Chapter 13 Multiple Regression Analysis

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File: Ch13, Chapter 13: Multiple Regression Analysis
True/False
1. Regression analysis with one dependent variable and two or more independent variables is
called multiple regression.
Ans: True
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
2. The model y =  0 +  1x1 +  2x2 +  is a second-order regression model.
Ans: False
Response: See section 13.1 The Multiple Regression Model
Difficulty: Medium
3. The model y =  0 +  1x1 +  2x2 +  3x3 +  is a first-order regression model.
Ans: True
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
4. In the multiple regression model y =  0 +  1x1 +  2x2 +  3x3 + , the  coefficients of the x
variables are called partial regression coefficients.
Ans: True
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
5. In the model y =  0 +  1x1 +  2x2 +  3x3 + y is the independent variable.
Ans: False
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
6. In a multiple regression model, the partial regression coefficient of an independent variable
represents the increase in the y variable when that independent variable is increased by one unit
if the values of all other independent variables are held constant.
Ans: True
Response: See section 13.1 The Multiple Regression Model
Difficulty: Medium
7. In the estimated multiple regression model y = b0 + b1x1 + b 2 x2 if the values of x1 and x2
are both increased by one unit, the value of y will increase by (b1+ b 2) units.
Ans: False
Response: See section 13.1 The Multiple Regression Model
Difficulty: Hard
8. In the model y =  0 +  1x1 +  2x2 +  3x3 +   is a constant.
Ans: False
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
9. In the estimated multiple regression model y = b0 + b1x1 + b 2 x2 if the value of x1 is
increased by 2 and the value of x2 is increased by 3 simultaneously, the value of y will increase
by (2b1+ 3b 2) units.
Ans: False
Response: See section 13.1 The Multiple Regression Model
Difficulty: Hard
10. Multiple t-tests are used to determine whether the overall regression model is significant.
Ans: False
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
11. The F test is used to determine whether the overall regression model is significant.
Ans: True
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
12. The F value that is used to test for the overall significance a multiple regression model is
calculated by dividing the mean square regression (MSreg) by the mean square error (MSerr).
Ans: True
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
13. The F value that is used to test for the overall significance a multiple regression model is
calculated by dividing the sum of mean squares regression (SSreg) by the sum of squares error
(SSerr).
Ans: False
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
14. The mean square error (MSerr) is calculated by dividing the sum of squares error (SSerr) by
the number of observations in the data set (N).
Ans: False
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Medium
15. The mean square error (MSerr) is calculated by dividing the sum of squares error (SSerr) by
the number of error degrees of freedom (dferr).
Ans: True
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
16. In a multiple regression analysis with N observations and k independent variables, the
degrees of freedom for the residual error is given by (N – k – 1).
Ans: True
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Medium
17. In a multiple regression analysis with N observations and k independent variables, the
degrees of freedom for the residual error is given by (N – k).
Ans: False
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Medium
18. The standard error of the estimate of a multiple regression model is essentially the standard
deviation of the residuals for the regression model.
Ans: True
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
19. The standard error of the estimate of a multiple regression model is computed by taking the
square root of the mean squares of error.
Ans: True
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Hard
20. In a multiple regression model, the proportion of the variation of the dependent variable, y,
accounted for the independent variables in the regression model is given by the coefficient of
multiple correlation.
Ans: False
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
Multiple Choice
21. A cost accountant is developing a regression model to predict the total cost of producing a
batch of printed circuit boards as a linear function of batch size (the number of boards produced
in one lot or batch), production plant (Kingsland, and Yorktown), and production shift (day, and
evening). The response variable in this model is ______.
a) batch size
b) production shift
c) production plant
d) total cost
e) variable cost
Ans: d
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
22. A cost accountant is developing a regression model to predict the total cost of producing a
batch of printed circuit boards as a linear function of batch size (the number of boards produced
in one lot or batch), production plant (Kingsland, and Yorktown), and production shift (day, and
evening). In this model, "shift" is ______.
a) a response variable
b) an independent variable
c) a quantitative variable
d) a dependent variable
e) a constant
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
23. A cost accountant is developing a regression model to predict the total cost of producing a
batch of printed circuit boards as a linear function of batch size (the number of boards produced
in one lot or batch), production plant (Kingsland, and Yorktown), and production shift (day, and
evening). In this model, "batch size" is ______.
