Exam 14: Introduction to Multiple Regression

SCENARIO 14-15 The superintendent of a school district wanted to predict the percentage of students passing a sixthgrade 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, X₁ = Salaries and X ₂ = 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 14-10 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 standard error of the estimate is .

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 at least one of the explanatory variables is related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

SCENARIO 14-15 The superintendent of a school district wanted to predict the percentage of students passing a sixthgrade 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, X₁ = Salaries and X ₂ = Spending: -Referring to Scenario 14-14,the fitted model for predicting mileages for 4-cylinder cars is .

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: Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917 -Referring to Scenario 14-4,one individual in the sample had an annual income of $100,000 and a family size of 10.This individual owned a home with an area of 7,000 square feet (House = 70.00).What is the residual (in hundreds of square feet)for this data point?

SCENARIO 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 2 variables: age (X₁ = Age) and experience in the field (X₂ = 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 F-statistic for testing the significance of the entire regression is .

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: Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917 -Referring to Scenario 14-4,what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000 and having a family size of 4?

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 99% confidence interval for the change in mean insurance premiums of a person who has become 1 year older (i.e. ,the slope coefficient for AGE)-1.4061 $\pm$ .

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,to test the significance of the multiple regression model,what is the form of the null hypothesis?

SCENARIO 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 2 variables: age (X₁ = Age) and experience in the field (X₂ = 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 estimated change in the mean salary (in $1,000)when an employee is a year older holding experience constant is .

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 age has an effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable at a 10% level of significance.

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 ( X₁ ) and the amount of insulation in inches ( X ₂ ). Given below is EXCEL output of the regression model. Also SSR (X₁ | X₂) = 8343.3572 and SSR (X₂ | X₁) = 4199.2672 -Referring to Scenario 14-6,what can we say about the regression model?

From the coefficient of multiple determination,you cannot detect the strength of the relationship between Y and any individual independent variable.

An interaction term in a multiple regression model may be used when the relationship between X₁ and Y changes for differing values of X₂.

Which of the following is used to determine observations that have influential effect on the fitted model?

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 14-17 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 at least one of the explanatory variables at a 10% 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,which of the following is the correct alternative hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable?

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: Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917 -Referring to Scenario 14-3,to test whether gross domestic product has a positive impact on consumption,the p-value is

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: Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917 -Referring to Scenario 14-4,the value of the partial F test statistic is _____ for H₀ : Variable X₂ does not significantly improve the model after variable X₁ has been included H₁ : Variable X₂ significantly improves the model after variable X₁ has been included