the estimated coefficient for X₂?

TABLE 13-15 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 mean of the percentage of students attending class (% Attendance), mean 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, = : % Attendance, = Salaries and = Spending: -Referring to Table 13-15, you can conclude that mean teacher salary has no impact on the mean percentage of students passing the proficiency test at a 5% level of significance using the 95% confidence interval estimate for β₂.

TABLE 13-7 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: -Referring to Table 13-7, the value of the adjusted coefficient of multiple determination, r²ₐdⱼ, is ________.

TABLE 13-7 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: -Referring to Table 13-7, 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 13-10 You worked as an intern at We Always Win Car Insurance Company last summer. You noticed 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 Microsoft Excel and obtained the following information: -Referring to Table 13-10, the adjusted r² is _________.

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?

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?

TABLE 13-10 You worked as an intern at We Always Win Car Insurance Company last summer. You noticed 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 Microsoft Excel and obtained the following information: -Referring to Table 13-10, the standard error of the estimate is _________.

TABLE 13-11 A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds). Two variables thought to affect weight loss are client's length of time on the weight loss program and time of session. These variables are described below: Y = Weight loss (in pounds) X1 = Length of time in weight-loss program (in months) X2 = 1 if morning session, 0 if not X3 = 1 if afternoon session, 0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + β1X1 + β2X2 + β3X3 + β4X1X2 + β5X1X3 + ε Partial output from Microsoft Excel follows: -Referring to Table 13-11, what null hypothesis would you test to determine whether the slope of the linear relationship between weight loss (Y)and time in the program (X₁)varies according to time of session?

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)?