Deck 13: Multiple Regression

Question 1

In regression analysis, the response variable is the

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

Answer 1

dependent variable

Question 2

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

Answer 2

3 and 43

Question 3

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.

Answer 3

Not enough information is provided to answer this question.

Question 4

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 5

The multiple coefficient of determination is

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

Question 6

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

Question 7

As the goodness of fit for the estimated multiple regression equation increases,

A)the value of the adjusted multiple coefficient of determination decreases
B)the value of the regression equation's constant b₀ decreases
C)the value of the multiple coefficient of determination increases
D)the value of the correlation coefficient increases

Question 8

In regression analysis, an outlier is an observation whose

A)mean is larger than the standard deviation
B)residual is zero
C)mean is zero
D)residual is much larger than the rest of the residual values

Question 9

A regression model involved 5 independent variables and 126 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

A)131 degrees of freedom
B)125 degrees of freedom
C)130 degrees of freedom
D)4 degrees of freedom

Question 10

A multiple regression model has the form = 7 + 2 x₁ + 9 x₂ As x₁ increases by 1 unit (holding x₂ constant), is expected to

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

Question 11

If a qualitative variable has k levels, the number of dummy variables required is

A)k - 1
B)k
C)k + 1
D)2k

Question 12

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

Question 13

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 14

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 15

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 16

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 17

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 18

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 19

The ratio of MSE/MSR yields

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

Question 20

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 21

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 alternative answers are correct.

Question 22

In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see

A)a horizontal band of points centered near zero
B)a widening band of points
C)a band of points having a slope consistent with that of the regression equation
D)a parabolic band of points

Question 23

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 24

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 25

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

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

Question 26

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 27

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 28

A multiple regression model has the form = 5 + 6x + 7w 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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

A regression analysis involved 17 independent variables and 697 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

A)696 degrees of freedom
B)16 degrees of freedom
C)713 degrees of freedom
D)714 degrees of freedom

Question 37

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 38

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 39

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 40

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 41

A dummy variable may take

A)only the value 0 or 1
B)only the value -1 or 1
C)only non-negative values
D)any value between 0 and 1

Question 42

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃
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 43

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃
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 44

Exhibit 13-4
a.
y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$
b.
E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂
c.= b_o + b₁ x₁ + b₂ x₂
d.
E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂

-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 45

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: = 7 - 3x₁ + 5x₂
For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. The multiple coefficient of determination for this problem is

A)0.4368
B)0.6960
C)0.3040
D)0.2289

Question 46

Exhibit 13-4
a.
y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$
b.
E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂
c.= b_o + b₁ x₁ + b₂ x₂
d.
E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂

-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 47

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄
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 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: = 7 - 3x₁ + 5x₂
For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. If SSR = 600 and SSE = 300, the test statistic F is

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

Question 49

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: = 7 - 3x₁ + 5x₂
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 50

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: = 7 - 3x₁ + 5x₂
For this model SSR = 3500, SSE = 1500, and the sample size is 18.
Refer to Exhibit 13-2. If we want to test for the significance of the regression model, the critical value of F at 95% confidence is

A)3.68
B)3.29
C)3.24
D)4.54

Question 51

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


-Refer to Exhibit 13-5. The estimated regression equation is

A)y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$
B)E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃
C)= 145.321 + 25.625x₁ - 5.720x₂ + 0.823x₃
D)11ec9ead_435e_cdb6_877e_c7e2c94bd808_TB2074_11= 48.682 + 9.15x₁ + 3.575x₂ + 0.183x₃

Question 52

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: = 7 - 3x₁ + 5x₂
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 53

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄
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 54

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

A)standard error
B)residual
C)predicted interval
D)variance

Question 55

Exhibit 13-4
a.
y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$
b.
E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂
c.= b_o + b₁ x₁ + b₂ x₂
d.
E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂

-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 56

Unlike a simple linear regression model, a multiple regression model has more than one

A)intercept
B)dependent variable
C)independent variable
D)error term

Question 57

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 58

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄
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 59

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃
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)0.400

Question 60

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄
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 61

Exhibit 13-6
Below you are given a partial Excel 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 62

Exhibit 13-6
Below you are given a partial Excel 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 63

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
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 64

Exhibit 13-5
Below you are given a partial Excel 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 65

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). = 30 + 0.7x₁ + 3x₂
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 66

Exhibit 13-6
Below you are given a partial Excel 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 67

Exhibit 13-6
Below you are given a partial Excel 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 68

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
Refer to Exhibit 13-7. The coefficient of determination is

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

Question 69

Exhibit 13-6
Below you are given a partial Excel 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 70

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). = 30 + 0.7x₁ + 3x₂
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 71

Exhibit 13-6
Below you are given a partial Excel 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 72

Exhibit 13-5
Below you are given a partial Excel 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 73

Exhibit 13-6
Below you are given a partial Excel 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 74

Exhibit 13-5
Below you are given a partial Excel 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 75

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
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

Question 76

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


-Refer to Exhibit 13-6. The estimated regression equation is

A)y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$
B)E(y) = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂
C)= 12.924 - 3.682 x₁ + 45.216 x₂
D)11ec9ead_435e_cdb6_877e_c7e2c94bd808_TB2074_11= 4.425 + 2.63 x₁ + 12.56 x₂

Question 77

Exhibit 13-5
Below you are given a partial Excel 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 78

Exhibit 13-6
Below you are given a partial Excel 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 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). = 30 + 0.7x₁ + 3x₂
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 80

Exhibit 13-6
Below you are given a partial Excel 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