Deck 14: Building Multiple Regression Models

Question 1

Stepwise regression is one of the ways to prevent the problem of multicollinearity.

Answer 1

True

Question 2

A linear regression model cannot be used to explore the possibility that a quadratic relationship may exist between two variables.

Answer 2

False

Question 3

The regression model y = $\beta$ ₀ + $\beta$ ₁ x₁ + $\beta$ ₂ x₂ + $\beta$ ₃ x₁x₂ + $\varepsilon$ is a first order model.

Answer 3

False

Question 4

If a data set contains k independent variables, the "all possible regression" search procedure will determine 2^k different models.

Question 5

Recoding data cannot improve the fit of a regression model.

Question 6

If each pair of independent variables is weakly correlated, there is no problem of multicollinearity.

Question 7

If two or more independent variables are highly correlated, the regression analysis is unlikely to suffer from the problem of multicollinearity.

Question 8

Regression models in which the highest power of any predictor variable is 1 and in which there are no cross product terms are referred to as first-order models.

Question 9

If the effect of an independent variable (e.g., square footage)on a dependent variable (e.g., price)is affected by different ranges of values for a second independent variable (e.g., age ), the two independent variables are said to interact.

Question 10

A linear regression model can be used to explore the possibility that a quadratic relationship may exist between two variables by suitably transforming the independent variable.

Question 11

A qualitative variable which represents categories such as geographical territories or job classifications may be included in a regression model by using indicator or dummy variables.

Question 12

A logarithmic transformation may be applied to both positive and negative numbers.

Question 13

If a qualitative variable has c categories, then only (c - 1)dummy variables must be included in the regression model.

Question 14

If a square-transformation is applied to a series of positive numbers, all greater than 1, the numerical values of the numbers in the transformed series will be smaller than the corresponding numbers in the original series.

Question 15

The regression model y = $\beta$ ₀ + $\beta$ ₁ x₁ + $\beta$ ₂ x²₁ + $\varepsilon$ is called a quadratic model.

Question 16

Qualitative data can be incorporated into linear regression models using indicator variables.

Question 17

If a data set contains k independent variables, the "all possible regression" search procedure will determine 2^k - 1 different models.

Question 18

If a qualitative variable has c categories, then c dummy variables must be included in the regression model, one for each category.

Question 19

The interaction between two independent variables can be examined by including a new variable, which is the sum of the two independent variables, in the regression model.

Question 20

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

Question 21

We may use logistic regression when the dependent variable is a dummy variable, coded 0 or 1.

Question 22

Multiple linear regression models can handle certain nonlinear relationships by ________.

A)biasing the sample
B)recoding or transforming variables
C)adjusting the resultant ANOVA table
D)adjusting the observed t and F values
E)performing nonlinear regression

Question 23

The following scatter plot indicates that _________.

A)a log x transform may be useful
B)a log y transform may be useful
C)a x² transform may be useful
D)no transform is needed
E)a 1/y transform may be useful

Question 24

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline & & & & \\\hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\\hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\\hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\\hline \text { Repression } & 2 & 58567032 & 29283516 & 57.34861 \\\hline \text { Residual } & 25 & 12765573 & 5106229 & \\\hline \text { Total } & 27 & 71332605 & & \\\hline\end{array}$$ The sample size for this analysis is ____________.

A)28
B)25
C)30
D)27
E)2

Question 25

If the variance inflation factor is bigger than 10, the regression analysis might suffer from the problem of multicollinearity.

Question 26

To test the overall effectiveness of a logistic regression, a chi-squared statistic is used.

Question 27

When structuring a logistic regression model, only one independent or predictor variable can be used.

Question 28

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline & & & & \\\hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\\hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\\hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\\hline \text { Repression } & 2 & 58567032 & 29283516 & 57.34861 \\\hline \text { Residual } & 25 & 12765573 & 5106229 & \\\hline \text { Total } & 27 & 71332605 & & \\\hline\end{array}$$ Using $\alpha$ = 0.10 to test the null hypothesis H₀: $\beta$ ₂ = 0, the critical t value is ____.

