Ch.14 Test Bank Multiple Regression

Introductory Statistics, 10e (Mann)

Chapter 14 Multiple Regression

14.1 Multiple Regression Analysis

1) A multiple regression model contains:

A) one independent variable and more than one dependent variable

B) more than one independent variable and one dependent variable

C) one independent and one dependent variable

D) more than one dependent variable

Diff: 1

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 001

2) In a first-order multiple regression model:

A) each term contains two independent variables

B) some terms contain an independent variable raised to powers larger than one

C) each term contains two or more independent variables raised to the first power

D) each term contains a single independent variable raised to the first power

Diff: 1

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 002

3) A first-order multiple regression model with a sample size of 45 and 8 independent variables has ________ degrees of freedom.

A) 7

B) 36

C) 37

D) 44

Diff: 2

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 003

4) y = 2.5 + 1.6x1 - 0.5x2 - 2.7x3 + 1.3x4

The change in y due to a one-unit change in x1 when all other independent variables included in the model are held constant, is a(n) ________ (increase / decrease) of ________. (Separate answers with a comma.)

A) increase, 1.6

B) decrease, 1.6

C) increase, 2.7

D) decrease, 2.7

Diff: 2

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 004

5) y = 2.7 + 1.9x1 - 0.9x2 - 2.5x3 + 1.3x4

The change in y due to a one-unit change in x3 when all other independent variables included in the model are held constant, is a(n) ________ (increase / decrease) of ________. (Separate answers with a comma.)

A) decrease, 2.5

B) increase, 2.5

C) decrease, 2.7

D) increase, 2.7

Diff: 2

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 005

6) y = 2.8 + 1.5x1 - 0.3x2 - 2.3x3 + 1.1x4

Which variable(s) have a negative relationship with y? (Separate answers with a comma, if applicable.)

A) ,

B) ,

C) ,

D) None of them

Diff: 2

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 006

7) y = 2.1 + 1.3x1 - 0.3x2 - 2.6x3 + 1.4x4

The change in y due to a three-unit change in x4 when all other independent variables included in the model are held constant, is a(n) ________ (increase / decrease) of ________. (Separate answers with a comma.)

A) increase, 4.2

B) increase, 6.3

C) decrease, 4.2

D) decrease, 6.3

Diff: 2

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 007

8) The estimated multiple regression equation is:

A) E(y) = A + B1x1 + B2x2 + B3x3 + … + Bkxk

B) y = A + B1x1 + B2x2 + B3x3 + … + Bkxk

C) y = a + b1x1 + b2x2 + b3x3 + … + bkxk

D) ŷ = a + b1x1 + b2x2 + b3x3 + … + bkxk

Diff: 1

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 008

9) a,b1,b2,b3,…,and bk are ________ and A,B1,B2,B3,…and Bk are ________.

A) sample statistics, population parameters

B) sample statistics, point estimators

C) point estimators, populations

D) samples, populations

Diff: 2

LO: 14.1.0 Demonstrate an understanding of the fundamentals of a multiple regression model.

Section: 14.1 Multiple Regression Analysis

Question Title: Chapter 14, Testbank Question 009

14.2 Assumptions of the Multiple Regression Model

1) Which of the following is not an assumption for the multiple regression model?

A) There is no linear association between the random error term ò and each independent variable xi.

B) The independent linear variables are linearly related.

C) The mean of the probability distribution of ò is zero.

D) The errors associated with different sets of values of independent variables are independent.

Diff: 1

LO: 14.2.0 Demonstrate an understanding of the assumptions of a multiple regression model.

Section: 14.2 Assumptions of the Multiple Regression Model

Question Title: Chapter 14, Testbank Question 010

2) When independent variables are strongly linearly related, this occurrence is referred to as:

A) linear correlation

B) multicollinearity

C) no relationship

D) exact relationship

Diff: 2

LO: 14.2.0 Demonstrate an understanding of the assumptions of a multiple regression model.

Section: 14.2 Assumptions of the Multiple Regression Model

Question Title: Chapter 14, Testbank Question 011

3) Which relationship among x1,x2, and x3, is invalid for the multiple regression model y = A + B1x1 + B2x2 + B3x3 + ϵ?

A) x1 = 7x2 + 4x3

B) = - 3

C) =

D) =

Diff: 2

LO: 14.2.0 Demonstrate an understanding of the assumptions of a multiple regression model.

Section: 14.2 Assumptions of the Multiple Regression Model

Question Title: Chapter 14, Testbank Question 012

14.3 Standard Deviation of Errors

1) Which phrase does not apply to σò?

A) measure of variation among errors

B) standard deviation of errors

C) standard error of the errors

D) standard error of the estimate

Diff: 1

LO: 14.3.0 Demonstrate an understanding of the standard deviation of errors of a multiple regression model.

Section: 14.3 Standard Deviation of Errors

Question Title: Chapter 14, Testbank Question 013

2) For a multiple regression model, the standard deviation for population data is denoted by ________ and the standard deviation for sample data is denoted by ________. (Separate answers with a comma.)

Diff: 1

LO: 14.3.0 Demonstrate an understanding of the standard deviation of errors of a multiple regression model.

Section: 14.3 Standard Deviation of Errors

Question Title: Chapter 14, Testbank Question 014

3) Use the following table to answer the question:

n = 7, k = 3

Calculate SSE to two decimal places.

Diff: 2

LO: 14.3.0 Demonstrate an understanding of the standard deviation of errors of a multiple regression model.

Section: 14.3 Standard Deviation of Errors

Question Title: Chapter 14, Testbank Question 015

4) Use the following table to answer the question:

n = 7, k = 3

Calculate se to two decimal places.