a) a response variable
b) an indicator variable
c) a dependent variable
d) a qualitative variable
e) an independent variable
Ans: e
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
24. A market analyst is developing a regression model to predict monthly household
expenditures on groceries as a function of family size, household income, and household
neighborhood (urban, suburban, and rural). The response variable in this model is _____.
a) family size
b) expenditures on groceries
c) household income
d) suburban
e) household neighborhood
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
25. A market analyst is developing a regression model to predict monthly household
expenditures on groceries as a function of family size, household income, and household
neighborhood (urban, suburban, and rural). The "neighborhood" variable in this model is
______.
a) an independent variable
b) a response variable
c) a quantitative variable
d) a dependent variable
e) a constant
Ans: a
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
26. A market analyst is developing a regression model to predict monthly household
expenditures on groceries as a function of family size, household income, and household
neighborhood (urban, suburban, and rural). The "income" variable in this model is ____.
a) an indicator variable
b) a response variable
c) a qualitative variable
d) a dependent variable
e) an independent variable
Ans: e
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
27. A human resources analyst is developing a regression model to predict electricity production
plant manager compensation as a function of production capacity of the plant, number of
employees at the plant, and plant technology (coal, oil, and nuclear). The response variable in
this model is ______.
a) plant manager compensation
b) plant capacity
c) number of employees
d) plant technology
e) nuclear
Ans: a
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
28. A human resources analyst is developing a regression model to predict electricity production
plant manager compensation as a function of production capacity of the plant, number of
employees at the plant, and plant technology (coal, oil, and nuclear). The "plant technology"
variable in this model is ______.
a) a response variable
b) a dependent variable
c) a quantitative variable
d) an independent variable
e) a constant
Ans: d
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
29. A human resources analyst is developing a regression model to predict electricity production
plant manager compensation as a function of production capacity of the plant, number of
employees at the plant, and plant technology (coal, oil, and nuclear). The "plant technology"
variable in this model is ______.
a) a qualitative variable
b) a dependent variable
c) a response variable
d) an indicator variable
e) an independent variable
Ans: a
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
30. A real estate appraiser is developing a regression model to predict the market value of single
family residential houses as a function of heated area, number of bedrooms, number of
bathrooms, age of the house, and central heating (yes, no). The response variable in this model is
_______.
a) heated area
b) number of bedrooms
c) market value
d) central heating
e) residential houses
Ans: c
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
31. A real estate appraiser is developing a regression model to predict the market value of single
family residential houses as a function of heated area, number of bedrooms, number of
bathrooms, age of the house, and central heating (yes, no). The "central heating" variable in this
model is _______.
a) a response variable
b) an independent variable
c) a quantitative variable
d) a dependent variable
e) a constant
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
32. A real estate appraiser is developing a regression model to predict the market value of single
family residential houses as a function of heated area, number of bedrooms, number of
bathrooms, age of the house, and central heating (yes, no). The "central heating" variable in this
model is _______.
a) a response variable
b) an indicator variable
c) a dependent variable
d) a qualitative variable
e) an independent variable
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
33. The multiple regression formulas used to estimate the regression coefficients are designed to
________________.
a) minimize the total sum of squares (SST)
b) minimize the sum of squares of error (SSE)
c) maximize the standard error of the estimate
d) maximize the p-value for the calculated F value
e) minimize the mean error
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Medium
34. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 616.6849
154.5534
-3.33833
2.333548
x1
1.780075
0.335605
x2
Source
Regression
Residual
Total
t Statistic
3.990108
-1.43058
5.30407
p-value
0.000947
0.170675
5.83E-05
df
SS
MS
F
p-value
2
121783 60891.48 14.76117 0.000286
15 61876.68 4125.112
17 183659.6
The regression equation for this analysis is ____________.
a) y = 616.6849 + 3.33833 x1 + 1.780075 x2
b) y = 154.5535 - 1.43058 x1 + 5.30407 x2
c) y = 616.6849 - 3.33833 x1 - 1.780075 x2
d) y = 154.5535 + 2.333548 x1 + 0.335605 x2
e) y = 616.6849 - 3.33833 x1 + 1.780075 x2
Ans: e
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
35. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 616.6849
154.5534
-3.33833
2.333548
x1
1.780075
0.335605
x2
Source
Regression
Residual
Total
t Statistic
3.990108
-1.43058
5.30407
p-value
0.000947
0.170675
5.83E-05
df
SS
MS
F
p-value
2
121783 60891.48 14.76117 0.000286
15 61876.68 4125.112
17 183659.6
The sample size for this analysis is ____________.
