# Chapter 13 Basic Multiple Regression Analysis

File: Ch13, Chapter 13: Basic Multiple Regression Analysis

True/False

- 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

- The model
*y*=*b*0+*b*1*x*1+*b*2*x*2 +*e*is a second-order regression model.

Ans: False

Response: See section 13.1 The Multiple Regression Model

Difficulty: Medium

- The model
*y*=*b*0+*b*1*x*1+*b*2*x*2 +*b*3*x*3 +*e*is a first-order regression model.

Ans: True

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

- In the multiple regression model
*y*=*b*0+*b*1*x*1+*b*2*x*2 +*b*3*x*3 +*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

- In the model
*y*=*b*0+*b*1*x*1+*b*2*x*2 +*b*3*x*3 +*e,**y*is the independent variable.

Ans: False

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

- 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

- In the estimated multiple regression model
*y*= b0+ b1*x*1+ b 2*x*2**if the values of*x*_{1}and*x*2 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

- In the model
*y*=*b*0+*b*1*x*1+*b*2*x*2 +*b*3*x*3 +*e*,*e*is a constant.

Ans: False

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

- In the estimated multiple regression model
*y*= b0+ b1*x*1+ b 2*x*2**if the value of*x*_{1}is increased by 2 and the value of*x*2 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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 *R*^{2}

Difficulty: Easy

- 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 *R*^{2}

Difficulty: Hard

- 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 *R*^{2}

Difficulty: Medium

Multiple Choice

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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 ____________.

- a)
*y*= 616.6849 + 3.33833*x*1+ 1.780075*x*2 - b)
*y*= 154.5535 – 1.43058*x*1+ 5.30407*x*2 - c)
*y*= 616.6849 – 3.33833*x*1- 1.780075*x*2 - d)
*y*= 154.5535 + 2.333548*x*1 + 0.335605*x*2 - e)
*y*= 616.6849 – 3.33833*x*1+ 1.780075*x*2

Ans: e

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

- 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 ____________.

- a) 19
- b) 17
- c) 34
- d) 15
- e) 18

Ans: e

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

- 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 ____.

- a) 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

- 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: *b*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

- 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 ____________.

- a) none of the predictor variables are significant at the 5% level
- b) each predictor variable is significant at the 5% level
- c)
*x*1is significant at the 5% level - d)
*x*2is 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

- 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 *x*1= 60 and *x*2 = 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

- 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 ____________.

- a)
*y*= 752.0833 + 11.87375*x*1+ 1.908183*x*2 - b)
*y*= 752.0833 + 336.3158*x*1+ 2.236241*x*2 - c)
*y*= 336.3158 + 5.32047*x*1+ 0.662742*x*2 - d)
*y*= 2.236241 + 2.231711*x*1 + 2.879226*x*2 - e)
*y*= 2.236241 + 2.231711*x*1- 2.879226*x*2

Ans: a

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

- 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 ____________.

- a) 12
- b) 15
- c) 14
- d) 28
- e) 24

Ans: b

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

- 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: *b*1 = *b*2 = 0, the critical* F *value is ____.

- a) 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

- 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: *b*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

- 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 ____________.

- a) none of the predictor variables are significant at the 5% level
- b) each predictor variable is significant at the 5% level
- c)
*x*1is the only predictor variable significant at the 5% level - d)
*x*2is 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

- 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 *x*1= 60 and *x*2 = 200, the predicted value of *y* is ____________.

- a) 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

- 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 *R*^{2}

Difficulty: Easy

- 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 __________.

- a) 1
- b) 4
- c) 34
- d) 30
- e) 35

Ans: b

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Easy

- 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 __________.

- a) 1
- b) 4
- c) 34
- d) 30
- e) 35

Ans: d

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Easy

- 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 *R*^{2}

Difficulty: Easy

- 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 *R*^{2}

Difficulty: Easy

- 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 *R*^{2}

Difficulty: Medium

- 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 *s*e 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 *R*^{2}

Difficulty: Easy

- 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* R*2 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 *R*^{2}

Difficulty: Medium

- 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* R*2 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 *R*^{2}

Difficulty: Medium

- 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 __________.

- a) 30
- b) 25
- c) 10
- d) 5
- e) 31

Ans: e

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Easy

- 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 __________.

- a) 30
- b) 25
- c) 1
- d) 5
- e) 2

Ans: d

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Medium

- 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 __________.

- a) 20
- b) 400
- c) 2000
- d) 500
- e) 30

Ans: b

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Medium

- 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 __________.

- a) 20
- b) 400
- c) 2000
- d) 500
- e) 2500

Ans: d

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Easy

- 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 __________.

- a) 20
- b) 400
- c) 2000
- d) 500
- e) 100

Ans: a

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Medium

- 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 __________.

- a) 20
- b) 400
- c) 2000
- d) 500
- e) 10

Ans: a

Response: See section 13.3 Residuals, Standard Error of the Estimate, and *R*^{2}

Difficulty: Medium

- 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 *s*e 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 *R*^{2}

Difficulty: Medium

- The following ANOVA table is from a multiple regression analysis.

Source | df | SS | MS | F |
p |

Regression | 5 | 2000 | |||

Error | 25 | ||||

Total | 2500 |

The* R*2 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 *R*^{2}

Difficulty: Medium

- 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* R*2 value is __________.

- a) 0.80
- 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 *R*^{2}

Difficulty: Medium

- 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 ____________.

- a) none of the predictor variables are significant at the 5% level
- b) each predictor variable is significant at the 5% level
- c)
*x*1is the only predictor variable significant at the 5% level - d)
*x*2is 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

- 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 *x*1= 30 and *x*2 = 100, the predicted value of *y* is ____________.

- a) 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

- 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 ____________.

- a) 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

- 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* R*^{2} 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

- 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 ____________.

- a)
*y*= 302689 + 1153309*x*1+ 1455998*x*2 - b)
*y*= -139.609 + 24.24619*x*1+ 32.10171*x*2 - c)
*y*= 2548.989 + 22.25267*x*1+ 17.44559*x*2 - d)
*y*= -0.05477 + 1.089586*x*1 + 1.840105*x*2 - e)
*y*= 0.05477 + 1.089586*x*1+ 1.840105*x*2

Ans: b

Response: See section 13.4 Interpreting Multiple Regression Computer Output

Difficulty: Easy

- 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 ____________.

- a) 17
- b) 13
- c) 16
- d) 11
- e) 15

Ans: c

Response: See section 13.4 Interpreting Multiple Regression Computer Output

Difficulty: Easy

- 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 ____.

- a) 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

- 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*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

- 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 ____________.

- a) none of the predictor variables are significant at the 5% level
- b) each predictor variable is significant at the 5% level
- c)
*x*1is the only predictor variable significant at the 5% level - d)
*x*2is 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

- 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 *x*1= 40 and *x*2 = 90, the predicted value of *y* is ____________.

- a) 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

- 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 ____________.

- a) 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

- 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* R*^{2} 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