Deck 13: Multiple Regression Analysis

Question 1

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 1

False

Question 2

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).

Answer 2

True

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

Question 5

Understand the limitations and pitfalls of multiple regression analysis.

Question 6

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 7

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

Question 8

Examine significance tests of both the overall regression model and the regression coefficients.

Question 9

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.

Question 10

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

Question 11

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 12

In the estimated multiple regression model y = b₀ + b₁x₁ + b₂ 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+ 3b₂)units.

Question 13

Explain how,by extending the simple regression model to a multiple regression model with two independent variables,it is possible to determine the multiple regression equation for any number of unknowns.

Question 14

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

Question 15

Calculate the residual,standard error of the estimate,coefficient of multiple determination,and adjusted coefficient of multiple determination of a regression model.

Question 16

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 17

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

Question 18

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

Question 19

Use a computer to find and interpret multiple regression outputs.

Question 20

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

Question 21

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 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

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 24

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 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 25

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 26

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

Question 27

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 28

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)a quantitative variable

Question 29

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 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 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)a quantitative variable
C)a dependent variable
D)a qualitative variable
E)an independent variable

Question 32

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 33

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 34

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 35

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 36

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 37

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 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 38

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 39

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 40

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 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 41

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 42

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 43

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 44

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 45

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 46

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 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

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 49

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 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: $\beta$ ₁ = 0,the critical t value is ___.

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

Question 52

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 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 error is ___.

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

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 $\alpha$ = 0.10 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 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

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 58

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 59

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 60

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 61

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 62

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 63

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 64

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 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)all variables are significant at 5% level

Question 66

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 67

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 68

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 69

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 70

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 71

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 72

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 73

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 74

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 75

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 76

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 77

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 78

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 79

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

Question 80

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

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