File: Ch13, Chapter 13: Basic 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 = b 0+ b 1x1+ b 2x2 + e is a second-order regression model.

 

Ans: False

Response: See section 13.1 The Multiple Regression Model

Difficulty: Medium

 

 

 

3. The model y = b 0+ b 1x1+ b 2x2 + b 3x3 + e 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 = b 0+ b 1x1+ b 2x2 + b 3x3 + e, the b 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 = b 0+ b 1x1+ b 2x2 + b 3x3 + e, 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 = b 0+ b 1x1+ b 2x2 + b 3x3 + e, e 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 (MS_reg) by the mean square error (MS_err).

 

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 (SS_reg) by the sum of squares error (SS_err).

 

Ans: False

Response: See section 13.2 Significance Tests of the Regression Model and its Coefficients

Difficulty: Easy

 

 

14. The mean square error (MS_err) is calculated by dividing the sum of squares error (SS_err) 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 (MS_err) is calculated by dividing the sum of squares error (SS_err) by the number of error degrees of freedom (df_err).

 

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 ______.
22. a) batch size
23. b) production shift
24. c) production plant
25. d) total cost
26. 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 ______.
23. a) a response variable
24. b) an independent variable
25. c) a quantitative variable
26. d) a dependent variable
27. 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 ______.
24. a) a response variable
25. b) an indicator variable
26. c) a dependent variable
27. d) a qualitative variable
28. 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 _____.
25. a) family size
26. b) expenditures on groceries
27. c) household income
28. d) suburban
29. 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 ______.
26. a) an independent variable
27. b) a response variable
28. c) a quantitative variable
29. d) a dependent variable
30. 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 ____.
27. a) an indicator variable
28. b) a response variable
29. c) a qualitative variable
30. d) a dependent variable
31. 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 ______.
28. a) plant manager compensation
29. b) plant capacity
30. c) number of employees
31. d) plant technology
32. 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 ______.
29. a) a response variable
30. b) a dependent variable
31. c) a quantitative variable
32. d) an independent variable
33. 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 ______.
30. a) a qualitative variable
31. b) a dependent variable
32. c) a response variable
33. d) an indicator variable
34. 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 _______.
31. a) heated area
32. b) number of bedrooms
33. c) market value
34. d) central heating
35. 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 _______.
32. a) a response variable
33. b) an independent variable
34. c) a quantitative variable
35. d) a dependent variable
36. 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 _______.
33. a) a response variable
34. b) an indicator variable
35. c) a dependent variable
36. d) a qualitative variable
37. 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 ________________.
34. a) minimize the total sum of squares (SST)
35. b) minimize the sum of squares of error (SSE)
36. c) maximize the standard error of the estimate
37. d) maximize the p-value for the calculated F value
38. 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	t Statistic	p-value
Intercept	616.6849	154.5534	3.990108	0.000947
x1	-3.33833	2.333548	-1.43058	0.170675
x2	1.780075	0.335605	5.30407	5.83E-05

 

Source	df	SS	MS	F	p-value
Regression	2	121783	60891.48	14.76117	0.000286
Residual	15	61876.68	4125.112
Total	17	183659.6

 

The regression equation for this analysis is ____________.

616. a) y = 616.6849 + 3.33833 x1+ 1.780075 x2
617. b) y = 154.5535 – 1.43058 x1+ 5.30407 x2
618. c) y = 616.6849 – 3.33833 x1- 1.780075 x2
619. d) y = 154.5535 + 2.333548 x1 + 0.335605 x2
620. 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	t Statistic	p-value
Intercept	616.6849	154.5534	3.990108	0.000947
x1	-3.33833	2.333548	-1.43058	0.170675
x2	1.780075	0.335605	5.30407	5.83E-05

 

Source	df	SS	MS	F	p-value
Regression	2	121783	60891.48	14.76117	0.000286
Residual	15	61876.68	4125.112
Total	17	183659.6

 

The sample size for this analysis is ____________.

1. a) 19
2. b) 17
3. c) 34
4. d) 15
5. 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	t Statistic	p-value
Intercept	616.6849	154.5534	3.990108	0.000947
x1	-3.33833	2.333548	-1.43058	0.170675
x2	1.780075	0.335605	5.30407	5.83E-05

 

Source	df	SS	MS	F	p-value
Regression	2	121783	60891.48	14.76117	0.000286
Residual	15	61876.68	4125.112
Total	17	183659.6

 

Using a = 0.01 to test the null hypothesis H0: b 1 = b 2 = 0, the critical F value is ____.

