Deck 13: Multiple Regression Analysis

Question 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).

Answer 1

True

Question 2

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.

Answer 2

False

Question 3

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).

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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 8

The mean square error (MS_err)is calculated by dividing the sum of squares error (SS_err)by the number of degrees of freedom in the error (df_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).

Question 10

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

Question 11

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

Question 12

The standard error of the estimate of a multiple regression model is computed by taking the square root of the SSE divided by the degrees of freedom of error for the model.

Question 13

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

Question 14

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 15

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

Question 16

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

Question 17

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

Question 18

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 19

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 20

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

Question 21

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Eror } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 616.6849 & 154.5534 & 3.990108 & 0.000947 \\\hline \boldsymbol { x } _ { 1 } & - 3.33833 & \mathbf { 2 . 3 3 3 5 4 8 } & - 1.43058 & \mathbf { 0 . 1 7 0 6 7 5 } \\\hline \mathbf { x } _ { 2 } & 1.780075 & \mathbf { 0 . 3 3 5 6 0 5 } & 5.30407 & 5.83 \mathrm { E } - 05 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 121783 & 60891.48 & 14.76117 & 0.000286 \\\hline \text { Residual } & 15 & 61876.68 & 4125.112 & & \\\hline \text { Total } & 17 & 183659.6 & & & \\\hline\end{array}$$ The sample size for this analysis is ____________.

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

Question 22

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 23

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 24

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 25

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 26

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 27

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

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

Question 28

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

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 "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 30

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 31

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 32

A human resources analyst is developing a regression model to predict electricity 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 33

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 34

A human resources analyst is developing a regression model to predict electricity 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 35

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Eror } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 616.6849 & 154.5534 & 3.990108 & 0.000947 \\\hline \boldsymbol { x } _ { 1 } & - 3.33833 & \mathbf { 2 . 3 3 3 5 4 8 } & - 1.43058 & \mathbf { 0 . 1 7 0 6 7 5 } \\\hline \mathbf { x } _ { 2 } & 1.780075 & \mathbf { 0 . 3 3 5 6 0 5 } & 5.30407 & 5.83 \mathrm { E } - 05 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 121783 & 60891.48 & 14.76117 & 0.000286 \\\hline \text { Residual } & 15 & 61876.68 & 4125.112 & & \\\hline \text { Total } & 17 & 183659.6 & & & \\\hline\end{array}$$ The regression equation for this analysis is ____________.

A) = 616.6849 + 3.33833 x₁ + 1.780075 x₂
B)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = 154.5535 - 1.43058 x₁ + 5.30407 x₂
C)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = 616.6849 - 3.33833 x₁ - 1.780075 x₂
D)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = 154.5535 + 2.333548 x₁ + 0.335605 x₂
E)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = 616.6849 - 3.33833 x₁ + 1.780075 x₂

Question 36

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

Question 37

A human resources analyst is developing a regression model to predict electricity 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 38

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 39

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 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 response variable in this model is _______.

A)heated area
B)number of bedrooms
C)market value
D)central heating
E)residential houses

Question 41

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficierts } & \text { Stardard Error } & \mathbf { E t a t i s t i c } & \boldsymbol { p } \text {-value } \\\hline \text { Irntercept } & 752.0833 & \mathbf { 3 3 6 3 1 5 8 } & \mathbf { 2 . 2 3 6 2 4 1 } & \mathbf { 0 . 0 4 2 1 3 2 } \\\hline \mathbf { x } _ { 1 } & 11.87375 & 5.32047 & \mathbf { 2 . 2 3 1 7 1 1 } & \mathbf { 0 . 0 4 2 4 9 3 } \\\hline \mathbf { x } _ { 2 } & 1.908183 & \mathbf { 0 . 6 6 2 7 4 2 } & \mathbf { 2 . 8 7 9 2 2 6 } & \mathbf { 0 . 0 1 2 1 3 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 203693.3 & 101846.7 & 6.745406 & 0.010884 \\\hline \text { Residual } & 12 & 181184.1 & 15098.67 & & \\\hline \text { Total } & 14 & 384877.4 & & & \\\hline\end{array}$$ 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 42

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ 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. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Eror } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 616.6849 & 154.5534 & 3.990108 & 0.000947 \\\hline \boldsymbol { x } _ { 1 } & - 3.33833 & \mathbf { 2 . 3 3 3 5 4 8 } & - 1.43058 & \mathbf { 0 . 1 7 0 6 7 5 } \\\hline \mathbf { x } _ { 2 } & 1.780075 & \mathbf { 0 . 3 3 5 6 0 5 } & 5.30407 & 5.83 \mathrm { E } - 05 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 121783 & 60891.48 & 14.76117 & 0.000286 \\\hline \text { Residual } & 15 & 61876.68 & 4125.112 & & \\\hline \text { Total } & 17 & 183659.6 & & & \\\hline\end{array}$$ 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

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 45

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ The number of degrees of freedom for this regression is __________.