A)± 1.316
B)± 1.314
C)± 1.703
D)± 1.780
E)± 1.708

Question 29

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline & & & & \\\hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\\hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\\hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\\hline \text { Repression } & 2 & 58567032 & 29283516 & 57.34861 \\\hline \text { Residual } & 25 & 12765573 & 5106229 & \\\hline \text { Total } & 27 & 71332605 & & \\\hline\end{array}$$ Using $\alpha$ = 0.10 to test the null hypothesis H₀: $\beta$ ₁ = 0, the critical t value is ____.

A)± 1.316
B)± 1.314
C)± 1.703
D)± 1.780
E)± 1.708

Question 30

The following scatter plot indicates that _________.

A)a log x transform may be useful
B)a log y transform may be useful
C)an x² transform may be useful
D)no transform is needed
E)a (- x)transform may be useful

Question 31

The following scatter plot indicates that _________.

A)a log x transform may be useful
B)a y² transform may be useful
C)a x² transform may be useful
D)no transform is needed
E)a 1/x transform may be useful

Question 32

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \mathbf { 5 s } & \mathrm { MS } & F & p \text {-value } \\\hline \text { Repression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & \mathbf { 3 3 8 5 2 3 . 3 } & & \\\hline \text { Total } & \mathbf { 2 9 } & 41195281 & & & \\\hline\end{array}$$ The sample size for this analysis is ____________.

A)27
B)29
C)30
D)25
E)28

Question 33

The logistic regression model constrains the estimated probabilities to lie between 0 and 100.

Question 34

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline & & & & \\\hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\\hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\\hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\\hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \\\hline \text { Residual } & 25 & 12765573 & 510622.9 & \\\hline \text { Total } & 27 & 71332605 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0, the critical F value is ____.

A)4.24
B)3.39
C)5.57
D)3.35
E)2.35

Question 35

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\\hline \boldsymbol { x } _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\\hline \boldsymbol { x } _ { 1 } { } ^ { 2 } & 7.721648 & \mathbf { 3 . 0 0 7 9 4 3 } & 2.567086 & 0.016115\\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\\hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \\\hline \text { Residual } & 25 & 12765573 & 510622.9 & \\\hline \text { Total } & 27 & 71332605 & & \\\hline\end{array}$$ For x₁= 20, the predicted value of y is ____________.

A)5,204.18.
B)2,031.38
C)2,538.86
D)6262.19
E)6,535.86

Question 36

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline & & & & \\\hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\\hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\\hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\\hline \text { Repression } & 2 & 58567032 & 29283516 & 57.34861 \\\hline \text { Residual } & 25 & 12765573 & 5106229 & \\\hline \text { Total } & 27 & 71332605 & & \\\hline\end{array}$$ The regression equation for this analysis is ____________.

A) = 762.1533 + 96.8433 x₁ + 3.007943 x₁²
B)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 1411.876 + 762.1533 x₁ + 1.852483 x₁²
C)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 1411.876 + 35.18215 x₁ + 7.721648 x₁²
D)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 762.1533 + 1.852483 x₁ + 0.074919 x₁²
E)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 762.1533 - 1.852483 x₁ + 0.074919 x₁²

Question 37

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\\hline \boldsymbol { x } _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\\hline \boldsymbol { x } _ { 1 } { } ^ { 2 } & 7.721648 & \mathbf { 3 . 0 0 7 9 4 3 } & 2.567086 & 0.016115\\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\\hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \\\hline \text { Residual } & 25 & 12765573 & 510622.9 & \\\hline \text { Total } & 27 & 71332605 & & \\\hline\end{array}$$ For x₁= 10, the predicted value of y is ____________.

A)8.88.
B)2,031.38
C)2,53.86
D)262.19
E)2,535.86

Question 38

The following scatter plot indicates that _________.