a) 19
b) 17
c) 34
d) 15
e) 18
Ans: e
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
36. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 616.6849
154.5534
-3.33833
2.333548
x1
1.780075
0.335605
x2
Source
Regression
Residual
Total
t Statistic
3.990108
-1.43058
5.30407
p-value
0.000947
0.170675
5.83E-05
df
SS
MS
F
p-value
2
121783 60891.48 14.76117 0.000286
15 61876.68 4125.112
17 183659.6
Using  = 0.01 to test the null hypothesis H0:  1 =  2 = 0, the critical F value is ____.
a) 8.68
b) 6.36
c) 8.40
d) 6.11
e) 3.36
Ans: b
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
37. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 616.6849
154.5534
-3.33833
2.333548
x1
1.780075
0.335605
x2
Source
Regression
Residual
Total
t Statistic
3.990108
-1.43058
5.30407
p-value
0.000947
0.170675
5.83E-05
df
SS
MS
F
p-value
2
121783 60891.48 14.76117 0.000286
15 61876.68 4125.112
17 183659.6
Using  = 0.05 to test the null hypothesis H0: 1 = 0, the critical t value is ____.
a) ± 1.753
b) ± 2.110
c) ± 2.131
d) ± 1.740
e) ± 2.500
Ans: c
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
38. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error t Statistic p-value
Intercept 616.6849
154.5534
3.990108 0.000947
-3.33833
2.333548
-1.43058 0.170675
x1
x2
Source
Regression
Residual
Total
1.780075
0.335605
5.30407 5.83E-05
df
SS
MS
F
p-value
2
121783 60891.48 14.76117 0.000286
15 61876.68 4125.112
17 183659.6
These results indicate that ____________.
a) none of the predictor variables are significant at the 5% level
b) each predictor variable is significant at the 5% level
c) x1 is significant at the 5% level
d) x2 is significant at the 5% level
e) the intercept is not significant at 5% level
Ans: d
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Medium
39. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 616.6849
154.5534
-3.33833
2.333548
x1
1.780075
0.335605
x2
Source
Regression
Residual
Total
t Statistic
3.990108
-1.43058
5.30407
p-value
0.000947
0.170675
5.83E-05
df
SS
MS
F
p-value
2
121783 60891.48 14.76117 0.000286
15 61876.68 4125.112
17 183659.6
For x1= 60 and x2 = 200, the predicted value of y is ____________.
a) 1,173.00
b) 772.40
c) 460.97
d) 615.13
e) 987.78
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
40. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 752.0833
336.3158
11.87375
5.32047
x1
1.908183
0.662742
x2
Source
Regression
Residual
Total
df
2
12
14
t Statistic
2.236241
2.231711
2.879226
p-value
0.042132
0.042493
0.01213
SS
MS
F
p-value
203693.3 101846.7 6.745406 0.010884
181184.1 15098.67
384877.4
The regression equation for this analysis is ____________.
a) y = 752.0833 + 11.87375 x1 + 1.908183 x2
b) y = 752.0833 + 336.3158 x1 + 2.236241 x2
c) y = 336.3158 + 5.32047 x1 + 0.662742 x2
d) y = 2.236241 + 2.231711 x1 + 2.879226 x2
e) y = 2.236241 + 2.231711 x1 - 2.879226 x2
Ans: a
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
41. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 752.0833
336.3158
11.87375
5.32047
x1
1.908183
0.662742
x2
Source
Regression
Residual
Total
df
2
12
14
t Statistic
2.236241
2.231711
2.879226
p-value
0.042132
0.042493
0.01213
SS
MS
F
p-value
203693.3 101846.7 6.745406 0.010884
181184.1 15098.67
384877.4
The sample size for this analysis is ____________.
