# Quiz 13: Multiple Regression

Statistics

Q 1Q 1

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of Ey) = β₀ + β₁x1 + β2x2 + ... + βpxp is
A) a simple linear regression model
B) a multiple nonlinear regression model
C) an estimated multiple regression equation
D) a multiple regression equation

Free

Multiple Choice

D

Q 2Q 2

The estimate of the multiple regression equation based on the sample data, which has the form of Ey) = = b₀ + b₁x1 + b2x2 + ... + bpxp is
A) a simple linear regression model
B) a multiple nonlinear regression model
C) an estimated multiple regression equation
D) a multiple regression equation

Free

Multiple Choice

C

Q 3Q 3

The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is
A) a simple nonlinear regression model
B) a multiple regression model
C) an estimated multiple regression equation
D) a multiple regression equation

Free

Multiple Choice

B

Q 4Q 4

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

Free

Multiple Choice

Q 5Q 5

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

Free

Multiple Choice

Q 6Q 6

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.

Free

Multiple Choice

Q 7Q 7

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of
A) zero
B) -1
C) 1
D) any value

Free

Multiple Choice

Q 8Q 8

In regression analysis, the response variable is the
A) independent variable
B) dependent variable
C) slope of the regression function
D) intercept

Free

Multiple Choice

Q 9Q 9

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

Free

Multiple Choice

Q 10Q 10

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

Free

Multiple Choice

Q 11Q 11

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

Free

Multiple Choice

Q 12Q 12

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

Free

Multiple Choice

Q 13Q 13

In a multiple regression model, the variance of the error term ε 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

Free

Multiple Choice

Q 14Q 14

In multiple regression analysis, the correlation among the independent variables is termed
A) homoscedasticity
B) linearity
C) multicollinearity
D) adjusted coefficient of determination

Free

Multiple Choice

Q 15Q 15

In a multiple regression model, the values of the error term ,ε, are assumed to be
A) zero
B) dependent on each other
C) independent of each other
D) always negative

Free

Multiple Choice

Q 16Q 16

In a multiple regression model, the error term ε 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

Free

Multiple Choice

Q 17Q 17

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

Free

Multiple Choice

Q 18Q 18

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.

Free

Multiple Choice

Q 19Q 19

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.

Free

Multiple Choice

Q 20Q 20

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

Free

Multiple Choice

Q 21Q 21

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

Free

Multiple Choice

Q 22Q 22

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

Free

Multiple Choice

Q 23Q 23

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

Free

Multiple Choice

Free

Multiple Choice

Q 25Q 25

A multiple regression model has the form Y = 7 + 2X1 + 9X2 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

Free

Multiple Choice

Q 26Q 26

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.

Free

Multiple Choice

Q 27Q 27

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.

Free

Multiple Choice

Q 28Q 28

The ratio of MSE/MSR yields
A) SST
B) the F statistic
C) SSR
D) None of these alternatives is correct.

Free

Multiple Choice

Q 29Q 29

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

Free

Multiple Choice

Q 30Q 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

Free

Multiple Choice

Q 31Q 31

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

Free

Multiple Choice

Q 32Q 32

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

Free

Multiple Choice

Q 33Q 33

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

Free

Multiple Choice

Q 34Q 34

A multiple regression model has the form Y = 12 - 8X1 + 3X2 As X1 increases by 2 units holding X2 constant), Y is expected to
A) increase by 8 units
B) decrease by 8 units
C) increase by 16 units
D) decrease by 16 units

Free

Multiple Choice

Q 35Q 35

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

Free

Multiple Choice

Q 36Q 36

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

Free

Multiple Choice

Q 37Q 37

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

Free

Multiple Choice

Q 38Q 38

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

Free

Multiple Choice

Q 39Q 39

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

Free

Multiple Choice

Q 40Q 40

A model in the form of y = β₀ + β₁z1 + β2z2 + . . . +βpzp + ε where each independent variable zj for j = 1, 2, . . ., p) is a function of xj . xj is known as the
A) general linear model
B) general curvilinear model
C) multiplicative model
D) multiplicative curvilinear model