A)a x² transform may be useful
B)a log y transform may be useful
C)a x⁴ transform may be useful
D)no transform is needed
E)a x³ transform may be useful

Question 39

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \mathbf { 5 s } & \mathrm { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\\hline \text { Total } & \mathbf { 2 9 } & 41195281 & & & \\\hline\end{array}$$ Using $\alpha$ = 0.01 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0, the critical F value is ____.

A)5.42
B)5.49
C)7.60
D)3.35
E)2.49

Question 40

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { Df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\\hline \text { Total } & 29 & 41195281 & & & \\\hline\end{array}$$ The regression equation for this analysis is ____________.

A)= 707.9144 + 2.903307 x₁ + 11.91297 x₁²
B)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00= 707.9144 + 435.1183 x₁ + 1.626947 x₁²
C)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 435.1183 + 81.62802 x₁ + 3.806211 x₁²
D)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 1.626947 + 0.035568 x₁ + 3.129878 x₁²
E)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 1.626947 + 0.035568 x₁ - 3.129878 x₁²

Question 41

After a transformation of the y-variable values into log y, and performing a regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Iritercept } & 2.005349 & 0.097351 & 20.59923 & 4.81 \mathrm { E } - 18 \\\hline \boldsymbol { x } & 0.027126 & 0.009518 & \mathbf { 2 . 8 4 9 8 4 3 } & \mathbf { 0 . 0 0 8 2 7 5 } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Regression } & 1 & 0.196642 & 0.196642 & 8.121607 & 0.008447 \\\hline \text { Residual } & 26 & 0.629517 & 0.024212 & & \\\hline \text { Total } & 27 & 0.826159 & & & \\\hline\end{array}$$ For x₁= 10, the predicted value of y is ____________.

A)155.79
B)1.25
C)2.42
D)189.06
E)18.90

Question 42

In multiple regression analysis, qualitative variables are sometimes referred to as ___.

A)dummy variables
B)quantitative variables
C)dependent variables
D)performance variables
E)cardinal variables

Question 43

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\\hline \text { Total } & 29 & 41195281 & & & \\\hline\end{array}$$ Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = 0, the critical t value is ____.

A)± 1.311
B)± 1.699
C)± 1.703
D)± 2.502
E)± 2.052

Question 44

Yvonne Yang, VP of Finance at Discrete Components, Inc.(DCI), wants a regression model which predicts the average collection period on credit sales.Her data set includes two qualitative variables: sales discount rates (0%, 2%, 4%, and 6%), and total assets of credit customers (small, medium, and large).The number of dummy variables needed for "total assets of credit customer" in Yvonne's regression model is ________.

A)1
B)2
C)3
D)4
E)7

Question 45

Hope Hernandez is the new regional Vice President for a large gasoline station chain.She wants a regression model to predict sales in the convenience stores.Her data set includes two qualitative variables: the gasoline station location (inner city, freeway, and suburbs), and curb appeal of the convenience store (low, medium, and high).The number of dummy variables needed for "curb appeal" in Hope's regression model is ______.

A)1
B)2
C)3
D)4
E)5

Question 46

Abby Kratz, a market specialist at the market research firm of Saez, Sikes, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is weekly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table. $$\begin{array} { | l | r | r | r | r | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Irtercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \\\hline x _ { 1 } \text { (incorne) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \\\hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \\\hline\end{array}$$ For two households, one suburban and one rural, Abby's model predicts ________.

A)equal weekly expenditures for groceries
B)the suburban household's weekly expenditures for groceries will be $49 more
C)the rural household's weekly expenditures for groceries will be $49 more
D)the suburban household's weekly expenditures for groceries will be $8 more
E)the rural household's weekly expenditures for groceries will be $49 less

Question 47

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { df } & \text { Ss } & \text { Ms } & F & p \text {-value } \\\hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\\hline \text { Total } & 29 & 41195281 & & & \\\hline\end{array}$$ For a child in grade 10 (x₁= 10)the predicted value of y is ____________.