Diff: 2

LO: 14.3.0 Demonstrate an understanding of the standard deviation of errors of a multiple regression model.

Section: 14.3 Standard Deviation of Errors

Question Title: Chapter 14, Testbank Question 016

5) Use the following table to answer the question:

n = 10, k = 4

Calculate SSE to two decimal places.

Diff: 2

LO: 14.3.0 Demonstrate an understanding of the standard deviation of errors of a multiple regression model.

Section: 14.3 Standard Deviation of Errors

Question Title: Chapter 14, Testbank Question 017

6) Use the following table to answer the question:

n = 10, k = 4

Calculate se to two decimal places.

Diff: 2

LO: 14.3.0 Demonstrate an understanding of the standard deviation of errors of a multiple regression model.

Section: 14.3 Standard Deviation of Errors

Question Title: Chapter 14, Testbank Question 018

14.4 Coefficient of Multiple Determination

1) Which phrase does not apply to R2?

A) R2 always lies in the range 0 to 1

B) coefficient of multiple determination

C) the proportion of the total sum of squares SST that is explained by the multiple regression model

D) the proportion of the error sum of squares SSE that is explained by the multiple regression model

Diff: 1

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 019

2) The coefficient of multiple determination is given by the ratio of:

A) SSE and SST

B) SSE and SSR

C) SST and SSR

D) SSR and SST

Diff: 1

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 020

3) The major shortcoming of R2 is that the value of R2 ________ as more and more explanatory variables are added to the regression model.

A) decreases

B) increases

C) stays the same

D) doubles

Diff: 1

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 021

4) Which phrase does not apply to 2?

A) The value of 2 may increase, decrease, or stay the same as more explanatory variables are added to the regression model

B) Adjusted coefficient of multiple determination

C) The value of 2 can never be negative

D) Coefficient of multiple determination adjusted for degrees of freedom

Diff: 1

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 022

5) Use the following table to answer the question:

n = 7, k = 2

Calculate SSE to two decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 023

6) Use the following table to answer the question:

n = 7, k = 2

Calculate to two decimal places.

Diff: 1

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 024

7) Use the following table to answer the question:

n = 7, k = 2

Calculate SST to two decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 025

8) Use the following table to answer the question:

n = 7, k = 2

Calculate SSR to two decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 026

9) Use the following table to answer the question:

n = 7, k = 2

Calculate R2 to three decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 027

10) Use the following table to answer the question:

n = 7, k = 2

Calculate 2 to three decimal places.

Diff: 3

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 028

11) Use the following table to answer the question:

n = 7, k = 3

Calculate SSE to two decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 029

12) Use the following table to answer the question:

n = 7, k = 3

Calculate to two decimal places.

Diff: 1

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 030

13) Use the following table to answer the question:

n = 7, k = 3

Calculate SST to two decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 031

14) Use the following table to answer the question:

n = 7, k = 3

Calculate SSR to two decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 032

15) Use the following table to answer the question:

n = 7, k = 3

Calculate R2 to three decimal places.

Diff: 2

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 033

16) Use the following table to answer the question:

n = 7, k = 3

Calculate 2 to three decimal places.

Diff: 3

LO: 14.4.0 Demonstrate an understanding of the coefficient of multiple determination in a multiple regression model.

Section: 14.4 Coefficient of Multiple Determination

Question Title: Chapter 14, Testbank Question 034

14.5 Computer Solution of Multiple Regression

Use the following table that gives data on variables y,x1,x2 and x3, and the MINITAB output of the multiple regression analysis to answer the questions below.

1) Using the solution obtained, write the estimated regression equation.

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 035

2) Explain the meaning of the estimated regression coefficients of the independent variables.

Diff: 3

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 036

3) What are the values of the standard deviation of errors, the coefficient of multiple determination, and the adjusted coefficient of multiple determination?

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 037

4) What is the predicted value of y for x1 =2,x2 =5 and x3 = 1?

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 038

5) What is the point estimate of the expected (mean) value of y for all elements given that x1 = 5,x2 = 4 and x3 =2?

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 039

6) Construct a 95% confidence interval for the coefficient of x2, to three decimal places.

Diff: 3

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 040

7) Using a 2.5% significance level will you reject that the coefficient of the null hypothesis of x3 is equal to zero?

Diff: 3

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 041

Use the following to answer the questions below.

A researcher wanted to find the effect of years of experience and the average number of days of operation per month on yearly net income of a food truck business. A random sample of 10 food truck businesses operating in the same city and having similar menu items was selected. The table lists the yearly net income (in dollars) earned by these food trucks, the food truck experience (in years), and the average number of days of operation per month during the past year (in days). The MINITAB output of the multiple regression analysis is given.

8) Using the solution obtained, write the estimated regression equation. Let y represent the yearly net income.

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 042

9) Explain the meaning of the estimated regression coefficients of the independent variables.

Diff: 3

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 043

10) Using the solution obtained, which independent variable has the largest effect on yearly net income, Experience or Days?

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 044

11) What are the values of the standard deviation of errors, the coefficient of multiple determination, and the adjusted coefficient of multiple determination?

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 045

12) What is the predicted value of net income for Experience = 4 and Days = 21?

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 046

13) What is the point estimate of the expected (mean) value of net income for all elements given that Experience = 6 and Days = 28?

Diff: 2

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 047

14) Construct a 95% confidence interval for the coefficient of Days, to two decimal places.

Diff: 3

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 048

15) Using a 2.5% significance level test will you reject or not reject the null hypothesis that the coefficient of Experience is positive.

Diff: 3

LO: 14.5.0 Demonstrate a complete regression analysis using MINITAB in the context of an application.

Section: 14.5 Computer Solution of Multiple Regression

Question Title: Chapter 14, Testbank Question 049

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