Free

Multiple Choice

Q 41Q 41

The following model Y=β₀+β₁X1+ε 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

Free

Multiple Choice

Q 42Q 42

In multiple regression analysis, the word linear in the term "general linear model" refers to the fact that
A) β₀, β₁, . . . βp, all have exponents of 0
B) β₀, β₁, . . . βp, all have exponents of 1
C) β₀, β₁, . . . βp, all have exponents of at least 1
D) β₀, β₁, . . . βp, all have exponents of less than 1

Free

Multiple Choice

Q 43Q 43

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.

Free

Multiple Choice

Q 44Q 44

A multiple regression model has the form Y = 70 - 14X1 + 5X2 As X1decreases by 1 unit holding X2 constant), Y is expected to
A) increase by 5 units
B) decrease by 5 units
C) increase by 14 units
D) decrease by 14 units

Free

Multiple Choice

Q 45Q 45

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) o.400

Free

Multiple Choice

Q 46Q 46

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

Free

Multiple Choice

Q 47Q 47

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

Free

Multiple Choice

Q 48Q 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. 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

Free

Multiple Choice

Q 49Q 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 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

Free

Multiple Choice

Q 50Q 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. 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

Free

Multiple Choice

Q 51Q 51

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. 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

Free

Multiple Choice

Q 52Q 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 multiple coefficient of correlation for this problem is
A) 0.70
B) 0.8367
C) 0.49
D) 0.2289

Free

Multiple Choice

Q 53Q 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 coefficient of determination for the above model is approximately
A) -0.875
B) 0.875
C) 0.125
D) 0.144

Free

Multiple Choice

Q 54Q 54

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

Free

Multiple Choice

Q 55Q 55

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

Free

Multiple Choice

Q 56Q 56

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

Free

Multiple Choice

Q 57Q 57

Exhibit 13-4
a. Y=β₀ + β₁X1 + β2X2 + ε
b. EY)=β₀ + β₁X1 + β2X2 + ε
c. =b₀ + b₁X1 + b2X2
d. EY)=β₀ + β₁X1 + β2X2
-Refer to Exhibit 13-4. Which equation describes the multiple regression model?
A) Equation A
B) Equation B
C) Equation C
D) Equation D

Free

Multiple Choice

Q 58Q 58

Exhibit 13-4
a. Y=β₀ + β₁X1 + β2X2 + ε
b. EY)=β₀ + β₁X1 + β2X2 + ε
c. =b₀ + b₁X1 + b2X2
d. EY)=β₀ + β₁X1 + β2X2
-Refer to Exhibit 13-4. Which equation gives the estimated regression line?
A) Equation A
B) Equation B
C) Equation C
D) Equation D

Free

Multiple Choice

Q 59Q 59

Exhibit 13-4
a. Y=β₀ + β₁X1 + β2X2 + ε
b. EY)=β₀ + β₁X1 + β2X2 + ε
c. =b₀ + b₁X1 + b2X2
d. EY)=β₀ + β₁X1 + β2X2
-Refer to Exhibit 13-4. Which equation describes the multiple regression equation?
A) Equation A
B) Equation B
C) Equation C
D) Equation D

Free

Multiple Choice

Q 60Q 60

Exhibit 13-5
Below you are given a partial Minitab output based on a sample of 25 observations.
-Refer to Exhibit 13-5. The estimated regression equation is
A) Y = β₀ + β₁X1 + β2X2 + β3X3 + ε
B) EY) = β₀ + β₁X1 + β2X2 + β3X3
C) =145.321+25.625X1 - 5.720X2+0.823X3
D) =48.682+9.15X1+3.575X2+1.183X3

Free

Multiple Choice

Q 61Q 61

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.