A)707.91
B)1,117.38
C)856.08
D)2,189.54
E)1,928.24

Question 48

Alan Bissell, a market analyst for City Sound Online Mart, is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's), and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3, 1 = other).Regression analysis of the data yielded the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Iritercept } & 1.7 & 0.384212 & 4.424638 & 0.00166 \\\hline x _ { 1 } \text { (websitevisitors) } & 0.04 & 0.014029 & 2.851146 & 0.019054 \\\hline x _ { 2 } \text { (download format) } & - 1.5666667 & 0.20518 & - 7.63558 & 3.21 E - 05 \\\hline\end{array}$$ For the same number of website visitors, what is difference between the predicted sales for MP3 versus 'other' heavy metal song downloads

A)$1,566,666 higher sales for 'other' formats
B)the same sales for both formats
C)$1,566,666 lower sales for the 'other' format
D)$1,700,000 higher sales for the MP3 format
E)$ 1,700,000 lower sales for the 'other' format

Question 49

Yvonne Yang, VP of Finance at Discrete Components, Inc.(DCI), wants a regression model which predicts the average collection period on credit sales.Her data set includes two qualitative variables: sales discount rates (0%, 2%, 4%, and 6%), and total assets of credit customers (small, medium, and large).The number of dummy variables needed for "sales discount rate" in Yvonne's regression model is ________.

A)1
B)2
C)3
D)4
E)7

Question 50

If a qualitative variable has 4 categories, how many dummy variables must be created and used in the regression analysis?

A)3
B)4
C)5
D)6
E)7

Question 51

Hope Hernandez is the new regional Vice President for a large gasoline station chain.She wants a regression model to predict sales in the convenience stores.Her data set includes two qualitative variables: the gasoline station location (inner city, freeway, and suburbs), and curb appeal of the convenience store (low, medium, and high).The number of dummy variables needed for Hope's regression model is ______.

A)2
B)4
C)6
D)8
E)9

Question 52

Abby Kratz, a market specialist at the market research firm of Saez, Sikes, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is weekly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \\\hline x _ { 1 } \text { (income) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \\\hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \\\hline\end{array}$$ For a rural household with $90,000 annual income, Abby's model predicts weekly grocery expenditure of ________________.

A)$156.19
B)$224.98
C)$444.62
D)$141.36
E)$175.86

Question 53

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { df } & \text { Ss } & \text { Ms } & F & p \text {-value } \\\hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\\hline \text { Total } & 29 & 41195281 & & & \\\hline\end{array}$$ For a child in grade 5 (x₁= 5), the predicted value of y is ____________.

A)707.91
B)1,020.26
C)781.99
D)840.06
E)1078.32

Question 54

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \mathbf { 5 s } & \mathrm { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\\hline \text { Total } & \mathbf { 2 9 } & 41195281 & & & \\\hline\end{array}$$ These results indicate that ____________.

A)none of the predictor variables is 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)x₁² is the only predictor variable significant at the 5% level
E)each predictor variable is insignificant at the 5% level

Question 55

Alan Bissell, a market analyst for City Sound Online Mart, is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's), and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3, 1 = other).Regression analysis of the data yielded the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Iritercept } & 1.7 & 0.384212 & 4.424638 & 0.00166 \\\hline x _ { 1 } \text { (websitevisitors) } & 0.04 & 0.014029 & 2.851146 & 0.019054 \\\hline x _ { 2 } \text { (download format) } & - 1.5666667 & 0.20518 & - 7.63558 & 3.21 E - 05 \\\hline\end{array}$$ For 'other' download formats with 10,000 website visitors, Alan's model predicts annual sales of heavy metal song downloads of ________________.