8. a) 68
9. b) 6.36
10. c) 8.40
11. d) 6.11
12. 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	t Statistic	p-value
Intercept	616.6849	154.5534	3.990108	0.000947
x1	-3.33833	2.333548	-1.43058	0.170675
x2	1.780075	0.335605	5.30407	5.83E-05

 

Source	df	SS	MS	F	p-value
Regression	2	121783	60891.48	14.76117	0.000286
Residual	15	61876.68	4125.112
Total	17	183659.6

 

Using a = 0.05 to test the null hypothesis H0: b1 = 0, the critical t value is ____.

1. a) ± 1.753
2. b) ± 2.110
3. c) ± 2.131
4. d) ± 1.740
5. 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
x1	-3.33833	2.333548	-1.43058	0.170675
x2	1.780075	0.335605	5.30407	5.83E-05

 

Source	df	SS	MS	F	p-value
Regression	2	121783	60891.48	14.76117	0.000286
Residual	15	61876.68	4125.112
Total	17	183659.6

 

These results indicate that ____________.

1. a) none of the predictor variables are significant at the 5% level
2. b) each predictor variable is significant at the 5% level
3. c) x1is significant at the 5% level
4. d) x2is significant at the 5% level
5. 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	t Statistic	p-value
Intercept	616.6849	154.5534	3.990108	0.000947
x1	-3.33833	2.333548	-1.43058	0.170675
x2	1.780075	0.335605	5.30407	5.83E-05

 

Source	df	SS	MS	F	p-value
Regression	2	121783	60891.48	14.76117	0.000286
Residual	15	61876.68	4125.112
Total	17	183659.6

 

For x1= 60 and x2 = 200, the predicted value of y is ____________.

173. a) 1,173.00
174. b) 772.40
175. c) 460.97
176. d) 615.13
177. 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	t Statistic	p-value
Intercept	752.0833	336.3158	2.236241	0.042132
x1	11.87375	5.32047	2.231711	0.042493
x2	1.908183	0.662742	2.879226	0.01213

 

Source	df	SS	MS	F	p-value
Regression	2	203693.3	101846.7	6.745406	0.010884
Residual	12	181184.1	15098.67
Total	14	384877.4

 

The regression equation for this analysis is ____________.

752. a) y = 752.0833 + 11.87375 x1+ 1.908183 x2
753. b) y = 752.0833 + 336.3158 x1+ 2.236241 x2
754. c) y = 336.3158 + 5.32047 x1+ 0.662742 x2
755. d) y = 2.236241 + 2.231711 x1 + 2.879226 x2
756. 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	t Statistic	p-value
Intercept	752.0833	336.3158	2.236241	0.042132
x1	11.87375	5.32047	2.231711	0.042493
x2	1.908183	0.662742	2.879226	0.01213

 

Source	df	SS	MS	F	p-value
Regression	2	203693.3	101846.7	6.745406	0.010884
Residual	12	181184.1	15098.67
Total	14	384877.4

 

The sample size for this analysis is ____________.

1. a) 12
2. b) 15
3. c) 14
4. d) 28
5. 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	t Statistic	p-value
Intercept	752.0833	336.3158	2.236241	0.042132
x1	11.87375	5.32047	2.231711	0.042493
x2	1.908183	0.662742	2.879226	0.01213

 

Source	df	SS	MS	F	p-value
Regression	2	203693.3	101846.7	6.745406	0.010884
Residual	12	181184.1	15098.67
Total	14	384877.4

 

Using a = 0.05 to test the null hypothesis H0: b1 = b2 = 0, the critical F value is ____.

3. a) 74
4. b) 3.89
5. c) 4.75
6. d) 4.60
7. 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	t Statistic	p-value
Intercept	752.0833	336.3158	2.236241	0.042132
x1	11.87375	5.32047	2.231711	0.042493
x2	1.908183	0.662742	2.879226	0.01213

 

Source	df	SS	MS	F	p-value
Regression	2	203693.3	101846.7	6.745406	0.010884
Residual	12	181184.1	15098.67
Total	14	384877.4

 

Using a = 0.10 to test the null hypothesis H0: b2 = 0, the critical t value is ____.