a) 12
b) 15
c) 14
d) 28
e) 24
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
42. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 752.0833
336.3158
11.87375
5.32047
x1
1.908183
0.662742
x2
Source
Regression
Residual
Total
df
2
12
14
t Statistic
2.236241
2.231711
2.879226
p-value
0.042132
0.042493
0.01213
SS
MS
F
p-value
203693.3 101846.7 6.745406 0.010884
181184.1 15098.67
384877.4
Using  = 0.05 to test the null hypothesis H0: 1 = 2 = 0, the critical F value is ____.
a) 3.74
b) 3.89
c) 4.75
d) 4.60
e) 2.74
Ans: b
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
43. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 752.0833
336.3158
11.87375
5.32047
x1
1.908183
0.662742
x2
Source
Regression
Residual
Total
df
2
12
14
t Statistic
2.236241
2.231711
2.879226
p-value
0.042132
0.042493
0.01213
SS
MS
F
p-value
203693.3 101846.7 6.745406 0.010884
181184.1 15098.67
384877.4
Using  = 0.10 to test the null hypothesis H0: 2 = 0, the critical t value is ____.
a) ±1.345
b) ±1.356
c) ±1.761
d) ±2.782
e) ±1.782
Ans: e
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
44. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 752.0833
336.3158
11.87375
5.32047
x1
1.908183
0.662742
x2
Source
Regression
Residual
Total
df
2
12
14
t Statistic
2.236241
2.231711
2.879226
p-value
0.042132
0.042493
0.01213
SS
MS
F
p-value
203693.3 101846.7 6.745406 0.010884
181184.1 15098.67
384877.4
These results indicate that ____________.
a) none of the predictor variables are significant at the 5% level
b) each predictor variable is significant at the 5% level
c) x1 is the only predictor variable significant at the 5% level
d) x2 is the only predictor variable significant at the 5% level
e) the intercept is not significant at the 5% level
Ans: b
Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients
Difficulty: Easy
45. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error t Statistic p-value
Intercept 752.0833
336.3158
2.236241 0.042132
11.87375
5.32047
2.231711 0.042493
x1
x2
Source
Regression
Residual
Total
1.908183
df
2
12
14
0.662742
2.879226 0.01213
SS
MS
F
p-value
203693.3 101846.7 6.745406 0.010884
181184.1 15098.67
384877.4
For x1= 60 and x2 = 200, the predicted value of y is ____________.
a) 658.24
b) 711.98
c) 788.09
d) 1,846.15
e) 2,546.98
Ans: d
Response: See section 13.1 The Multiple Regression Model
Difficulty: Medium
46. In regression analysis, outliers may be identified by examining the ________.
a) coefficient of determination
b) coefficient of correlation
c) p-values for the partial coefficients
d) residuals
e) R-squared value
Ans: d
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
47. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
Regression
Error
Total
df
SS
700
MS
F
1000
The number of degrees of freedom for regression is __________.
a) 1
b) 4
c) 34
p
d) 30
e) 35
Ans: b
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
48. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
Regression
Error
Total
df
SS
700
MS
F
p
1000
The number of degrees of freedom for error is __________.
a) 1
b) 4
c) 34
d) 30
e) 35
Ans: d
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
49. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
df
SS
MS
F
p
Regression
700
Error
Total
1000
The MSR value is __________.
a) 700.00
b) 350.00
c) 233.33
d) 175.00
e) 275.00
Ans: d
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
50. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
df
SS
MS
F
p
Regression
700
Error
Total
1000
The MSE value is __________.
a) 8.57
b) 8.82
c) 10.00
d) 75.00
e) 20.00
Ans: c
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
51. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
df
SS
MS
F
p
Regression
700
Error
Total
1000
The observed F value is __________.
a) 17.50
b) 2.33
c) 0.70
d) 0.43
e) 0.50
Ans: a
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
52. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
Regression
Error
Total
df
SS
700
MS
F
p
1000
The value of the standard error of the estimate se is __________.
a) 13.23
b) 3.16
c) 17.32
d) 26.46
e) 10.00
Ans: b
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
53. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
df
SS
MS
F
p
Regression
700
Error
Total
1000
The R2 value is __________.
a) 0.80
b) 0.70
c) 0.66
d) 0.76
e) 0.30
Ans: b
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
54. The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
Source
df
SS
MS
F
p
Regression
700
Error
Total
1000
The adjusted R2 value is __________.