A)$2,100,000
B)$524,507
C)$533,333
D)$729,683
E)$210,000

Question 56

Alan Bissell, a market analyst for City Sound Online Mart, is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's), and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3, 1 = other).Regression analysis of the data yielded the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Iritercept } & 1.7 & 0.384212 & 4.424638 & 0.00166 \\\hline x _ { 1 } \text { (websitevisitors) } & 0.04 & 0.014029 & 2.851146 & 0.019054 \\\hline x _ { 2 } \text { (download format) } & - 1.5666667 & 0.20518 & - 7.63558 & 3.21 E - 05 \\\hline\end{array}$$ For MP3 sales with 10,000 website visitors, Alan's model predicts annual sales of heavy metal song downloads of ________________.

A)$2,100,000
B)$524,507
C)$533,333
D)$729,683
E)$21,000,000

Question 57

Abby Kratz, a market specialist at the market research firm of Saez, Sikes, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is weekly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \\\hline x _ { 1 } \text { (income) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \\\hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \\\hline\end{array}$$ For a suburban household with $90,000 annual income, Abby's model predicts weekly grocery expenditure of ________________.

A)$156.19
B)$224.98
C)$444.62
D)$141.36
E)$175.86

Question 58

Alan Bissell, a market analyst for City Sound Online Mart, is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's), and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3, 1 = other).Regression analysis of the data yielded the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \begin{array} { c } \text { Stardard } \\\text { Error }\end{array} & \boldsymbol { t } \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 1.7 & 0.384212 & 4.424638 & 0.00166 \\\hline \boldsymbol { x } _ { 1 } \text { (website visitors) } & 0.04 & 0.014029 & \mathbf { 2 . 8 5 1 1 4 6 } & 0.019054 \\\hline \mathbf { x } _ { 2 } \text { (download fommat) } & - 1.5666667 & 0.20518 & - 7.63558 & \mathbf { 3 . 2 1 E - 0 5 } \\\hline\end{array}$$ Alan's model is ________________.

A) = 1.7 + 0.384212 x₁ + 4.424638 x₂ + 0.00166 x₃
B)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 1.7 + 0.04 x₁ + 1.5666667 x₂
C)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 0.384212 + 0.014029 x₁ + 0.20518 x₂
D)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 4.424638 + 2.851146 x₁ - 7.63558 x₂
E)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 1.7 + 0.04 x₁ - 1.5666667 x₂

Question 59

Abby Kratz, a market specialist at the market research firm of Saez, Sikes, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is weekly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table.
$\begin{array}{c}\begin{array}{|l|}\hline \text { } \\\hline \text {Intercept}\\\hline \text {\( X_{1} \) (income)}\\\hline \text {\( \mathrm{X}_{2} \)}\\ \text {(neighborhood)}\\\hline \end{array}\begin{array}{l}\hline \text { Coefficients }\\\hline 19.68247 \\\hline 1.735272 \\\hline 49.12456\\\\\hline \end{array}\begin{array}{|l|}\hline \text {Standard Error}\\\hline10.01176 \\\hline 0.174564 \\\hline 7.655776\\\\\hline \end{array}\begin{array}{l|}\hline t \text { Statistic } \\\hline 1.965934 \\\hline 9.940612 \\\hline 6.416667 \\\\\hline \end{array}\begin{array}{l|}\hline p \text {-value }\\\hline0.077667\\\hline1.68 \mathrm{E}-06\\\hline7.67 \mathrm{E}-05\\\\\hline\end{array}\end{array}$
Abby's model is ________________.