1. a) ±1.345
2. b) ±1.356
3. c) ±1.761
4. d) ±2.782
5. 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	t Statistic	p-value
Intercept	752.0833	336.3158	2.236241	0.042132
x1	11.87375	5.32047	2.231711	0.042493
x2	1.908183	0.662742	2.879226	0.01213

 

Source	df	SS	MS	F	p-value
Regression	2	203693.3	101846.7	6.745406	0.010884
Residual	12	181184.1	15098.67
Total	14	384877.4

 

These results indicate that ____________.

1. a) none of the predictor variables are significant at the 5% level
2. b) each predictor variable is significant at the 5% level
3. c) x1is the only predictor variable significant at the 5% level
4. d) x2is the only predictor variable significant at the 5% level
5. 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
x1	11.87375	5.32047	2.231711	0.042493
x2	1.908183	0.662742	2.879226	0.01213

 

Source	df	SS	MS	F	p-value
Regression	2	203693.3	101846.7	6.745406	0.010884
Residual	12	181184.1	15098.67
Total	14	384877.4

 

For x1= 60 and x2 = 200, the predicted value of y is ____________.

658. a) 24
659. b) 711.98
660. c) 788.09
661. d) 1,846.15
662. 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 ________.
47. a) coefficient of determination
48. b) coefficient of correlation
49. c) p-values for the partial coefficients
50. d) residuals
51. 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	df	SS	MS	F	p
Regression		700
Error
Total		1000

 

The number of degrees of freedom for regression is __________.

1. a) 1
2. b) 4
3. c) 34
4. d) 30
5. 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	df	SS	MS	F	p
Regression		700
Error
Total		1000

 

The number of degrees of freedom for error is __________.

1. a) 1
2. b) 4
3. c) 34
4. d) 30
5. 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 __________.

700. a) 700.00
701. b) 350.00
702. c) 233.33
703. d) 175.00
704. 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 __________.

8. a) 8.57
9. b) 8.82
10. c) 10.00
11. d) 75.00
12. 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 __________.

17. a) 17.50
18. b) 2.33
19. c) 0.70
20. d) 0.43
21. 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	df	SS	MS	F	p
Regression		700
Error
Total		1000

 

The value of the standard error of the estimate se is __________.

13. a) 13.23
14. b) 3.16
15. c) 17.32
16. d) 26.46
17. 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 __________.

1. a) 0.80
2. b) 0.70
3. c) 0.66
4. d) 0.76
5. 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 __________.

1. a) 0.80
2. b) 0.70
3. c) 0.66
4. d) 0.76
5. 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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The sample size for the analysis is __________.

1. a) 30
2. b) 25
3. c) 10
4. d) 5
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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The number of independent variables in the analysis is __________.

1. a) 30
2. b) 25
3. c) 1
4. d) 5
5. e) 2

 

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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The MSR value is __________.

1. a) 20
2. b) 400
3. c) 2000
4. d) 500
5. 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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The SSE value is __________.

1. a) 20
2. b) 400
3. c) 2000
4. d) 500
5. 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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The MSE value is __________.

1. a) 20
2. b) 400
3. c) 2000
4. d) 500
5. 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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The observed F value is __________.

1. a) 20
2. b) 400
3. c) 2000
4. d) 500
5. 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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The value of the standard error of the estimate se is __________.

20. a) 20.00
21. b) 44.72
22. c) 4.47
23. d) 22.36
24. 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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The R2 value is __________.

1. a) 0.80
2. b) 0.70
3. c) 0.66
4. d) 0.76
5. 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	df	SS	MS	F	p
Regression	5	2000
Error	25
Total		2500

 

The adjusted R2 value is __________.

1. a) 0.80
2. b) 0.70
3. c) 0.66
4. d) 0.86
5. 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	t Statistic	p-value
Intercept	624.5369	78.49712	7.956176	6.88E-06
x1	8.569122	1.652255	5.186319	0.000301
x2	4.736515	0.699194	6.774248	3.06E-05

 

Source	df	SS	MS	F	p-value
Regression	2	1660914	830457.1	58.31956	1.4E-06
Residual	11	156637.5	14239.77
Total	13	1817552

 

These results indicate that ____________.