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

Question 46

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Eror } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 616.6849 & 154.5534 & 3.990108 & 0.000947 \\\hline \boldsymbol { x } _ { 1 } & - 3.33833 & \mathbf { 2 . 3 3 3 5 4 8 } & - 1.43058 & \mathbf { 0 . 1 7 0 6 7 5 } \\\hline \mathbf { x } _ { 2 } & 1.780075 & \mathbf { 0 . 3 3 5 6 0 5 } & 5.30407 & 5.83 \mathrm { E } - 05 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 121783 & 60891.48 & 14.76117 & 0.000286 \\\hline \text { Residual } & 15 & 61876.68 & 4125.112 & & \\\hline \text { Total } & 17 & 183659.6 & & & \\\hline\end{array}$$ 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 47

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ The MSE value is __________.

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

Question 48

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ The adjusted R² value is __________.

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

Question 49

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ The MSR value is __________.

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

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

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. 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 53

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficierts } & \text { Stardard Error } & \mathbf { E t a t i s t i c } & \boldsymbol { p } \text {-value } \\\hline \text { Irntercept } & 752.0833 & \mathbf { 3 3 6 3 1 5 8 } & \mathbf { 2 . 2 3 6 2 4 1 } & \mathbf { 0 . 0 4 2 1 3 2 } \\\hline \mathbf { x } _ { 1 } & 11.87375 & 5.32047 & \mathbf { 2 . 2 3 1 7 1 1 } & \mathbf { 0 . 0 4 2 4 9 3 } \\\hline \mathbf { x } _ { 2 } & 1.908183 & \mathbf { 0 . 6 6 2 7 4 2 } & \mathbf { 2 . 8 7 9 2 2 6 } & \mathbf { 0 . 0 1 2 1 3 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 203693.3 & 101846.7 & 6.745406 & 0.010884 \\\hline \text { Residual } & 12 & 181184.1 & 15098.67 & & \\\hline \text { Total } & 14 & 384877.4 & & & \\\hline\end{array}$$ 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 54

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 55

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ The 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. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Eror } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 616.6849 & 154.5534 & 3.990108 & 0.000947 \\\hline \boldsymbol { x } _ { 1 } & - 3.33833 & \mathbf { 2 . 3 3 3 5 4 8 } & - 1.43058 & \mathbf { 0 . 1 7 0 6 7 5 } \\\hline \mathbf { x } _ { 2 } & 1.780075 & \mathbf { 0 . 3 3 5 6 0 5 } & 5.30407 & 5.83 \mathrm { E } - 05 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 121783 & 60891.48 & 14.76117 & 0.000286 \\\hline \text { Residual } & 15 & 61876.68 & 4125.112 & & \\\hline \text { Total } & 17 & 183659.6 & & & \\\hline\end{array}$$ 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 57

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficierts } & \text { Stardard Error } & \mathbf { E t a t i s t i c } & \boldsymbol { p } \text {-value } \\\hline \text { Irntercept } & 752.0833 & \mathbf { 3 3 6 3 1 5 8 } & \mathbf { 2 . 2 3 6 2 4 1 } & \mathbf { 0 . 0 4 2 1 3 2 } \\\hline \mathbf { x } _ { 1 } & 11.87375 & 5.32047 & \mathbf { 2 . 2 3 1 7 1 1 } & \mathbf { 0 . 0 4 2 4 9 3 } \\\hline \mathbf { x } _ { 2 } & 1.908183 & \mathbf { 0 . 6 6 2 7 4 2 } & \mathbf { 2 . 8 7 9 2 2 6 } & \mathbf { 0 . 0 1 2 1 3 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 203693.3 & 101846.7 & 6.745406 & 0.010884 \\\hline \text { Residual } & 12 & 181184.1 & 15098.67 & & \\\hline \text { Total } & 14 & 384877.4 & & & \\\hline\end{array}$$ 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 with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ The observed F value is __________.

