Exam 14: Introduction to Multiple Regression

TABLE 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,X₁ = Salaries and X₂ = Spending: -Referring to Table 14-15,which of the following is a correct statement?

TABLE 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: -If a categorical independent variable contains 2 categories,then ________ dummy variable(s)will be needed to uniquely represent these categories.

TABLE 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 Table 14-8,the value of the partial F test statistic is ________ for H₀ : Variable X₁ does not significantly improve the model after variable X₂ has been included H₁ : Variable X₁ significantly improves the model after variable X₂ has been included

TABLE 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 (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672 -True or False: When an additional explanatory variable is introduced into a multiple regression model,the adjusted r² can never decrease.

TABLE 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 (credits)and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: -Referring to Table 14-7,the department head wants to test H₀ : β₁ = β₂ = 0.The value of the F-test statistic is ________.

TABLE 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,X₁ = Salaries and X₂ = Spending: -True or False: Referring to Table 14-15,the null hypothesis should be rejected at a 5% level of significance when testing whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables.

TABLE 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). The PHStat output is given below: -Referring to Table 14-18,what is the p-value of the test statistic when testing whether SAT makes a significant contribution to the model in the presence of Toefl90?

TABLE 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 Table 14-10,the estimated mean change in insurance premiums for every 2 additional tickets received is ________.

TABLE 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. -True or False: Referring to Table 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 β₂ ≠ 0.

TABLE 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 Table 14-8,the coefficient of partial determination is ________.

TABLE 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 (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672 -Referring to Table 14-6,________% of the variation in heating cost can be explained by the variation in minimum outside temperature while holding the amount of insulation constant.

TABLE 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: -True or False: Referring to Table 14-17,there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on all of the explanatory variables at a 10% level of significance.

TABLE 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,X₁ = Salaries and X₂ = Spending: -True or False: Referring to Table 14-15,there is sufficient evidence that both of the explanatory variables are related to the percentage of students passing the proficiency test at a 5% level of significance.

TABLE 14-12 As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price ($)per hour of parking,blocks to the quadrangle,and whether the parking is on or off campus.The population regression model hypothesized is Y_i = α + β₁X_1i + β₂X_2i + ε where Y is the meter price per hour. X₁ is the number of blocks to the quad. X₂ is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise. The following Excel results are obtained. -Referring to Table 14-12,predict the cost per hour if one parks off campus and 3 blocks from the quad.

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars)and lawn size (Lawn Size,in thousands of square feet). The PHStat output is given below: -True or False: Referring to Table 14-19,there is not enough evidence to conclude that Income makes a significant contribution to the model in the presence of LawnSize at a 0.05 level of significance.

TABLE 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 Table 14-2,an employee who took 12 economics courses scores 10 on the performance rating.What is her estimated expected wage rate?

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions)is influenced by gross domestic product ($ billions)and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. -Referring to Table 14-3,what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

TABLE 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 (X₂ ∣ X₁)= 3297.7917 -Referring to Table 14-4,the observed value of the F-statistic is missing from the printout.What are the degrees of freedom for this F-statistic?

TABLE 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 Table 14-8,________% of the variation in salary can be explained by the variation in age while holding experience constant.

TABLE 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,X₁ = Salaries and X₂ = Spending: -Referring to Table 14-15,what is the standard error of estimate?