Deck 13: Multiple Regression Analysis

Question 1

Regression analysis with two dependent variables and two or more independent variables is called multiple regression.

Answer 1

False

Question 2

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).

Answer 2

False

Question 3

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).

Answer 3

False

Question 4

In the model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$ , $\varepsilon$ is a constant.

Question 5

The F value that is used to test for the overall significance of a multiple regression model is calculated by dividing the sum of mean squares regression (SS_reg)by the sum of squares error (SS_err).

Question 6

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).

Question 7

The standard error of the estimate of a multiple regression model is computed by taking the square root of the mean squares of error.

Question 8

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$ is a second-order regression model.

Question 9

A slope in a multiple regression model is known as a partial slope because it ignores the effects of other explanatory variables.

Question 10

The F test is used to determine whether the overall regression model is significant.

Question 11

The F value that is used to test for the overall significance of a multiple regression model is calculated by dividing the mean square regression (MS_reg)by the mean square error (MS_err).

Question 12

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).

Question 13

In the multiple regression model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$ ,the $\beta$ coefficients of the x variables are called partial regression coefficients.

Question 14

Multiple t-tests are used to determine whether the independent variables in the regression model are significant.

Question 15

If we reject H₀: β₁= β₂=0 using the F-test,then we should conclude that both slopes are different from zero.

Question 16

In the model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$ ,y is the independent variable.

Question 17

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$ is a first-order regression model.

Question 18

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.

Question 19

The standard error of the estimate of a multiple regression model is essentially the standard deviation of the residuals for the regression model.

Question 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.

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

A multiple regression analysis produced the following tables. For x₁= 360 and x₂ = 220,the predicted value of y is ____________.

A) 1314.70
B) 1959.71
C) 1077.58
D) 2635.19
E) 2265.57

Question 26

A multiple regression analysis produced the following tables. 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

Question 27

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

Question 28

A multiple regression analysis produced the following tables. The regression equation for this analysis is ____________.

A) y = 1959.71 + 0.46 x₁ + 2.16 x₂
B) y = 1959.71 - 0.46 x₁ + 2.16 x₂
C) y = 1959.71 - 0.46 x₁ - 2.16 x₂
D) y =1959.71 + 0.46 x₁ - 2.16 x₂
E) y =- 0.46 x₁ - 2.16 x₂

Question 29

A multiple regression analysis produced the following tables. The sample size for this analysis is ____________.

A) 19
B) 17
C) 34
D) 15
E) 18

Question 30

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

Question 31

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 "number of employees at the plant" 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

Question 32

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

Question 33

The value of R² always goes up when a nontrivial explanatory variable is added to a regression model.

Question 34

Minitab and Excel output for a multiple regression model show the F test for the overall model,but do not provide the t tests for the regression coefficients.

Question 35

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

Question 36

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

Question 37

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

Question 38

Minitab and Excel output for a multiple regression model show the t tests for the regression coefficients but do not provide a t test for the regression constant.

Question 39

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

Question 40

The value of adjusted R² always goes up when a nontrivial explanatory variable is added to a regression model.

Question 41

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. The MSR value is __________.

A) 700.00
B) 350.00
C) 233.33
D) 175.00
E) 275.00

Question 42

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. 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

Question 43

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = 0,the correct decision is ____.

A) fail to reject the null hypothesis
B) reject the null hypothesis
C) fail to reject the alternative hypothesis
D) reject the alternative hypothesis
E) there is not enought information provided to make a decision

Question 44

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.10 to test the null hypothesis H₀: $\beta$ ₂ = 0,the critical t value is ____.

A) ±1.345
B) ±1.356
C) ±1.761
D) ±2.782
E) ±1.782

Question 45

A multiple regression analysis produced the following tables. The sample size for this analysis is ____________.

A) 12
B) 15
C) 17
D) 18
E) 24

Question 46

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. The MSE value is __________.

A) 8.57
B) 8.82
C) 10.00
D) 75.00
E) 20.00

Question 47

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.01 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0,the critical F value is ____.

A) 8.68
B) 6.36
C) 8.40
D) 6.11
E) 3.36

Question 48

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. The number of degrees of freedom for error is __________.

A) 1
B) 4
C) 34
D) 30
E) 35

Question 49

A multiple regression analysis produced the following tables. 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

Question 50

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

Question 51

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₂ = 0,the correct decision is ____.

A) fail to reject the null hypothesis
B) reject the null hypothesis
C) fail to reject the alternative hypothesis
D) reject the alternative hypothesis
E) there is not enought information provided to make a decision

Question 52

A multiple regression analysis produced the following tables. These results indicate that ____________.