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

Question 59

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 60

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & & 700 & & & \\\hline \text { Error } & & & & & \\\hline \text { Total } & & 1000 & & & \\\hline\end{array}$$ The number of degrees of freedom for error is __________.

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

Question 61

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & - 139.609 & 2548.989 & - 0.05477 & 0.957154 \\\hline \boldsymbol { x } _ { 1 } & 24.24619 & 22.25267 & 1.089586 & \mathbf { 0 . 2 9 5 6 8 2 } \\\hline \mathbf { x } _ { 2 } & 32.10171 & 17.44559 & 1.840105 & 0.08869 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 302689 & 151344.5 & 1.705942 & 0.219838 \\\hline \text { Residual } & 13 & 1153309 & 88716.07 & & \\\hline \text { Total } & 15 & 1455998 & & & \\\hline\end{array}$$ The regression equation for this analysis is ____________.

A) = 302689 + 1153309 x₁ + 1455998 x₂
B)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = -139.609 + 24.24619 x₁ + 32.10171 x₂
C)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = 2548.989 + 22.25267 x₁ + 17.44559 x₂
D)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = -0.05477 + 1.089586 x₁ + 1.840105 x₂
E)11efcd22_071b_cfd6_b057_0f6ae9b62e31_TB7041_00 = 0.05477 + 1.089586 x₁ + 1.840105 x₂

Question 62

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & - 139.609 & 2548.989 & - 0.05477 & 0.957154 \\\hline \boldsymbol { x } _ { 1 } & 24.24619 & 22.25267 & 1.089586 & \mathbf { 0 . 2 9 5 6 8 2 } \\\hline \mathbf { x } _ { 2 } & 32.10171 & 17.44559 & 1.840105 & 0.08869 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 302689 & 151344.5 & 1.705942 & 0.219838 \\\hline \text { Residual } & 13 & 1153309 & 88716.07 & & \\\hline \text { Total } & 15 & 1455998 & & & \\\hline\end{array}$$ The sample size for this analysis is ____________.

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

Question 63

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The MSE value is closest to__________.

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

Question 64

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The observed F value is __________.

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

Question 65

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & - 139.609 & 2548.989 & - 0.05477 & 0.957154 \\\hline \boldsymbol { x } _ { 1 } & 24.24619 & 22.25267 & 1.089586 & \mathbf { 0 . 2 9 5 6 8 2 } \\\hline \mathbf { x } _ { 2 } & 32.10171 & 17.44559 & 1.840105 & 0.08869 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 302689 & 151344.5 & 1.705942 & 0.219838 \\\hline \text { Residual } & 13 & 1153309 & 88716.07 & & \\\hline \text { Total } & 15 & 1455998 & & & \\\hline\end{array}$$ 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 66

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The R² value is __________.

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

Question 67

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 624.5369 & 78.49712 & 7.956176 & 6.88 E - 06 \\\hline \boldsymbol { x } _ { 1 } & 8.569122 & 1.652255 & 5.186319 & \mathbf { 0 . 0 0 0 3 0 1 } \\\hline \mathbf { x } _ { 2 } & 4.736515 & 0.699194 & 6.774248 & \mathbf { 3 . 0 6 E - 0 5 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 1660914 & \mathbf { 8 3 0 4 5 7 . 1 } & 58.31956 & 1.4 \mathrm { E } - 06 \\\hline \text { Residual } & 11 & 156637.5 & 14239.77 & & \\\hline \text { Total } & 13 & 1817552 & & & \\\hline\end{array}$$ 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

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The sample size for the analysis is __________.

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

Question 69

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & - 139.609 & 2548.989 & - 0.05477 & 0.957154 \\\hline \boldsymbol { x } _ { 1 } & 24.24619 & 22.25267 & 1.089586 & \mathbf { 0 . 2 9 5 6 8 2 } \\\hline \mathbf { x } _ { 2 } & 32.10171 & 17.44559 & 1.840105 & 0.08869 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 302689 & 151344.5 & 1.705942 & 0.219838 \\\hline \text { Residual } & 13 & 1153309 & 88716.07 & & \\\hline \text { Total } & 15 & 1455998 & & & \\\hline\end{array}$$ 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

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ 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 71

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 624.5369 & 78.49712 & 7.956176 & 6.88 E - 06 \\\hline \boldsymbol { x } _ { 1 } & 8.569122 & 1.652255 & 5.186319 & \mathbf { 0 . 0 0 0 3 0 1 } \\\hline \mathbf { x } _ { 2 } & 4.736515 & 0.699194 & 6.774248 & \mathbf { 3 . 0 6 E - 0 5 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 1660914 & \mathbf { 8 3 0 4 5 7 . 1 } & 58.31956 & 1.4 \mathrm { E } - 06 \\\hline \text { Residual } & 11 & 156637.5 & 14239.77 & & \\\hline \text { Total } & 13 & 1817552 & & & \\\hline\end{array}$$ 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. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The MSR value is __________.