Free

Multiple Choice

Q 62Q 62

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 β₁ is significant. The test statistic equals
A) 0.357
B) 2.8
C) 14
D) 1.96

Free

Multiple Choice

Q 63Q 63

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

Free

Multiple Choice

Q 64Q 64

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 β₁ at the 5% level. The null hypothesis should be
A) rejected
B) not rejected
C) revised
D) None of these alternatives is correct.

Free

Multiple Choice

Q 65Q 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 estimated regression equation is
A) Y = β₀ + β₁X1 + β2X2 + ε
B) EY) = β₀ + β₁X1 + β2X2
C) =12.924 - 3.682X1 + 45.216X2
D) =4.425+2.63X1+12.56X2

Free

Multiple Choice

Q 66Q 66

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.

Free

Multiple Choice

Q 67Q 67

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 β₁ is significant. The test statistic equals
A) -1.4
B) 1.4
C) 3.6
E) 5

Free

Multiple Choice

Q 68Q 68

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

Free

Multiple Choice

Q 69Q 69

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 β₁ at the 1% level. The null hypothesis should be
A) rejected
B) not rejected
C) revised
D) None of these alternatives is correct.

Free

Multiple Choice

Q 70Q 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 degrees of freedom for the sum of squares explained by the regression SSR) are
A) 2
B) 3
C) 13
D) 15

Free

Multiple Choice

Q 71Q 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 sum of squares due to error SSE) equals
A) 37.33
B) 485.3
C) 4,853
D) 6,308.9

Free

Multiple Choice

Q 72Q 72

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

Free

Multiple Choice

Q 73Q 73

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

Free

Multiple Choice

Q 74Q 74

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.

Free

Multiple Choice

Q 75Q 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. The coefficient of determination is
A) 0.3636
B) 0.7333
C) 0.275
D) 0.5

Free

Multiple Choice

Q 76Q 76

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

Free

Multiple Choice

Q 77Q 77

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

Free

Multiple Choice

Q 78Q 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).
=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

Free

Multiple Choice

Q 79Q 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

Free

Multiple Choice

Q 80Q 80

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

Free

Multiple Choice

Q 81Q 81

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 multiple coefficient of determination is
A) 0.32
B) 0.42
C) 0.68
D) 0.50

Free

Multiple Choice

Q 82Q 82

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. 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

Free

Multiple Choice

Q 83Q 83

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 test statistic for testing the significance of the model is
A) 0.73
B) 1.47
C) 28.69
D) 5.22

Free

Multiple Choice

Q 84Q 84

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 model
A) is significant
B) is not significant
C) would be significant is the sample size was larger than 30
D) None of these alternatives is correct.

Free

Multiple Choice

Q 85Q 85

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 estimated income of a 30-year-old male is
A) $51,000
B) $5,100
C) $510
D) $51

Free

Multiple Choice

Q 86Q 86

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. If you want to determine whether or not the coefficients of the independent variables are significant, the critical value of t statistic at α = 0.05 is
A) 2.080
B) 2.060
C) 2.064
D) 1.96

Free

Multiple Choice

Q 87Q 87

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The coefficient of X1
A) is significant
B) is not significant
C) can not be tested, because not enough information is provided
D) None of these alternatives is correct.

Free

Multiple Choice

Q 88Q 88

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The coefficient of X2
A) is significant
B) is not significant
C) can not be tested, because not enough information is provided
D) None of these alternatives is correct.

Free

Multiple Choice

Q 89Q 89

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The coefficient of X3
A) is significant
B) is not significant
C) can not be tested, because not enough information is provided
D) None of these alternatives is correct.

