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 14-6,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 14-13 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 fitted model for predicting demand in Los Angeles 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,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 14-17 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,what is the value of the test statistic 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?

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 analyst wants to use a t test to test for the significance of the coefficient of X₂.At a level of significance of 0.01,the department head would decide that $\beta$ ₂ $\neq$ 0 .

The following two statements are equivalent in meaning: A.The test of significance for a specific regression coefficient in a multiple regression model is a test of significance for adding that variable into the model given the other variable is included. B.The t test for a regression coefficient is actually a test for the contribution of that independent variable.

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 that,holding constant the effect of the other independent variable,there is 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 5% level of significance if we use only 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 14-10 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 is .

The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

An interaction term in a multiple regression model may be used when

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

A regression had the following results: SST = 82.55,SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the 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,what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one thousand dollar increase in mean teacher salary on the mean percentage of students passing the proficiency test?

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 value of 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?

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, which of the following is the correct interpretation for the Toefl90 Slope coefficient?

SCENARIO 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y)depends on his performance rating (X₁)and the number of economics courses the employee successfully completed in college (X₂).The professor randomly selects 6 workers and collects the following information: -Referring to Scenario 14-2,suppose an employee had never taken an economics course and managed to score a 5 on his performance rating.What is his estimated expected wage rate?

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 use a t test to test for the significance of the coefficient of X₁.The value of the test statistic 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,which of the independent variables in the model are significant at the 5% level?

SCENARIO 14-1 A manager of a product sales group believes the number of sales made by an employee (Y)depends on how many years that employee has been with the company (X₁)and how he/she scored on a business aptitude test (X₂).A random sample of 8 employees provides the following: -Referring to Scenario 14-1,for these data,what is the estimated coefficient for the variable representing scores on the aptitude test,b₂?

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 .At a level of significance of 0.05,the null hypothesis is rejected.