a) 0.80
b) 0.70
c) 0.66
d) 0.76
e) 0.30
Ans: c
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
55. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
SS
2000
MS
F
p
2500
The sample size for the analysis is __________.
a) 30
b) 25
c) 10
d) 5
e) 31
Ans: e
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
56. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
SS
2000
MS
F
2500
The number of independent variables in the analysis is __________.
a) 30
b) 25
c) 1
d) 5
e) 2
p
Ans: d
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
57. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
SS
2000
MS
F
p
2500
The MSR value is __________.
a) 20
b) 400
c) 2000
d) 500
e) 30
Ans: b
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
58. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
SS
2000
MS
F
p
2500
The SSE value is __________.
a) 20
b) 400
c) 2000
d) 500
e) 2500
Ans: d
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Easy
59. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
SS
2000
MS
F
p
2500
The MSE value is __________.
a) 20
b) 400
c) 2000
d) 500
e) 100
Ans: a
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
60. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
SS
2000
MS
F
p
2500
The observed F value is __________.
a) 20
b) 400
c) 2000
d) 500
e) 10
Ans: a
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
61. The following ANOVA table is from a multiple regression analysis.
Source
Regression
df
5
SS
2000
MS
F
p
Error
Total
25
2500
The value of the standard error of the estimate se is __________.
a) 20.00
b) 44.72
c) 4.47
d) 22.36
e) 12.47
Ans: c
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
62. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
SS
2000
MS
F
p
2500
The R2 value is __________.
a) 0.80
b) 0.70
c) 0.66
d) 0.76
e) 1.00
Ans: a
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
63. The following ANOVA table is from a multiple regression analysis.
Source
Regression
Error
Total
df
5
25
The adjusted R2 value is __________.
a) 0.80
SS
2000
2500
MS
F
p
b) 0.70
c) 0.66
d) 0.86
e) 0.76
Ans: e
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
64. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 624.5369
78.49712
x1
8.569122
1.652255
x2
4.736515
0.699194
Source
Regression
Residual
Total
t Statistic
7.956176
5.186319
6.774248
p-value
6.88E-06
0.000301
3.06E-05
df
SS
MS
F
p-value
2 1660914 830457.1 58.31956 1.4E-06
11 156637.5 14239.77
13 1817552
These results indicate that ____________.
a) none of the predictor variables are significant at the 5% level
b) each predictor variable is significant at the 5% level
c) x1 is the only predictor variable significant at the 5% level
d) x2 is the only predictor variable significant at the 5% level
e) the intercept is not significant at 5% level
Ans: b
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
65. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 624.5369
78.49712
x1
8.569122
1.652255
x2
4.736515
0.699194
Source
df
SS
MS
t Statistic
7.956176
5.186319
6.774248
p-value
6.88E-06
0.000301
3.06E-05
F
p-value
Regression
Residual
Total
2 1660914 830457.1 58.31956 1.4E-06
11 156637.5 14239.77
13 1817552
For x1= 30 and x2 = 100, the predicted value of y is ____________.
a) 753.77
b) 1,173.00
c) 1,355.26
d) 615.13
e) 6153.13
Ans: c
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
66. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept 624.5369
78.49712
x1
8.569122
1.652255
x2
4.736515
0.699194
Source
Regression
Residual
Total
t Statistic
7.956176
5.186319
6.774248
p-value
6.88E-06
0.000301
3.06E-05
df
SS
MS
F
p-value
2 1660914 830457.1 58.31956 1.4E-06
11 156637.5 14239.77
13 1817552
The coefficient of multiple determination is ____________.
a) 0.0592
b) 0.9138
c) 0.1149
d) 0.9559
e) 1.0000
Ans: b
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
67. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error t Statistic p-value
Intercept
x1
x2
Source
Regression
Residual
Total
624.5369
8.569122
4.736515
78.49712
1.652255
0.699194
7.956176 6.88E-06
5.186319 0.000301
6.774248 3.06E-05
df
SS
MS
F
p-value
2 1660914 830457.1 58.31956 1.4E-06
11 156637.5 14239.77
13 1817552
The adjusted R2 is ____________.