Free

Multiple Choice

Q 90Q 90

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The multiple coefficient of determination is
A) 0.27
B) 0.73
C) 0.50
D) 0.33

Free

Multiple Choice

Q 91Q 91

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. If we are interested in testing for the significance of the relationship among the variables i.e., significance of the model) the critical value of F at α = 0.05 is
A) 2.76
B) 2.78
C) 3.10
D) 3.07

Free

Multiple Choice

Q 92Q 92

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The test statistic for testing the significance of the model is
A) 0.730
B) 18.926
C) 3.703
D) 1.369

Free

Multiple Choice

Q 93Q 93

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
=10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The p-value for testing the significance of the regression model 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 0.1

Free

Multiple Choice

Q 94Q 94

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The value of SSE is
A) 3,740
B) 170
C) 260
D) 2000

Free

Multiple Choice

Q 95Q 95

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The degrees of freedom associated with SSR are
A) 24
B) 6
C) 19
D) 5

Free

Multiple Choice

Q 96Q 96

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The degrees of freedom associated with SSE are
A) 24
B) 6
C) 19
D) 5

Free

Multiple Choice

Q 97Q 97

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The degrees of freedom associated with SST are
A) 24
B) 6
C) 19
D) None of these alternatives is correct.

Free

Multiple Choice

Q 98Q 98

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The value of MSR is
A) 10.40
B) 348
C) 10.83
D) 52

Free

Multiple Choice

Q 99Q 99

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The value of MSE is
A) 348
B) 10.40
C) 10.83
D) 32.13

Free

Multiple Choice

Q 100Q 100

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The test statistic F for testing the significance of the above model is
A) 32.12
B) 6.69
C) 4.8
D) 58

Free

Multiple Choice

Q 101Q 101

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The p-value for testing the significance of the regression model 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 0.1

Free

Multiple Choice

Q 102Q 102

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
=170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The coefficient of determination for this model is
A) 0.6923
B) 0.1494
C) 0.1300
D) 0.8700

Free

Multiple Choice

Q 103Q 103

Exhibit 13-11
Below you are given a partial computer output based on a sample of 25 observations.
-Refer to Exhibit 13-11. The estimated regression equation is
A) Y = β₀ + β₁X1 + β2X2 + β3X3 + ε
B) EY) = β₀ + β₁X1 + β2X2 + β3X3
C) =29+5X1+6X2+4X3
D) =145+20X1 - 18X2+4X3

Free

Multiple Choice

Q 104Q 104

Exhibit 13-11
Below you are given a partial computer output based on a sample of 25 observations.
-Refer to Exhibit 13-11. We want to test whether the parameter β2 is significant. The test statistic equals
A) 4
B) 5
C) 3
D) -3

Free

Multiple Choice

Q 105Q 105

Exhibit 13-11
Below you are given a partial computer output based on a sample of 25 observations.
-Refer to Exhibit 13-11. The critical 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

Free

Multiple Choice

Q 106Q 106

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. From the above function, it can be said that the life expectancy of rats that were given agent X2 is
A) 1.7 months more than those who did not take agent X2
B) 1.7 months less than those who did not take agent X2
C) 0.8 months less than those who did not take agent X2
D) 0.8 months more than those who did not take agent X2

Free

Multiple Choice

Q 107Q 107

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The life expectancy of a rat that was given 3 units of protein daily, and who took agent X2 is
A) 36.7
B) 36
C) 49
D) 38.4

Free

Multiple Choice

Q 108Q 108

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The life expectancy of a rat that was not given any protein and that did not take agent X2 is
A) 36.7
B) 34.3
C) 36
D) 38.4

Free

Multiple Choice

Q 109Q 109

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The degrees of freedom associated with SSR are
A) 2
B) 33
C) 32
D) 30

Free

Multiple Choice

Q 110Q 110

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The degrees of freedom associated with SSE are
A) 3
B) 33
C) 32
D) 30

Free

Multiple Choice

Q 111Q 111

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The multiple coefficient of determination is
A) 0.2
B) 0.5
C) 0.333
D) 5

Free

Multiple Choice

Q 112Q 112

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. If we want to test for the significance of the model, the critical value of F at 95% confidence is
A) 4.17
B) 3.32
C) 2.92
D) 1.96

Free

Multiple Choice

Q 113Q 113

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The test statistic for testing the significance of the model is
A) 0.50
B) 5.00
C) 0.25
D) 0.33

Free

Multiple Choice

Q 114Q 114

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The p-value for testing the significance of the regression model 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

Free

Multiple Choice

Q 115Q 115

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
=36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The model
A) is significant
B) is not significant
C) Not enough information is provided to answer this question.
D) None of these alternatives is correct.

