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 ( 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,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: Also SSR (X₁ | X₂) = 36400.6326 and SSR (X₁ | X₂) = 3297.7917 -Referring to Scenario 14-4,what annual income (in thousands of dollars)would an individual with a family size of 9 need to attain a predicted 5,000 square foot home (House = 50)?

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 instructional spending per pupil has an effect on percentage of students passing the proficiency test while holding constant the effect of mean teacher salary 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: 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 income while holding the family size constant.

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 variable,age has an impact on the mean number of weeks a worker is unemployed due to a layoff at a 10% level of significance if all we have is 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 14-8 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,_____% of the variation in salary can be explained by the variation in experience while holding age constant.

In a particular model,the sum of the squared residuals was 847.If the model had 5 independent variables,and the data set contained 40 points,the value of the standard error of the estimate is 24.912.

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,which of the following is a correct statement?

When a dummy variable is included in a multiple regression model,the interpretation of the estimated slope coefficient does not make any sense anymore.

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 14-9,the value of adjusted r ² 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,the null hypothesis H₀: $\beta$ ₁= $\beta$ ₂=0implies that the number of weeks a worker is unemployed due to a layoff is not affected by some of the explanatory variables.

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,which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?

A dummy variable is used as an independent variable in a regression model when

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 fraction of the variability in sales is explained by spending on capital and wages?

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,what is the estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?

SCENARIO 14-8 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 14-7,the estimate of the unit change in the mean of Y per unit change in X₁,holding X₂ constant,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 14-3,to test whether aggregate price index has a negative impact on consumption,the p-value is ?

In a multiple regression model,which of the following is correct regarding the value of the adjusted r² ?

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 fraction of the variability in house size is explained by income and size of family?

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 14-7,the department head wants to test H₀: $\beta$ ₁ = $\beta$ ₂ = 0 .The p-value of the test is .