Exam 14: Introduction to Multiple Regression

SCENARIO 14-13 An econometrician is interested in evaluating the relationship of demand for building materials to mortgage rates in Los Angeles and San Francisco.He believes that the appropriate model is Y = 10 + 5X₁ + 8X₂ where X₁ = mortgage rate in % X₂ = 1 if SF,0 if LA Y = demand in $100 per capita -Referring to Scenario 14-13,the predicted demand in Los Angeles when the mortgage rate is 8% is .

Consider a regression in which b₂ = - 1.5 and the standard error of this coefficient equals 0.3.To determine whether X₂ is a significant explanatory variable,you would compute an observed t-value of - 5.0.

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,what is the p-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 14-17 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.

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 14-15 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 predicted mileage for a 300 horsepower,6-cylinder car 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 partial F test 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 has _____ and _____degrees of freedom.

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,_____% of the variation in the house size can be explained by the variation in the family size while holding the family income constant.

A multiple regression is called "multiple" because it has several explanatory variables.

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 estimated mean change in insurance premiums for every 2 additional tickets received is .

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,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 $\beta$ ₁ .

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)for an employee who has one additional year of experience holding age constant is .

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,what are the numerator and denominator degrees of freedom,respectively,for 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?

A regression had the following results: SST = 82.55,SSE = 29.85.It can be said that 73.4% of the variation in the dependent variable is explained by the independent variables in the 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 ( 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 14-5,what is the p-value for testing whether Wages have a positive impact on corporate sales?

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 14-5,what are the predicted sales (in millions of dollars)for a company spending $500 million on capital and $200 million on wages?

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,you can conclude definitively that mean teacher salary individually has no impact on the mean percentage of students passing the proficiency test,considering the effect of instructional spending per pupil,at a 1% level of significance based solely on but not actually computing the 99% confidence interval estimate for $\beta$ ₁.

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 6-cylinder cars is .

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 and allowing for a 1% probability of committing a type I error,what is the decision and conclusion for the test H₀ : $\beta$ ₁ =0 $\beta$ ₂ = 0 vs. H₁ : At least one $\beta$ _j $\neq$ 0,j = 1,2 ^?

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 should be rejected at a 10% level of significance when testing 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.