Exam 14: Introduction to Multiple Regression

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 and the amount of insulation in inches Given below is EXCEL output of the regression model. -Referring to Scenario 14-6, ____% of the variation in heating cost can be explained by the variation in minimum outside temperature while holding the amount of insulation constant.

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: -Referring to Scenario 14-19, what is the p-value of the test statistic when testing whether LawnSize makes a significant contribution to the model in the presence of Income?

SCENARIO 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: -Referring to Scenario 14-17, there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on all of the explanatory variables at a 10% level of significance.

SCENARIO 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. -Referring to Scenario 14-5, what fraction of the variability in sales is explained by spending on capital and wages?

SCENARIO 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: -Referring to Scenario 14-17, we can conclude definitively that, holding constant the effect of the other independent variables, there is not a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not at a 10% level of significance if all we have is the information of the 95% confidence interval estimate for the difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not.

SCENARIO 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes, 0 otherwise.)The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).There are 80 universities in the sample. The PHStat output is given below: -Referring to Scenario 14-18, what is the p-value of the test statistic when testing whether Toefl90 makes a significant contribution to the model in the presence of SAT?

SCENARIO 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: -Referring to Scenario 14-17, what are the numerator and denominator degrees of freedom, respectively, for the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

SCENARIO 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: -Referring to Scenario 14-17, the null hypothesis implies that the number of weeks a worker is unemployed due to a layoff is not related to one of the explanatory variables.

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: -Referring to Scenario 14-19, which of the following is the correct expression for the estimated model?

SCENARIO 14-16 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 30 different vehicle models were collected: Y (Accel Time): Acceleration time in sec. X₁ (Engine Size): c.c. X₂(Sedan): 1 if the vehicle model is a sedan and 0 otherwise 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 partial determinations are 0.3301 and 0.0594 respectively. The coefficient of determination for the regression model using each of the 2 independent variables as the dependent variable and the other independent variable as independent variables are, respectively, 0.0077 and 0.0077. -Referring to Scenario 14-16, what is the p-value of the test statistic to determine whether being a sedan or not makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

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: -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?

In a multiple regression model, the adjusted

SCENARIO 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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, = Salaries and Spending: -Referring to Scenario 14-15, what is the 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?

SCENARIO 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: -Referring to Scenario 14-17, which of the following is a correct statement?

SCENARIO 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. -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?

SCENARIO 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000)and 2 variables: age = Age)and experience in the field = Exper).He took a sample of 20 employees and obtained the following Microsoft Excel output: Also, the sum of squares due to the regression for the model that includes only Age is 5022.0654 while the sum of squares due to the regression for the model that includes only Exper is 125.9848. -Referring to Scenario 14-8, the analyst wants to use an F-test to test .The appropriate alternative hypothesis is ________.

SCENARIO 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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, = Salaries and Spending: -Referring to Scenario 14-15, there is sufficient evidence that the percentage of students passing the proficiency test depends on both of the explanatory variables at a 5% level of significance.

SCENARIO 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: -Referring to Scenario 14-17, there is sufficient evidence that all of the explanatory variables are related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

SCENARIO 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y)depends on his performance rating and the number of economics courses the employee successfully completed in college 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?

To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term.