A) none of the predictor variables are significant at the 10% level
B) each predictor variable is significant at the 10% level
C) x₁ is significant at the 10% level
D) x₂ is significant at the 10% level
E) the intercept is not significant at 10% level

Question 53

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = 0,the critical t value is ____.

A) ± 1.753
B) ± 2.110
C) ± 2.131
D) ± 1.740
E) ± 2.500

Question 54

A multiple regression analysis produced the following tables. 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

Question 55

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0,the critical F value is ____.

A) 3.74
B) 3.89
C) 4.75
D) 4.60
E) 2.74

Question 56

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. The observed F value is __________.

A) 17.50
B) 2.33
C) 0.70
D) 0.43
E) 0.50

Question 57

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. The adjusted R² value is __________.

A) 0.80
B) 0.70
C) 0.66
D) 0.76
E) 0.30

Question 58

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. The number of degrees of freedom for regression is __________.

A) 1
B) 4
C) 34
D) 30
E) 35

Question 59

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. The R² value is __________.

A) 0.80
B) 0.70
C) 0.66
D) 0.76
E) 0.30

Question 60

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.01 to test the model,these results indicate that ____________.

A) at least one of the regression variables is a significant predictor of y
B) none of the regression variables are significant predictors of y
C) y cannot be sufficiently predicted using these data
D) y is a good predictor of the regression variables in the model
E) the y intercept in this model is the best predictor variable

Question 61

The following ANOVA table is from a multiple regression analysis. The value of the standard error of the estimate s_e is __________.

A) 30.77
B) 5.55
C) 4.03
D) 3.20
E) 0.73

Question 62

A multiple regression analysis produced the following tables. The coefficient of multiple determination is ____________.

A) 0.0592
B) 0.9138
C) 0.1149
D) 0.9559
E) 1.0000

Question 63

The following ANOVA table is from a multiple regression analysis. The SSE value is __________.

A) 30
B) 1500
C) 500
D) 800
E) 2300

Question 64

The following ANOVA table is from a multiple regression analysis. The number of independent variables in the analysis is __________.

A) 30
B) 26
C) 1
D) 3
E) 2

Question 65

A multiple regression analysis produced the following tables. 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

Question 66

A multiple regression analysis produced the following tables. The coefficient of multiple determination is ____________.

A) 0.2079
B) 0. 0860
C) 0.5440
D) 0.7921
E) 0.5000

Question 67

The following ANOVA table is from a multiple regression analysis. The observed F value is __________.

A) 16.25
B) 30.77
C) 500
D) 0.049
E) 0.039

Question 68

The following ANOVA table is from a multiple regression analysis. The adjusted R² value is __________.

A) 0.65
B) 0.39
C) 0.61
D) 0.53
E) 0.78

Question 69

A multiple regression analysis produced the following tables.
Using $\alpha$ = 0.01 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0,the critical F value is ____.

A) 5.99
B) 5.70
C) 1.96
D) 4.84
E) 6.70

Question 70

A multiple regression analysis produced the following tables. The regression equation for this analysis is ____________.

A) y = 302689 + 1153309 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

Question 71

The following ANOVA table is from a multiple regression analysis. The R² value is __________.

A) 0.65
B) 0.53
C) 0.35
D) 0.43
E) 1.37

Question 72

A multiple regression analysis produced the following tables. The sample size for this analysis is ____________.

A) 17
B) 13
C) 16
D) 11
E) 15

Question 73

A multiple regression analysis produced the following tables. 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

Question 74

The following ANOVA table is from a multiple regression analysis. The MSE value is __________.

A) 31
B) 500
C) 16
D) 2300
E) 8.7

Question 75

The following ANOVA table is from a multiple regression analysis. The sample size for the analysis is __________.

B) 26
C) 3
D) 29
E) 31

Question 76

A multiple regression analysis produced the following tables. 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

Question 77

A multiple regression analysis produced the following tables. The adjusted R² is ____________.

A) 0.9138
B) 0.9408
C) 0.8981
D) 0.8851
E) 0.8891

Question 78

The following ANOVA table is from a multiple regression analysis. The MSR value is __________.

A) 1500
B) 50
C) 2300
D) 500
E) 31

Question 79

A multiple regression analysis produced the following tables. 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

Question 80

A multiple regression analysis produced the following tables. Using $\alpha$ = 0.01 to test the null hypothesis H₀: $\beta$ ₂ = 0,the critical t value is ____.

A) ± 1.174
B) ± 2.093
C) ± 2.131
D) ± 4.012
E) ± 3.012