Deck 13: Multiple Regression

Question 1

A multiple regression model has

A)only one independent variable
B)more than one dependent variable
C)more than one independent variable
D)at least 2 dependent variables

Answer 1

C

Question 2

In multiple regression analysis, the correlation among the independent variables is termed

A)homoscedasticity
B)linearity
C)multicollinearity
D)adjusted coefficient of determination

Answer 2

C

Question 3

In a multiple regression model, the error term $\varepsilon$ is assumed to be a random variable with a mean of

A)zero
B)-1
C)1
D)any value

Answer 3

zero

Question 4

The numerical value of the coefficient of determination

A)is always larger than the coefficient of correlation
B)is always smaller than the coefficient of correlation
C)is negative if the coefficient of determination is negative
D)can be larger or smaller than the coefficient of correlation

Question 5

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

A)an interaction
B)a constant variable
C)a dummy variable
D)None of these alternatives is correct.

Question 6

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A)47 and 3
B)3 and 47
C)2 and 43
D)3 and 43

Question 7

In a multiple regression model, the error term $\varepsilon$ is assumed to

A)have a mean of 1
B)have a variance of zero
C)have a standard deviation of 1
D)be normally distributed

Question 8

In a multiple regression model, the values of the error term , $\varepsilon$ , are assumed to be

A)zero
B)dependent on each other
C)independent of each other
D)always negative

Question 9

In regression analysis, the response variable is the

A)independent variable
B)dependent variable
C)slope of the regression function
D)intercept

Question 10

A regression model in which more than one independent variable is used to predict the dependent variable is called

A)a simple linear regression model
B)a multiple regression model
C)an independent model
D)None of these alternatives is correct.

Question 11

A term used to describe the case when the independent variables in a multiple regression model are correlated is

A)regression
B)correlation
C)multicollinearity
D)None of the above answers is correct.

Question 12

In a multiple regression model, the variance of the error term $\varepsilon$ is assumed to be

A)the same for all values of the dependent variable
B)zero
C)the same for all values of the independent variable
D)-1

Question 13

The mathematical equation that explains how the dependent variable y is related to several independent variables x₁, x₂, ...., x_p and the error term $\varepsilon$ is

A)a simple nonlinear regression model
B)a multiple regression model
C)an estimated multiple regression equation
D)a multiple regression equation

Question 14

In multiple regression analysis,

A)there can be any number of dependent variables but only one independent variable
B)there must be only one independent variable
C)the coefficient of determination must be larger than 1
D)there can be several independent variables, but only one dependent variable

Question 15

A measure of goodness of fit for the estimated regression equation is the

A)multiple coefficient of determination
B)mean square due to error
C)mean square due to regression
D)sample size

Question 16

The estimate of the multiple regression equation based on the sample data, which has the form of E(y) = is

A)a simple linear regression model
B)a multiple nonlinear regression model
C)an estimated multiple regression equation
D)a multiple regression equation

Question 17

The adjusted multiple coefficient of determination is adjusted for

A)the number of dependent variables
B)the number of independent variables
C)the number of equations
D)detrimental situations

Question 18

A variable that cannot be measured in numerical terms is called

A)a nonmeasurable random variable
B)a constant variable
C)a dependent variable
D)a qualitative variable

Question 19

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called

A)an interaction
B)a constant variable
C)a category variable
D)a qualitative variable

Question 20

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y) = is

A)a simple linear regression model
B)a multiple nonlinear regression model
C)an estimated multiple regression equation
D)a multiple regression equation

Question 21

The multiple coefficient of determination is

A)MSR/MST
B)MSR/MSE
C)SSR/SST
D)SSE/SSR

Question 22

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is

A)0.80
B)0.90
C)0.25
D)0.15

Question 23

A multiple regression model has the form As X increases by 1 unit (holding W constant), Y is expected to

A)increase by 11 units
B)decrease by 11 units
C)increase by 6 units
D)decrease by 6 units