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

Question 73

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The adjusted R² value is __________.

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

Question 74

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The number of independent variables in the analysis is __________.

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

Question 75

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & - 139.609 & 2548.989 & - 0.05477 & 0.957154 \\\hline \boldsymbol { x } _ { 1 } & 24.24619 & 22.25267 & 1.089586 & \mathbf { 0 . 2 9 5 6 8 2 } \\\hline \mathbf { x } _ { 2 } & 32.10171 & 17.44559 & 1.840105 & 0.08869 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 302689 & 151344.5 & 1.705942 & 0.219838 \\\hline \text { Residual } & 13 & 1153309 & 88716.07 & & \\\hline \text { Total } & 15 & 1455998 & & & \\\hline\end{array}$$ 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 76

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & - 139.609 & 2548.989 & - 0.05477 & 0.957154 \\\hline \boldsymbol { x } _ { 1 } & 24.24619 & 22.25267 & 1.089586 & \mathbf { 0 . 2 9 5 6 8 2 } \\\hline \mathbf { x } _ { 2 } & 32.10171 & 17.44559 & 1.840105 & 0.08869 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 302689 & 151344.5 & 1.705942 & 0.219838 \\\hline \text { Residual } & 13 & 1153309 & 88716.07 & & \\\hline \text { Total } & 15 & 1455998 & & & \\\hline\end{array}$$ The coefficient of multiple determination is ____________.

A)0.2079
B)0.0860
C)0.5440
D)0.7921
E)0.5000

Question 77

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 624.5369 & 78.49712 & 7.956176 & 6.88 E - 06 \\\hline \boldsymbol { x } _ { 1 } & 8.569122 & 1.652255 & 5.186319 & \mathbf { 0 . 0 0 0 3 0 1 } \\\hline \mathbf { x } _ { 2 } & 4.736515 & 0.699194 & 6.774248 & \mathbf { 3 . 0 6 E - 0 5 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 1660914 & \mathbf { 8 3 0 4 5 7 . 1 } & 58.31956 & 1.4 \mathrm { E } - 06 \\\hline \text { Residual } & 11 & 156637.5 & 14239.77 & & \\\hline \text { Total } & 13 & 1817552 & & & \\\hline\end{array}$$ 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. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 624.5369 & 78.49712 & 7.956176 & 6.88 E - 06 \\\hline \boldsymbol { x } _ { 1 } & 8.569122 & 1.652255 & 5.186319 & \mathbf { 0 . 0 0 0 3 0 1 } \\\hline \mathbf { x } _ { 2 } & 4.736515 & 0.699194 & 6.774248 & \mathbf { 3 . 0 6 E - 0 5 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 1660914 & \mathbf { 8 3 0 4 5 7 . 1 } & 58.31956 & 1.4 \mathrm { E } - 06 \\\hline \text { Residual } & 11 & 156637.5 & 14239.77 & & \\\hline \text { Total } & 13 & 1817552 & & & \\\hline\end{array}$$ 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 79

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline \text { Predictor } & \text { Coefficients } & \text { Stardard Error } & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & - 139.609 & 2548.989 & - 0.05477 & 0.957154 \\\hline \boldsymbol { x } _ { 1 } & 24.24619 & 22.25267 & 1.089586 & \mathbf { 0 . 2 9 5 6 8 2 } \\\hline \mathbf { x } _ { 2 } & 32.10171 & 17.44559 & 1.840105 & 0.08869 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 302689 & 151344.5 & 1.705942 & 0.219838 \\\hline \text { Residual } & 13 & 1153309 & 88716.07 & & \\\hline \text { Total } & 15 & 1455998 & & & \\\hline\end{array}$$ 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 80

The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \\\hline \text { Repression } & 3 & 1500 & & & \\\hline \text { Error } & 26 & & & & \\\hline \text { Total } & & 2300 & & & \\\hline\end{array}$$ The SSE value is __________.

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