Exam 14: Introduction to Multiple Regression

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: -Referring to Scenario 14-7, the department head wants to use a t test to test for the significance of the coefficient of At a level of significance of 0.05, the department head would decide that

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, one individual in the sample had an annual income of $40,000 and a family size of 1.This individual owned a home with an area of 1,000 square feet (House = 10.00).What is the residual (in hundreds of square feet)for this data point?

The coefficient of multiple determination

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 where -Referring to Scenario 14-13, the fitted model for predicting demand in San Francisco is ________.

SCENARIO 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y)depends on his performance rating and the number of economics courses the employee successfully completed in college The professor randomly selects 6 workers and collects the following information: -Referring to Scenario 14-2, for these data, what is the value for the regression 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, 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.

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 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y)depends on his performance rating and the number of economics courses the employee successfully completed in college The professor randomly selects 6 workers and collects the following information: -Referring to Scenario 14-2, for these data, what is the estimated coefficient for the number of economics courses taken,

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: -Referring to Scenario 14-7, the department head wants to test .The p-value of the test is ________.

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 14-18 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 14-15 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 instructional spending per pupil has no impact on the mean percentage of students passing the proficiency test, considering the effect of mean teacher salary, at a 5% level of significance using the confidence interval estimate for

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, estimate the mean percentage of students passing the proficiency test for all the schools that have a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

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 analyst wants to use a t test to test for the significance of the coefficient of For a level of significance of 0.01, the critical values of the test are ________.

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 multiple regression model is significant at a 10% level of significance.

You have just computed a regression model in which the value of coefficient of multiple determination is 0.57.To determine if this indicates that the independent variables explain a significant portion of the variation in the dependent variable, you would perform an F-test.

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 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: -Referring to Scenario 14-7, the department head wants to test .The value of the F-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: -Referring to Scenario 14-4, the partial F test for H₀ : Variable does not significantly improve the model after variable has been included H₁ : Variable significantly improves the model after variable has been included has ____ and ____ degrees of freedom.

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 and the amount of insulation in inches Given below is EXCEL output of the regression model. -Referring to Scenario 14-6, the value of the partial F test statistic is ____ for H₀ : Variable does not significantly improve the model after variable has been included H₁ : Variable significantly improves the model after variable has been included