Question 24

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is

A)0.300
B)0.192
C)0.500
D)0.700

Question 25

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is

A)0.81
B)0.11
C)0.35
D)0.65

Question 26

In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A)8 and 121
B)7 and 120
C)8 and 112
D)7 and 112

Question 27

A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

A)98 degrees of freedom
B)97 degrees of freedom
C)90 degrees of freedom
D)7 degrees of freedom

Question 28

A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

A)18 degrees of freedom
B)200 degrees of freedom
C)199 degrees of freedom
D)181 degrees of freedom

Question 29

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

A)t test
B)F test
C)Either a t test or a chi-square test can be used.
D)chi-square test

Question 30

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A)14 and 255
B)255 and 14
C)13 and 240
D)14 and 240

Question 31

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

A)0.333
B)0.275
C)0.300
D)0.75

Question 32

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is

A)0.1389
B)0.1220
C)0.878
D)0.7317

Question 33

A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

A)27 degrees of freedom
B)26 degrees of freedom
C)21 degrees of freedom
D)20 degrees of freedom

Question 34

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is

A)0.25
B)4.00
C)250
D)0.75

Question 35

A multiple regression model has the form As x₁ increases by 1 unit (holding x₂ constant), y is expected to

A)increase by 9 units
B)decrease by 9 units
C)increase by 2 units
D)decrease by 2 units

Question 36

The ratio of MSE/MSR yields

A)SST
B)the F statistic
C)SSR
D)None of these alternatives is correct.

Question 37

In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A)4 and 36
B)3 and 35
C)4 and 31
D)4 and 32

Question 38

A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

A)121 degrees of freedom
B)135 degrees of freedom
C)130 degrees of freedom
D)4 degrees of freedom

Question 39

In a multiple regression analysis SSR = 1,000 and SSE = 200. The F statistic for this model is

A)5.0
B)1,200
C)800
D)Not enough information is provided to answer this question.

Question 40

The correct relationship between SST, SSR, and SSE is given by

A)SSR = SST + SSE
B)SSR = SST - SSE
C)SSE = SSR - SST
D)None of these alternatives is correct.

Question 41

Exhibit 13-2
A regression model between sales (Y in $1,000), unit price (X₁ in dollars) and television advertisement (X₂ in dollars) resulted in the following function: For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. The coefficient of the unit price indicates that if the unit price is

A)increased by $1 (holding advertising constant), sales are expected to increase by $3
B)decreased by $1 (holding advertising constant), sales are expected to decrease by $3
C)increased by $1 (holding advertising constant), sales are expected to increase by $4,000
D)increased by $1 (holding advertising constant), sales are expected to decrease by $3,000

Question 42

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained. For this model SSR = 600 and SSE = 400.
Refer to Exhibit 13-1. The coefficient of determination for the above model is

A)0.667
B)0.600
C)0.336
D)o.400

Question 43

In multiple regression analysis, the word linear in the term "general linear model" refers to the fact that

A) $\beta$ ₀, $\beta$ ₁, . . . $\beta$ _p, all have exponents of 0
B) $\beta$ ₀, $\beta$ ₁, . . . $\beta$ _p, all have exponents of 1
C) $\beta$ ₀, $\beta$ ₁, . . . $\beta$ _p, all have exponents of at least 1
D) $\beta$ ₀, $\beta$ ₁, . . . $\beta$ _p, all have exponents of less than 1

Question 44

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100.
Refer to Exhibit 13-3. The critical F value at 95% confidence is

A)2.53
B)2.69
C)2.76
D)2.99

Question 45

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100.
Refer to Exhibit 13-3. The computed F statistic for testing the significance of the above model is

A)43.75
B)0.875
C)50.19
D)7.00

Question 46

Exhibit 13-2
A regression model between sales (Y in $1,000), unit price (X₁ in dollars) and television advertisement (X₂ in dollars) resulted in the following function: For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. The coefficient of X₂ indicates that if television advertising is increased by $1 (holding the unit price constant), sales are expected to

