Deck 13: Multiple Regression Analysis

Question 1

In the estimated multiple regression model y = b₀ + b₁x₁ + b₂ x₂, if the value of x₁ is increased by 3 and the value of x₂ is increased by 2 simultaneously, the value of y will increase by (3b₁+ 2b₂)units.

Answer 1

False

Question 2

In the estimated multiple regression model y = b₀ + b₁x₁ + b₂ x₂, if the values of x₁ and x₂ are both increased by one unit, the value of y will increase by (b₁+ b₂)units.

Answer 2

False

Question 3

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.

Answer 3

True

Question 4

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 5

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).

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

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

Question 8

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

Question 9

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 10

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).

Question 11

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

Question 12

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

Question 13

Multiple t tests are used to determine whether the overall regression model is significant.

Question 14

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).

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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 20

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

Question 21

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 22

A human resources consultant 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)a quantitative variable

Question 23

A real estate agent 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)a quantitative variable
C)a dependent variable
D)a qualitative variable
E)an independent variable

Question 24

A human resources consultant 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: The regression equation for this analysis is ___.

A)y = 752.0833 + 11.87375 x₁ + 1.908183 x₂
B)y = 752.0833 + 336.3158 x₁ + 2.236241 x₂
C)y = 336.3158 + 5.32047 x₁+ 0.662742 x₂₂
D)y = 2.236241 + 2.231711 x₁ + 2.879226 x₂
E)y = 2.236241 + 2.231711 x₁ - 2.879226 x₂

Question 26

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 27

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 28

A human resources consultant 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 29

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

A)12
B)15
C)14
D)28
E)24

Question 30

A multiple regression analysis produced the following tables: For x₁= 60 and x₂ = 200, the predicted value of y is ___.

A)658.24
B)711.98
C)788.09
D)1,846.14
E)2,546.98

Question 31

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 32

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 (Kitchener and Hamilton), 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 33

A market research company is developing a regression model to predict monthly household expenditures on groceries as a function of family size, household income, and household neighbourhood (urban, suburban, and rural).The "neighbourhood" 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 34

A market research company is developing a regression model to predict monthly household expenditures on groceries as a function of family size, household income, and household neighbourhood (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 neighbourhood

Question 35

A market research company is developing a regression model to predict monthly household expenditures on groceries as a function of family size, household income, and household neighbourhood (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 (Kitchener and Hamilton), 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 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 (Kitchener and Hamilton), 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 38

A multiple regression analysis produced the following tables: For x₁= 60 and x₂ = 200, the predicted value of y is ___.

A)1,173.00
B)772.40
C)460.97
D)615.13
E)987.78

Question 39

A real estate agent 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 40

A real estate agent 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

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 42

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

A)20
B)400
C)2000
D)500
E)30

Question 43

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

A)20
B)400
C)2000
D)500
E)2500

Question 44

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 45

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 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 R² value is ___.

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

Question 48

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

A)30
B)25
C)10
D)5
E)31

Question 49

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 50

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

A)30
B)25
C)1
D)5
E)2

Question 51

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 52

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

A)20
B)400
C)2000
D)500
E)10

Question 53

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 54

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 55

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 56

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 57

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 58

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

A)20
B)400
C)2000
D)500
E)100

Question 59

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 60

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 61

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

A)0.80
B)0.70
C)0.66
D)0.76
E)1.00

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

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 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

The following ANOVA table is from a multiple regression analysis: 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

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: 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 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)all variables are significant at 5% level

Question 69

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

A)0.9138
B)0.9408
C)0.8982
D)0.8851
E)0.8891

Question 70

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

A)0.2079
B)0.0860
C)0.5440
D)0.7921
E)1.0000

Question 71

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 72

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 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

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 75

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

A)0.80
B)0.70
C)0.66
D)0.86
E)0.76