A)$\mathrm{X}_{2}$ }\\ \text {(neighborhood)}\\ \hline \end{array} \begin{array}{l} \hline \text { Coefficients }\\ \hline 19.68247 \\ \hline 1.735272 \\ \hline 49.12456\\ \\ \hline \end{array} \begin{array}{|l|} \hline \text {Standard Error}\\ \hline10.01176 \\ \hline 0.174564 \\ \hline 7.655776\\ \\ \hline \end{array} \begin{array}{l|} \hline t \text { Statistic } \\ \hline 1.965934 \\ \hline 9.940612 \\ \hline 6.416667 \\ \\ \hline \end{array} \begin{array}{l|} \hline p \text {-value }\\ \hline0.077667\\ \hline1.68 \mathrm{E}-06\\ \hline7.67 \mathrm{E}-05\\ \\ \hline \end{array} \end{array} Abby's model is ________________. A) = 19.68247 + 10.01176 x₁ + 1.965934 x₂ B) = 1.965934 + 9.940612 x₁ + 6.416667 x₂ C) = 10.01176 + 0.174564 x₁ + 7.655776 x₂ D) = 19.68247 - 1.735272 x₁ + 49.12456 x₂ E) = 19.68247 + 1.735272 x₁ + 49.12456 x₂ " class="answers-bank-image d-block" loading="lazy" > = 19.68247 + 10.01176 x₁ + 1.965934 x₂
B)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00= 1.965934 + 9.940612 x₁ + 6.416667 x₂
C)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00= 10.01176 + 0.174564 x₁ + 7.655776 x₂
D)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00= 19.68247 - 1.735272 x₁ + 49.12456 x₂
E)11efcd21_6411_aee5_b057_4518c9fddc20_TB7041_00 = 19.68247 + 1.735272 x₁ + 49.12456 x₂

Question 60

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between the academic grade level for the child and the total costs spent per child per academic year.They performed a multiple regression analysis using total cost as the dependent variable and academic year (x₁)as the independent variables.The multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\\hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\\hline \mathbf { x } _ { 1 } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { df } & \text { SS } & \text { MS } & F & p \text {-value } \\\hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\\hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\\hline \text { Total } & 29 & 41195281 & & & \\\hline\end{array}$$ Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₂ = 0, the critical t value is ____.

A)± 1.311
B)± 1.699
C)± 1.703
D)± 2.052
E)± 2.502

Question 61

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. $$\begin{array} { | c | r | c | r | c | c | r | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\\hline y & 1 & & & & & \\\hline x _ { 1 } & - 0.0857 & 1 & & & & \\\hline x _ { 2 } & - 0.20246 & 0.868358 & 1 & & & \\\hline x _ { 3 } & - 0.22631 & - 0.10604 & - 0.14853 & 1 & & \\\hline x _ { 4 } & - 0.28175 & - 0.0685 & 0.41468 & - 0.14151 & 1 & \\\hline x _ { 5 } & 0.271105 & 0.150796 & 0.129388 & - 0.15243 & 0.00821 & 1 \\\hline\end{array}$$

A)x₁ and x₂
B)x₁ and x₄
C)x₄ and x₅
D)x₄ and x₃
E)x₅ and y

Question 62

Inspection of the following table of t values for variables in a multiple regression analysis reveals that the first independent variable that will be entered into the regression model by the forward selection procedure will be ___________. $$\begin{array} { | c | r | c | r | c | c | r | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\\hline y & 1 & & & & & \\\hline x _ { 1 } & - 0.0857 & 1 & & & & \\\hline x _ { 2 } & - 0.20246 & 0.868358 & 1 & & & \\\hline x _ { 3 } & - 0.22631 & - 0.10604 & - 0.14853 & 1 & & \\\hline x _ { 4 } & - 0.28175 & - 0.0685 & 0.41468 & - 0.14151 & 1 & \\\hline x _ { 5 } & 0.271105 & 0.150796 & 0.129388 & - 0.15243 & 0.00821 & 1 \\\hline\end{array}$$

A)x₁
B)x₂
C)x₃
D)x₄
E)x₅

Question 63

An appropriate method to identify multicollinearity in a regression model is to ____.

A)examine a residual plot
B)examine the ANOVA table
C)examine a correlation matrix
D)examine the partial regression coefficients
E)examine the R² of the regression model

Question 64

Which of the following iterative search procedures for model-building in a multiple regression analysis adds variables to model as it proceeds, but does not reevaluate the contribution of previously entered variables?