a) 0.9138
b) 0.9408
c) 0.8981
d) 0.8851
e) 0.8891
Ans: c
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
68. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept -139.609
2548.989
x1
24.24619
22.25267
x2
32.10171
17.44559
Source
Regression
Residual
Total
df
2
13
15
t Statistic
-0.05477
1.089586
1.840105
p-value
0.957154
0.295682
0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
1153309 88716.07
1455998
The regression equation for this analysis is ____________.
a) y
x1 + 1455998 x2
b) y = -139.609 + 24.24619 x1 + 32.10171 x2
c) y = 2548.989 + 22.25267 x1 + 17.44559 x2
d) y = -0.05477 + 1.089586 x1 + 1.840105 x2
e) y = 0.05477 + 1.089586 x1 + 1.840105 x2
Ans: b
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Easy
69. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept -139.609
2548.989
x1
24.24619
22.25267
x2
32.10171
17.44559
Source
Regression
Residual
Total
df
2
13
15
t Statistic
-0.05477
1.089586
1.840105
p-value
0.957154
0.295682
0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
1153309 88716.07
1455998
The sample size for this analysis is ____________.
a) 17
b) 13
c) 16
d) 11
e) 15
Ans: c
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Easy
70. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept -139.609
2548.989
x1
24.24619
22.25267
x2
32.10171
17.44559
Source
Regression
Residual
Total
df
2
13
15
t Statistic
-0.05477
1.089586
1.840105
p-value
0.957154
0.295682
0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
1153309 88716.07
1455998
Using  = 0.01 to test the null hypothesis H0:  1 =  2 = 0, the critical F value is ____.
a) 5.99
b) 5.70
c) 1.96
d) 4.84
e) 6.70
Ans: e
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
71. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept -139.609
2548.989
x1
24.24619
22.25267
x2
32.10171
17.44559
Source
Regression
Residual
Total
df
2
13
15
t Statistic
-0.05477
1.089586
1.840105
p-value
0.957154
0.295682
0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
1153309 88716.07
1455998
Using  = 0.01 to test the null hypothesis H0: 2 = 0, the critical t value is ____.
a) ± 1.174
b) ± 2.093
c) ± 2.131
d) ± 4.012
e) ± 3.012
Ans: e
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
72. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept -139.609
2548.989
x1
24.24619
22.25267
x2
32.10171
17.44559
Source
Regression
df
2
t Statistic
-0.05477
1.089586
1.840105
p-value
0.957154
0.295682
0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
Residual
Total
13
15
1153309 88716.07
1455998
These results indicate that ____________.
a) none of the predictor variables are significant at the 5% level
b) each predictor variable is significant at the 5% level
c) x1 is the only predictor variable significant at the 5% level
d) x2 is the only predictor variable significant at the 5% level
e) all variables are significant at 5% level
Ans: a
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
73. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept -139.609
2548.989
x1
24.24619
22.25267
x2
32.10171
17.44559
Source
Regression
Residual
Total
df
2
13
15
t Statistic
-0.05477
1.089586
1.840105
p-value
0.957154
0.295682
0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
1153309 88716.07
1455998
For x1= 40 and x2 = 90, the predicted value of y is ____________.
a) 753.77
b) 1,173.00
c) 1,355.26
d) 3,719.39
e) 1,565.75
Ans: d
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
74. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error t Statistic p-value
Intercept
x1
x2
Source
Regression
Residual
Total
-139.609
24.24619
32.10171
df
2
13
15
2548.989
22.25267
17.44559
-0.05477 0.957154
1.089586 0.295682
1.840105 0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
1153309 88716.07
1455998
The coefficient of multiple determination is ____________.
a) 0.2079
b) 0. 0860
c) 0.5440
d) 0.7921
e) 0.5000
Ans: a
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
75. A multiple regression analysis produced the following tables.
Predictor Coefficients Standard Error
Intercept -139.609
2548.989
x1
24.24619
22.25267
x2
32.10171
17.44559
Source
Regression
Residual
Total
df
2
13
15
t Statistic
-0.05477
1.089586
1.840105
p-value
0.957154
0.295682
0.08869
SS
MS
F
p-value
302689 151344.5 1.705942 0.219838
1153309 88716.07
1455998
The adjusted R2 is ____________.
a) 0.2079
b) 0.0860
c) 0.5440
d) 0.7921
e) 1.0000
Ans: b
Response: See section 13.4 Interpreting Multiple Regression Computer Output
Difficulty: Medium
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