Free

Multiple Choice

Q 116Q 116

Multiple regression analysis was used to study how an individual's income Y in thousands of dollars) is influenced by age X1 in years), level of education X2 ranging from 1 to 5), and the person's gender X3 where 0 =female and 1=male). The following is a partial result of a computer program that was used on a sample of 20 individuals.
Coefficient Standard Error
X1 0.6251 0.094
X2 0.9210 0.190
X3 -0.5100 0.920
Analysis of Variance
Source of Variation
Degrees of Freedom
Sum of Squares
Mean
Square F
Regression 84
Error 112
a. Compute the coefficient of determination.
b. Perform a t test and determine whether or not the coefficient of the variable "level of education" i.e., X2) is significantly different from zero. Let α = 0.05.
c. At α = 0.05, perform an F test and determine whether or not the regression model is significant.
d. As you note the coefficient of X3 is -0.510. Fully interpret the meaning of this coefficient.

Free

Essay

Q 117Q 117

The following results were obtained from a multiple regression analysis.
a. How many independent variables were involved in this model?
b. How many observations were involved?
c. Determine the F statistic.

Free

Essay

Q 118Q 118

Shown below is a partial computer output from a regression analysis.
Coefficient Standard Error
Constant 10.00 2.00
X1 -2.00 1.50
X2 6.00 2.00
X3 -4.00 1.00
Analysis of Variance
Source of Variation
Degrees of Freedom
Sum of Squares
Mean
Square F
Regression 60
Error
Total 19 140
a. Use the above results and write the regression equation.
b. Compute the coefficient of determination and fully interpret its meaning.
c. At α = 0.05, test to see if there is a relation between X1 and Y.
d. At α = 0.05, test to see if there is a relation between X3 and Y.
e. Is the regression model significant? Perform an F test and let α = 0.05.

Free

Essay

Q 119Q 119

The following is part of the results of a regression analysis involving sales Y in millions of dollars), advertising expenditures X1 in thousands of dollars), and number of salespeople X2) for a corporation. The regression was performed on a sample of 10 observations.
a. Write the regression equation.
b. Interpret the coefficients of the estimated regression equation found in Part a).
c. At α =0.05, test for the significance of the coefficient of advertising.
d. At α =0.05, test for the significance of the coefficient of number of salespeople.
e. If the company uses $50,000 in advertisement and has 800 salespersons, what are the expected sales? Give your answer in dollars.

Free

Essay

Q 120Q 120

The following is part of the results of a regression analysis involving sales Y in millions of dollars), advertising expenditures X1 in thousands of dollars), and number of sales people X2) for a corporation:
ANALYSIS OF VARIANCE
Source of Variation
Degrees of Freedom
Sum of Squares
Mean
Square F
Regression 2 822.088
Error 7 736.012
a. At α = 0.05 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable.
b. Determine the multiple coefficient of determination.
c. Determine the adjusted multiple coefficient of determination.
d. What has been the sample size for this regression analysis?

Free

Essay

Q 121Q 121

Below you are given a partial computer output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month Y), unit price X1 in $1,000) and the number of advertising spots X2) they used on a local television station.
ANOVA
DF SS MS F Significance F
Regression 2 655.955
Residual 9
Total 838.917
a. At α = 0.05 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable.
b. Determine the multiple coefficient of determination.
c. Determine the adjusted multiple coefficient of determination.

