Exam 14: Introduction to Multiple 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, there is not enough evidence to conclude that LawnSize makes a significant contribution to the model in the presence of Income at a 0.05 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, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?

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, which of the independent variables in the model are significant at the 5% level?

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 when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary?

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, which of the following is the correct null hypothesis to test whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil?

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 should be rejected at a 5% level of significance when testing whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of 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 should be rejected at a 5% level of significance when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary.

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, which of the following values for the level of significance is the smallest for which at least one explanatory variable is significant individually?

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 value of the coefficient of multiple determination is ________.

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 the model is a good-fitting model?

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 alternative hypothesis : At least one of for j = 1, 2 implies that the number of weeks a worker is unemployed due to a layoff is affected by at least one of the explanatory variables.

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, there is not enough evidence to conclude that Toefl90 makes a significant contribution to the model in the presence of SAT at a 0.05 level of significance.

SCENARIO 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 and the number of traffic tickets received by the individual.You performed a regression analysis in EXCEL and obtained the following partial information: -Referring to Scenario 14-10, the proportion of the total variability in insurance premiums that can be explained by AGE and TICKETS after adjusting for the number of observations and the number independent variables is _________.

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 is the p-value for testing whether Capital has a negative influence on corporate sales?

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, predict the number of weeks being unemployed due to a layoff for a worker who is a thirty-year old and is a manager.

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

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, you can conclude that mean teacher salary has no impact on the mean percentage of students passing the proficiency test, considering the effect of instructional spending per pupil, at a 5% level of significance using the confidence interval estimate for

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, 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?

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, there is not enough evidence to conclude that the model is not a good-fitting model at a 0.05 level of significance.

The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by