Deck 13: Multiple Regression Analysis

Question 1

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

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

Answer 3

True

Question 4

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

Question 5

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 6

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

Question 7

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

Question 8

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 9

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 10

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 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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 16

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).

Question 17

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

Question 18

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 19

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 20

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 21

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 22

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 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 "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 24

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 25

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

Question 26

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 27

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 28

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 29

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 30

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 31

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 32

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 33

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 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 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 36

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 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,"shift" is ______.

A)a response variable
B)an independent variable
C)a quantitative variable
D)a dependent variable
E)a constant

Question 38

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

Question 39

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 40

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 41

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 42

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 43

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 44

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 45

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 46

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 47

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 48

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 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 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 50

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 51

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 52

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 53

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 54

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 se is __________.

A)13.23
B)3.16
C)17.32
D)26.46
E)10.00

Question 55

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 56

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 57

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 58

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 59

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 60

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 61

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 62

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 63

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 64

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 65

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 66

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

Question 67

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 68

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 69

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 70

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

A)30
B)26
C)3
D)29
E)31

Question 71

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 72

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

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

Question 73

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 74

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 75

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 76

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 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

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 79

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 80

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

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