A)increase by $5
B)increase by $12,000
C)increase by $5,000
D)decrease by $2,000

Question 47

Exhibit 13-2
A regression model between sales (Y in $1,000), unit price (X₁ in dollars) and television advertisement (X₂ in dollars) resulted in the following function: For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. To test for the significance of the model, the test statistic F is

A)2.33
B)0.70
C)17.5
D)1.75

Question 48

Exhibit 13-2
A regression model between sales (Y in $1,000), unit price (X₁ in dollars) and television advertisement (X₂ in dollars) resulted in the following function: For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. To test for the significance of the model, the p-value is

A)less than 0.01
B)between 0.01 and 0.025
C)between 0.025 and 0.05
D)between 0.05 and 0.10

Question 49

Exhibit 13-4
a. b. c. d.
Refer to Exhibit 13-4. Which equation describes the multiple regression model?

A)Equation A
B)Equation B
C)Equation C
D)Equation D

Question 50

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100.
Refer to Exhibit 13-3. The coefficient of determination for the above model is approximately

A)-0.875
B)0.875
C)0.125
D)0.144

Question 51

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100.
Refer to Exhibit 13-3. The conclusion is that the

A)model is not significant
B)model is significant
C)slope of X₁ is significant
D)slope of X₂ is significant

Question 52

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained. For this model SSR = 600 and SSE = 400.
Refer to Exhibit 13-1. MSR for this model is

A)200
B)10
C)1,000
D)43

Question 53

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained. For this model SSR = 600 and SSE = 400.
Refer to Exhibit 13-1. The computed F statistics for testing the significance of the above model is

A)1.500
B)20.00
C)0.600
D)0.6667

Question 54

Exhibit 13-4
a. b. c. d.
Refer to Exhibit 13-4. Which equation describes the multiple regression equation?

A)Equation A
B)Equation B
C)Equation C
D)Equation D

Question 55

All the variables in a multiple regression analysis

A)must be quantitative
B)must be either quantitative or qualitative but not a mix of both
C)must be positive
D)None of these alternatives is correct.

Question 56

The following model is referred to as a

A)curvilinear model
B)curvilinear model with one predictor variable
C)simple second-order model with one predictor variable
D)simple first-order model with one predictor variable

Question 57

Exhibit 13-2
A regression model between sales (Y in $1,000), unit price (X₁ in dollars) and television advertisement (X₂ in dollars) resulted in the following function: For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. The multiple coefficient of correlation for this problem is

A)0.70
B)0.8367
C)0.49
D)0.2289

Question 58

Exhibit 13-4
a. b. c. d.
Refer to Exhibit 13-4. Which equation gives the estimated regression line?

A)Equation A
B)Equation B
C)Equation C
D)Equation D

Question 59

Exhibit 13-5
Below you are given a partial Minitab output based on a sample of 25 observations.

Refer to Exhibit 13-5. The interpretation of the coefficient on X₁ is that

A)a one unit change in X₁ will lead to a 25.625 unit change in Y
B)a one unit change in X₁ will lead to a 25.625 unit increase in Y when all other variables are held constant
C)a one unit change in X₁ will lead to a 25.625 unit increase in X₂ when all other variables are held constant
D)It is impossible to interpret the coefficient.

Question 60

A model in the form of y = $\beta$ ₀ + $\beta$ ₁z₁ + $\beta$ ₂z₂ + . . . + $\beta$ _pz_p + $\varepsilon$ where each independent variable z_j (for j = 1, 2, . . ., p) is a function of x_j . x_j is known as the

A)general linear model
B)general curvilinear model
C)multiplicative model
D)multiplicative curvilinear model

Question 61

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.

Refer to Exhibit 13-6. The interpretation of the coefficient of X₁ is that

A)a one unit change in X₁ will lead to a 3.682 unit decrease in Y
B)a one unit increase in X₁ will lead to a 3.682 unit decrease in Y when all other variables are held constant
C)a one unit increase in X₁ will lead to a 3.682 unit decrease in X₂ when all other variables are held constant
D)It is impossible to interpret the coefficient.

Question 62

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.

Refer to Exhibit 13-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are

A)2
B)3
C)13
D)15

Question 63

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.