Free

Essay

Q 122Q 122

Below you are given a computer output based on a sample of 30 days of the price of a company's stock Y in dollars), the Dow Jones industrial average X1), and the stock price of the company's major competitor X2 in dollars).
a. Use the output shown above and write an equation that can be used to predict the price of the stock.
b. If the Dow Jones Industrial Average is 10,000 and the price of the competitor is $50, what would you expect the price of the stock to be?
c. At α = 0.05, test to determine if the Dow Jones average is a significant variable.
d. At α = 0.05, test to determine if the stock price of the major competitor is a significant variable.

Free

Essay

Q 123Q 123

Below you are given a partial computer output relating the price of a company's stock Y in dollars), the Dow Jones industrial average X1), and the stock price of the company's major competitor X2 in dollars).
ANOVA
Regression
DF SS MS F
Residual 20 40
Total 800
a. What has been the sample size for this regression analysis?
b. At α = 0.05 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable.
c. Determine the multiple coefficient of determination.

Free

Essay

Q 124Q 124

A regression was performed on a sample of 16 observations. The estimated equation is =23.5 - 14.28X1+6.72X2+15.68X3. The standard errors for the coefficients are Sb₁ = 4.2, Sb2 = 5.6, and Sb3 = 2.8. For this model, SST = 3809.6 and SSR = 3285.4.
a. Compute the appropriate t ratios.
b. Test for the significance of β₁, β2 and β3at the 5% level of significance.
c. Do you think that any of the variables should be dropped from the model? Explain.
d. Compute R² and Ra2 . Interpret R².
e. Test the significance of the relationship among the variables at the 5% level of significance.

Free

Essay

Q 125Q 125

The following results were obtained from a multiple regression analysis of supermarket profitability. The dependent variable, Y, is the profit in thousands of dollars) and the independent variables, X1 and X2, are the food sales and nonfood sales also in thousands of dollars).
ANOVA
DF SS
Regression 2 562.363
Residual 9 225.326
Total
a. Write the estimated regression equation for the relationship between the variables.
b. Compute the coefficient of determination and fully interpret its meaning.
c. Carry out a test of whether Y is significantly related to the independent variables. Use a 0.05 level of significance.
d. Carry out a test to determine if there is a significant relationship between X1 and Y. Use a .05 level of significance.
e. How many supermarkets were in the sample used here?

Free

Essay

Q 126Q 126

A regression was performed on a sample of 20 observations. Two independent variables were included in the analysis, X and Z. The relationship between X and Z is Z = X2. The following estimated equation was obtained.
=23.72+12.61X+0.798Z
The standard errors for the coefficients are Sb₁ = 4.85 and Sb2 = 0.21 For this model, SSR = 520.2 and SSE = 340.6
a. Estimate the value of Y when X = 5.
b. Compute the appropriate t ratios.
c. Test for the significance of the coefficients at the 5% level. Which variables) is are) significant?
d. Compute the coefficient of determination and the adjusted coefficient of determination. Interpret the meaning of the coefficient of determination.
e. Test the significance of the relationship among the variables at the 5% level of significance.

Free

Essay

Q 127Q 127

A student used multiple regression analysis to study how family spending Y) is influenced by income X1), family size X2), and additions to savings X3). The variables Y, X1, and X3 are measured in thousands of dollars. The following results were obtained.
ANOVA
DF SS
Regression 3 45.9634
Residual 11 2.6218 Total
a. Write out the estimated regression equation for the relationship between the variables.
b. Compute R². What can you say about the strength of this relationship?
c. Carry out a test of whether Y is significantly related to the independent variables. Use a .05 level of significance.
d. Carry out a test to see if X3 and Y are significantly related. Use a .05 level of significance.

Free

Essay

Q 128Q 128

A regression model involving 3 independent variables for a sample of 20 periods resulted in the following sum of squares.
Sum of Squares
Regression 90
Residual Error) 100
a. Compute the coefficient of determination and fully explain its meaning.
b. At α = 0.05 level of significance, test to determine whether or not there is a significant relationship between the independent variables and the dependent variable.

