Exam 14: Introduction to Multiple Regression

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, you can conclude that, holding constant the effect of the other independent variable, age has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 5% level of significance if we use only the information of the 95% confidence interval estimate for the effect of a one year increase in age on the mean number of weeks a worker is unemployed due to a layoff.

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 14-15 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, the null hypothesis implies that percentage of students passing the proficiency test is not related to one of the explanatory variables.

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, which of the following assumptions is most likely violated based on the residual plot of the residuals versus predicted Y?

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 value of the test statistic to determine whether engine size makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

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 estimated odds ratio for a home owner with a family income of $50,000 and a lawn size of 2,000 square feet?

A regression had the following results: SST = 102.55, SSE = 82.04.It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

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 estimated probability that a home owner with a family income of $100,000 and a lawn size of 2,000 square feet will purchase a lawn service?

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 1% 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 SAT makes a significant contribution to the model in the presence of Toefl90?

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, the alternative hypothesis : At least one of for j = 1, 2 implies that percentage of students passing the proficiency test is affected by both 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, what is the estimated odds ratio for a home owner with a family income of $100,000 and a lawn size of 5,000 square feet?

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 interpretation for the Income slope coefficient?

SCENARIO 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. -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?

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 the correct null hypothesis 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 14-19 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 estimated odds ratio for a home owner with a family income of $50,000 and a lawn size of 5,000 square feet?

SCENARIO 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 and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: -Referring to Scenario 14-7, the estimate of the unit change in the mean of Y per unit change in holding constant, is ________.

A regression had the following results: SST = 102.55, SSE = 82.04.It can be said that 90.0% of the variation in the dependent variable is explained by the independent variables in the regression.

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 any of the explanatory variables.

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, the null hypothesis implies that percentage of students passing the proficiency test is not related to either of the explanatory variables.