Refer to Exhibit 13-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

A)3.41
B)3.63
C)3.81
D)19.41

Question 64

Exhibit 13-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X₁) and their gender (X₂) (0 if male and 1 if female). Also provided are SST = 1,200 and SSE = 384.
Refer to Exhibit 13-8. From the above function, it can be said that the expected yearly income of

A)males is $3 more than females
B)females is $3 more than males
C)males is $3,000 more than females
D)females is $3,000 more than males

Question 65

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.

Refer to Exhibit 13-6. The test statistic used to determine if there is a relationship among the variables equals

A)-1.4
B)0.2
C)0.77
D)5

Question 66

Exhibit 13-5
Below you are given a partial Minitab output based on a sample of 25 observations.


-Refer to Exhibit 13-5. We want to test whether the parameter $\beta$ ₁ is significant. The test statistic equals

A)0.357
B)2.8
C)14
D)1.96

Question 67

Exhibit 13-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X₁) and their gender (X₂) (0 if male and 1 if female). Also provided are SST = 1,200 and SSE = 384.
Refer to Exhibit 13-8. The yearly income of a 24-year-old female individual is

A)$19.80
B)$19,800
C)$49.80
D)$49,800

Question 68

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.


-Refer to Exhibit 13-6. Carry out the test of significance for the parameter $\beta$ ₁ at the 1% level. The null hypothesis should be

A)rejected
B)not rejected
C)revised
D)None of these alternatives is correct.

Question 69

Exhibit 13-5
Below you are given a partial Minitab output based on a sample of 25 observations.


-Refer to Exhibit 13-5. Carry out the test of significance for the parameter $\beta$ ₁ at the 5% level. The null hypothesis should be

A)rejected
B)not rejected
C)revised
D)None of these alternatives is correct.

Question 70

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.

Refer to Exhibit 13-6. The sum of squares due to error (SSE) equals

A)37.33
B)485.3
C)4,853
D)6,308.9

Question 71

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.

Refer to Exhibit 13-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

A)2.65
B)2.921
C)2.977
D)3.012

Question 72

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.


-Refer to Exhibit 13-6. We want to test whether the parameter $\beta$ ₁ is significant. The test statistic equals

A)-1.4
B)1.4
C)3.6
D)5

Question 73

Exhibit 13-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X₁) and their gender (X₂) (0 if male and 1 if female). Also provided are SST = 1,200 and SSE = 384.
Refer to Exhibit 13-8. The multiple coefficient of determination is

A)0.32
B)0.42
C)0.68
D)0.50

Question 74

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.

Refer to Exhibit 13-7. The test statistic from the information provided is

A)2.110
B)3.480
C)4.710
D)6.875

Question 75

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.

Refer to Exhibit 13-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

A)be rejected
B)not be rejected
C)revised
D)None of these alternatives is correct.

Question 76

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.

Refer to Exhibit 13-7. The coefficient of determination is

A)0.3636
B)0.7333
C)0.275
D)0.5

Question 77

Exhibit 13-5
Below you are given a partial Minitab output based on a sample of 25 observations.

Refer to Exhibit 13-5. The t value obtained from the table to test an individual parameter at the 5% level is

A)2.06
B)2.069
C)2.074
D)2.080

Question 78

Exhibit 13-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X₁) and their gender (X₂) (0 if male and 1 if female). Also provided are SST = 1,200 and SSE = 384.
Refer to Exhibit 13-8. The yearly income of a 24-year-old male individual is

A)$13.80
B)$13,800
C)$46,800
D)$49,800

Question 79

Exhibit 13-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X₁) and their gender (X₂) (0 if male and 1 if female). Also provided are SST = 1,200 and SSE = 384.
Refer to Exhibit 13-8. If we want to test for the significance of the model, the critical value of F at 95% confidence is

A)3.33
B)3.35
C)3.34
D)2.96

Question 80

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.

Refer to Exhibit 13-7. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) is

A)3.06
B)3.48
C)3.34
D)3.11