Free

Essay

Q 129Q 129

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares.
SSE = 306
SST = 1800
a. Compute the coefficient of determination.
b. At α = 0.05, test to determine whether or not the model is significant.

Free

Essay

Q 130Q 130

In a regression model involving 46 observations, the following estimated regression equation was obtained.
=17+4X1 - 3X2+8X3+5X4+8X5
For this model, SST = 3410 and SSE = 510.
a. Compute the coefficient of determination.
b. Perform an F test and determine whether or not the regression model is significant.

Free

Essay

Q 131Q 131

The following is part of the results of a regression analysis involving sales Y in millions of dollars), advertising expenditures X1 in thousands of dollars), and number of salespeople X2) for a corporation. The regression was performed on a sample of 10 observations.
a. If the company uses $40,000 in advertisement and has 30 salespersons, what are the expected sales? Give your answer in dollars.
b. At α = 0.05, test for the significance of the coefficient of advertising.
c. At α = 0.05, test for the significance of the coefficient of the number of salespeople.

Free

Essay

Q 132Q 132

Sherri Cola Company has developed a regression model relating its sales Y in $10,000s) with four independent variables. The four independent variables are price per unit PRICE, in dollars), competitor's price COMPRICE, in dollars), advertising ADV, in $1,000s) and type of container used CONTAIN; 1 = Cans and 0 = Bottles). Part of the regression results is shown below. Assume n = 25)
a. If the manufacturer uses can containers, his price is $1.25, advertising $200,000, and his competitor's price is $1.50, what is your estimate of his sales? Give your answer in dollars.
b. Test to see if there is a significant relationship between sales and unit price. Let α = 0.05.
c. Test to see if there is a significant relationship between sales and advertising. Let α = 0.05.
d. Is the type of container a significant variable? Let α = 0.05.
e. Test to see if there is a significant relationship between sales and competitor's price. Let α = 0.05.

Free

Essay

Q 133Q 133

The Brock Juice Company has developed a regression model relating sales Y in $10,000s) with four independent variables. The four independent variables are price per unit X1, in dollars), competitor's price X2, in dollars), advertising X3, in $1,000s) and type of container used X4) 1 = Cans and 0 = Bottles). Part of the regression results are shown below:
Analysis of Variance
Source of Variation
Degrees of Freedom
Sum of Squares
Regression 4 283,940.60
Error Residuals) 18 621,735.14
a. Compute the coefficient of determination and fully interpret its meaning.
b. Is the regression model significant? Explain what your answer implies. Let α = 0.05.
c. What has been the sample size for this analysis?

Free

Essay

Q 134Q 134

The following regression model has been proposed to predict sales at a furniture store.
= 10 - 4X1+7X2+18X3
where
X1 = competitor's previous day's sales in $1,000s) X2 = population within 1 mile in 1,000s)
X3 = 1 if any form of advertising was used, 0 if otherwise
= sales in $1,000s)
a. Fully interpret the meaning of the coefficient of X3.
b. Predict sales in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within 1 mile, and six radio advertisements.

Free

Essay

Q 135Q 135

The following regression model has been proposed to predict sales at a fast food outlet.
=18 - 2X1+7X2+15X3
where
X1 = the number of competitors within 1 mile X2 = the population within 1 mile
X3 = 1 if drive-up windows are present, 0 if otherwise
= sales in $1,000s)
a. What is the interpretation of 15 the coefficient of X3) in the regression equation?
b. Predict sales for a store with 2 competitors, a population of 10,000 within one mile, and one drive-up window give the answer in dollars).
c. Predict sales for the store with 2 competitors, a population of 10,000 within one mile, and no drive-up window give the answer in dollars).

