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 and the amount of insulation in inches Given below is EXCEL output of the regression model. -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 At least one

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 and how he/she scored on a business aptitude test 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 years an employee has been with the company,

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 estimated change in the mean salary (in $1,000)for an employee who has one additional year of experience holding age constant is ________.

SCENARIO 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.The Microsoft Excel output below shows results of this multiple regression. -Referring to Scenario 14-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an value of 0.601.What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?

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, to test the significance of the multiple regression model, the null hypothesis should be rejected while allowing for 1% probability of committing a type I error.

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, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one thousand dollars increase in instructional spending per pupil on the mean percentage of students passing the proficiency test?

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

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 coefficient of partial determination is ____.

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 value of the coefficient of multiple determination, is ________.

SCENARIO 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: -Referring to Scenario 14-19, what is the estimated probability that a home owner with a family income of $50,000 and a lawn size of 2,000 square feet will purchase a lawn service?

When an explanatory variable is dropped from a multiple regression model, the adjusted can increase.

SCENARIO 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: -Referring to Scenario 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether LawnSize makes a significant contribution to the model in the presence of Income at a 0.05 level of significance?

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 net regression coefficient of is ________.

SCENARIO 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 Scenario 14-3, to test for the significance of the coefficient on aggregate price, the value of the relevant t-statistic is

SCENARIO 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: -Referring to Scenario 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Income makes a significant contribution to the model in the presence of LawnSize at a 0.05 level of significance?

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

Multiple regression is the process of using several independent variables to predict a number of dependent variables.

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 alternative hypothesis : At least one of for j = 1, 2 implies that the number of weeks a worker is unemployed due to a layoff is affected by all of the explanatory variables.

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, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary?

SCENARIO 14-12 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 where Y is the meter price per hour is the number of blocks to the quad 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 Scenario 14-12, what is the correct interpretation for the estimated coefficient for