Chapter 13 Basic Multiple Regression Analysis

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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. In a multiple regression analysis with N observations and k independent variables, the degrees of freedom for the residual error is given by (Nk).

 

Ans: False

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

Difficulty: Medium

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 ______.
  2. a) batch size
  3. b) production shift
  4. c) production plant
  5. d) total cost
  6. e) variable cost

 

Ans: d

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ______.
  2. a) a response variable
  3. b) an independent variable
  4. c) a quantitative variable
  5. d) a dependent variable
  6. e) a constant

 

Ans: b

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ______.
  2. a) a response variable
  3. b) an indicator variable
  4. c) a dependent variable
  5. d) a qualitative variable
  6. e) an independent variable

 

Ans: e

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 _____.
  2. a) family size
  3. b) expenditures on groceries
  4. c) household income
  5. d) suburban
  6. e) household neighborhood

 

Ans: b

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ______.
  2. a) an independent variable
  3. b) a response variable
  4. c) a quantitative variable
  5. d) a dependent variable
  6. e) a constant

 

Ans: a

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ____.
  2. a) an indicator variable
  3. b) a response variable
  4. c) a qualitative variable
  5. d) a dependent variable
  6. e) an independent variable

 

Ans: e

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ______.
  2. a) plant manager compensation
  3. b) plant capacity
  4. c) number of employees
  5. d) plant technology
  6. e) nuclear

 

Ans: a

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ______.
  2. a) a response variable
  3. b) a dependent variable
  4. c) a quantitative variable
  5. d) an independent variable
  6. e) a constant

 

Ans: d

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ______.
  2. a) a qualitative variable
  3. b) a dependent variable
  4. c) a response variable
  5. d) an indicator variable
  6. e) an independent variable

 

Ans: a

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 _______.
  2. a) heated area
  3. b) number of bedrooms
  4. c) market value
  5. d) central heating
  6. e) residential houses

 

Ans: c

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 _______.
  2. a) a response variable
  3. b) an independent variable
  4. c) a quantitative variable
  5. d) a dependent variable
  6. e) a constant

 

Ans: b

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 _______.
  2. a) a response variable
  3. b) an indicator variable
  4. c) a dependent variable
  5. d) a qualitative variable
  6. e) an independent variable

 

Ans: b

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. The multiple regression formulas used to estimate the regression coefficients are designed to ________________.
  2. a) minimize the total sum of squares (SST)
  3. b) minimize the sum of squares of error (SSE)
  4. c) maximize the standard error of the estimate
  5. d) maximize the p-value for the calculated F value
  6. e) minimize the mean error

 

Ans: b

Response: See section 13.1 The Multiple Regression Model

Difficulty: Medium

 

 

 

  1. 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 ____________.

  1. a) y = 616.6849 + 3.33833 x1+ 1.780075 x2
  2. b) y = 154.5535 – 1.43058 x1+ 5.30407 x2
  3. c) y = 616.6849 – 3.33833 x1- 1.780075 x2
  4. d) y = 154.5535 + 2.333548 x1 + 0.335605 x2
  5. e) y = 616.6849 – 3.33833 x1+ 1.780075 x2

 

Ans: e

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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

 

 

 

  1. 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 ____.

  1. a) 68
  2. b) 6.36
  3. c) 8.40
  4. d) 6.11
  5. e) 3.36

 

Ans: b

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

Difficulty: Easy

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 ____________.

  1. a) 1,173.00
  2. b) 772.40
  3. c) 460.97
  4. d) 615.13
  5. e) 987.78

 

Ans: b

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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 ____________.

  1. a) y = 752.0833 + 11.87375 x1+ 1.908183 x2
  2. b) y = 752.0833 + 336.3158 x1+ 2.236241 x2
  3. c) y = 336.3158 + 5.32047 x1+ 0.662742 x2
  4. d) y = 2.236241 + 2.231711 x1 + 2.879226 x2
  5. e) y = 2.236241 + 2.231711 x1- 2.879226 x2

 

Ans: a

Response: See section 13.1 The Multiple Regression Model

Difficulty: Easy

 

 

 

  1. 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

 

 

 

  1. 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 ____.

  1. a) 74
  2. b) 3.89
  3. c) 4.75
  4. d) 4.60
  5. e) 2.74

 

Ans: b

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

Difficulty: Easy

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 ____________.

  1. a) 24
  2. b) 711.98
  3. c) 788.09
  4. d) 1,846.15
  5. e) 2,546.98

 

Ans: d

Response: See section 13.1 The Multiple Regression Model

Difficulty: Medium

 

 

 

  1. In regression analysis, outliers may be identified by examining the ________.
  2. a) coefficient of determination
  3. b) coefficient of correlation
  4. c) p-values for the partial coefficients
  5. d) residuals
  6. e) R-squared value

 

Ans: d

Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2

Difficulty: Easy

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 __________.

  1. a) 700.00
  2. b) 350.00
  3. c) 233.33
  4. d) 175.00
  5. e) 275.00

 

Ans: d

Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2

Difficulty: Easy

 

 

 

  1. 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 __________.

  1. a) 8.57
  2. b) 8.82
  3. c) 10.00
  4. d) 75.00
  5. e) 20.00

 

Ans: c

Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2

Difficulty: Easy

 

 

 

  1. 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 __________.

  1. a) 17.50
  2. b) 2.33
  3. c) 0.70
  4. d) 0.43
  5. e) 0.50

 

Ans: a

Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2

Difficulty: Medium

 

 

 

  1. 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 __________.

  1. a) 13.23
  2. b) 3.16
  3. c) 17.32
  4. d) 26.46
  5. e) 10.00

 

Ans: b

Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2

Difficulty: Easy

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 __________.

  1. a) 20.00
  2. b) 44.72
  3. c) 4.47
  4. d) 22.36
  5. e) 12.47

 

Ans: c

Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2

Difficulty: Medium

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 ____________.

  1. a) 77
  2. b) 1,173.00
  3. c) 1,355.26
  4. d) 615.13
  5. e) 6153.13

 

Ans: c

Response: See section 13.4 Interpreting Multiple Regression Computer Output

Difficulty: Medium

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 ____.

  1. a) 99
  2. b) 5.70
  3. c) 1.96
  4. d) 4.84
  5. e) 6.70

 

Ans: e

Response: See section 13.4 Interpreting Multiple Regression Computer Output

Difficulty: Medium

 

 

 

  1. 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

 

 

 

  1. 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

 

 

 

  1. 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 ____________.

  1. a) 77
  2. b) 1,173.00
  3. c) 1,355.26
  4. d) 3,719.39
  5. e) 1,565.75

 

Ans: d

Response: See section 13.4 Interpreting Multiple Regression Computer Output

Difficulty: Medium

 

 

 

  1. 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

 

 

 

  1. 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