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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