Free

Essay

Q 136Q 136

The following regression model has been proposed to predict sales at a computer store.
= 50 - 3X1 + 20X2 + 10X3
where
X1 = competitor's previous days sales in $1,000s) X2 = population within 1 mile in 1,000s)
X3 =
= sales in $1,000s)
Predict sales in dollars) for a store with the competitor's previous day's sale of $5,000, a population of 20,000 within 1 mile, and nine radio advertisements.

Free

Short Answer

Q 137Q 137

The following regression model has been proposed to predict monthly sales at a shoe store.
= 40 - 3X1 + 12X2 + 10X3
where
X1 = competitor's previous month's sales in $1,000s) X2 = store's previous month's sales in $1,000s)
X3 =
= sales in $1,000s)
a. Predict sales in dollars) for the shoe store if the competitor's previous month's sales were
$9,000, the store's previous month's sales were $30,000, and no radio advertisements were run.
b. Predict sales in dollars) for the shoe store if the competitor's previous month's sales were
$9,000, the store's previous month's sales were $30,000, and 10 radio advertisements were run.

Free

Essay

Q 138Q 138

In a regression analysis involving 20 observations and five independent variables, the following information was obtained.
ANALYSIS OF VARIANCE
Fill in all the blanks in the above ANOVA table.

Free

Essay

Q 139Q 139

Multiple regression analysis was used to study the relationship between a dependent variable, Y, and three independent variables X1, X2 and, X3. The following is a partial result of the regression analysis involving 20 observations.
F
a. Compute the coefficient of determination.
b. Perform a t test and determine whether or not β₁ is significantly different from zero α = 0.05).
c. Perform a t test and determine whether or not β2 is significantly different from zero α = 0.05).
d. Perform a t test and determine whether or not β3 is significantly different from zero α = 0.05).
e. At α = 0.05, perform an F test and determine whether or not the regression model is significant.

Free

Essay

Q 140Q 140

Multiple regression analysis was used to study the relationship between a dependent variable, Y, and four independent variables; X1, X2, X3 and, X4. The following is a partial result of the regression analysis involving 31 observations.
a. Compute the coefficient of determination.
b. Perform a t test and determine whether or not β₁ is significantly different from zero α = 0.05).
c. Perform a t test and determine whether or not β4 is significantly different from zero α = 0.05).
d. At α = 0.05, perform an F test and determine whether or not the regression model is significant.

Free

Essay

Q 141Q 141

A regression model relating a dependent variable, Y, with one independent variable, X1, resulted in an SSE of 400. Another regression model with the same dependent variable, Y, and two independent variables, X1 and X2, resulted in an SSE of 320. At α = .05, determine if X2 contributed significantly to the model. The sample size for both models was 20.

Free

Essay

Q 142Q 142

A regression model relating units sold Y), price X1), and whether or not promotion was used X2 = 1 if promotion was used and 0 if it was not) resulted in the following model.
=120 - 0.03X1 =0.7X2
and the following information is provided.
n= 15 Sb₁ = .01 Sb2 = 0.1
a. Is price a significant variable?
b. Is promotion significant?

Free

Essay

Q 143Q 143

In a regression analysis involving 18 observations and four independent variables, the following information was obtained.
Multiple R = 0.6000 R Square = 0.3600
Standard Error = 4.8000
Based on the above information, fill in all the blanks in the following ANOVA table.
ANALYSIS OF VARIANCE
Source of Variation
Degrees of Freedom
Sum of Squares
Mean
Squares F
Regression _____? _____? _____? _____?
Error _____? _____? _____?

Free

Essay

Q 144Q 144

The following are partial results of a regression analysis involving sales Y in millions of dollars), advertising expenditures X1 in thousands of dollars), and number of salespeople X2) for a corporation. The regression was performed on a sample of 10 observations.
a. At α = 0.05, test for the significance of the coefficient of advertising.
b. If the company uses $20,000 in advertisement and has 300 salespersons, what are the expected sales? Give your answer in dollars.)

Free

Essay