1. a) none of the predictor variables are significant at the 5% level
2. b) each predictor variable is significant at the 5% level
3. c) x1is the only predictor variable significant at the 5% level
4. d) x2is the only predictor variable significant at the 5% level
5. 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	t Statistic	p-value
Intercept	624.5369	78.49712	7.956176	6.88E-06
x1	8.569122	1.652255	5.186319	0.000301
x2	4.736515	0.699194	6.774248	3.06E-05

 

Source	df	SS	MS	F	p-value
Regression	2	1660914	830457.1	58.31956	1.4E-06
Residual	11	156637.5	14239.77
Total	13	1817552

 

For x1= 30 and x2 = 100, the predicted value of y is ____________.

753. a) 77
754. b) 1,173.00
755. c) 1,355.26
756. d) 615.13
757. 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	t Statistic	p-value
Intercept	624.5369	78.49712	7.956176	6.88E-06
x1	8.569122	1.652255	5.186319	0.000301
x2	4.736515	0.699194	6.774248	3.06E-05

 

Source	df	SS	MS	F	p-value
Regression	2	1660914	830457.1	58.31956	1.4E-06
Residual	11	156637.5	14239.77
Total	13	1817552

 

The coefficient of multiple determination is ____________.

1. a) 0592
2. b) 0.9138
3. c) 0.1149
4. d) 0.9559
5. 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	624.5369	78.49712	7.956176	6.88E-06
x1	8.569122	1.652255	5.186319	0.000301
x2	4.736515	0.699194	6.774248	3.06E-05

 

Source	df	SS	MS	F	p-value
Regression	2	1660914	830457.1	58.31956	1.4E-06
Residual	11	156637.5	14239.77
Total	13	1817552

 

The adjusted R² is ____________.

1. a) 0.9138
2. b) 0.9408
3. c) 0.8981
4. d) 0.8851
5. 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	t Statistic	p-value
Intercept	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

The regression equation for this analysis is ____________.

1. a) y = 302689 + 1153309 x1+ 1455998 x2
2. b) y = -139.609 + 24.24619 x1+ 32.10171 x2
3. c) y = 2548.989 + 22.25267 x1+ 17.44559 x2
4. d) y = -0.05477 + 1.089586 x1 + 1.840105 x2
5. 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	t Statistic	p-value
Intercept	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

The sample size for this analysis is ____________.

1. a) 17
2. b) 13
3. c) 16
4. d) 11
5. 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	t Statistic	p-value
Intercept	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

Using a = 0.01 to test the null hypothesis H0: b 1 = b 2 = 0, the critical F value is ____.

5. a) 99
6. b) 5.70
7. c) 1.96
8. d) 4.84
9. 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	t Statistic	p-value
Intercept	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

Using a = 0.01 to test the null hypothesis H0: b2 = 0, the critical t value is ____.

1. a) ± 1.174
2. b) ± 2.093
3. c) ± 2.131
4. d) ± 4.012
5. 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	t Statistic	p-value
Intercept	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

These results indicate that ____________.

1. a) none of the predictor variables are significant at the 5% level
2. b) each predictor variable is significant at the 5% level
3. c) x1is the only predictor variable significant at the 5% level
4. d) x2is the only predictor variable significant at the 5% level
5. 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	t Statistic	p-value
Intercept	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

For x1= 40 and x2 = 90, the predicted value of y is ____________.

753. a) 77
754. b) 1,173.00
755. c) 1,355.26
756. d) 3,719.39
757. 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	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

The coefficient of multiple determination is ____________.

1. a) 2079
2. b) 0. 0860
3. c) 0.5440
4. d) 0.7921
5. 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	t Statistic	p-value
Intercept	-139.609	2548.989	-0.05477	0.957154
x1	24.24619	22.25267	1.089586	0.295682
x2	32.10171	17.44559	1.840105	0.08869

 

Source	df	SS	MS	F	p-value
Regression	2	302689	151344.5	1.705942	0.219838
Residual	13	1153309	88716.07
Total	15	1455998

 

The adjusted R² is ____________.

1. a) 0.2079
2. b) 0.0860
3. c) 0.5440
4. d) 0.7921
5. e) 1.0000

 

Ans: b

Response: See section 13.4 Interpreting Multiple Regression Computer Output

Difficulty: Medium