A)Backward elimination
B)Stepwise regression
C)Forward selection
D)All possible regressions
E)Forward elimination

Question 65

Inspection of the following table of t values for variables in a multiple regression analysis reveals that the first independent variable that will be entered into the regression model by the forward selection procedure will be ___________. $$\begin{array} { | c | c | c | c | c | c | c | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\\hline y & 1 & & & & & \\\hline x _ { 1 } & 0.854168 & 1 & & & & \\\hline x _ { 2 } & - 0.11828 & - 0.00383 & 1 & & & \\\hline x _ { 3 } & - 0.12003 & - 0.08499 & - 0.14523 & 1 & & \\\hline x _ { 4 } & 0.525901 & 0.118169 & - 0.14876 & 0.050042 & 1 & \\\hline x _ { 5 } & - 0.18105 & - 0.07371 & 0.995886 & - 0.14151 & - 0.16934 & 1 \\\hline\end{array}$$

A)x₁
B)x₂
C)x₃
D)x₄
E)x₅

Question 66

Which of the following iterative search procedures for model-building in a multiple regression analysis starts with all independent variables in the model and then drops non-significant independent variables is a step-by-step manner?

A)Backward elimination
B)Stepwise regression
C)Forward selection
D)All possible regressions
E)Backward selection

Question 67

An acceptable method of managing multicollinearity in a regression model is the ___.

A)use the forward selection procedure
B)use the backward elimination procedure
C)use the forward elimination procedure
D)use the stepwise regression procedure
E)use all possible regressions

Question 68

An "all possible regressions" search of a data set containing 5 independent variables will produce ______ regressions.

A)31
B)10
C)25
D)32
E)24

Question 69

Inspection of the following table of t values for variables in a multiple regression analysis reveals that the first independent variable entered by the forward selection procedure will be ___________. $$\begin{array} { | c | c | c | c | c | c | c | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\\hline y & 1 & & & & & \\\hline x _ { 1 } & - 0.44008 & 1 & & & & \\\hline x _ { 2 } & 0.566053 & - 0.51728 & 1 & & & \\\hline x _ { 3 } & 0.064919 & - 0.22264 & - 0.00734 & 1 & & \\\hline x _ { 4 } & - 0.35711 & 0.028957 & - 0.49869 & 0.260586 & 1 & \\\hline x _ { 5 } & 0.426363 & - 0.20467 & 0.078916 & 0.207477 & 0.023839 & 1 \\\hline\end{array}$$

A)x₁
B)x₂
C)x₃
D)x₄
E)x₅

Question 70

An "all possible regressions" search of a data set containing "k" independent variables will produce __________ regressions.

A)2k -1
B)2^{k - 1}
C)k² - 1
D)2^k - 1
E)2k

Question 71

Carlos Cavazos, Director of Human Resources, is exploring employee absenteeism at the Plano Piano Plant.A multiple regression analysis was performed using the following variables.The results are presented below. $$\begin{array} { | l | l | } \hline \text { Variable } & \text { Description } \\\hline Y & \text { number of days absent last fiscal year } \\\hline x _ { 1 } & \text { comrnuting distarnce (in miles) } \\\hline x _ { 2 } & \text { employee's age (in years) } \\\hline x _ { 3 } & \text { single-parent household } ( 0 = \text { no, } 1 = \text { yes } ) \\\hline x _ { 4 } & \text { length of employment at PpP (in years) } \\\hline x _ { 5 } & \text { shift } ( 0 = \text { day } 1 = \text { night) } \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Statistic } & p \text {-value } \\\hline \text { Intercept } & 6.594146 & \mathbf { 3 . 2 7 3 0 0 5 } & \mathbf { 2 . 0 1 4 7 0 7 } & \mathbf { 0 . 0 4 7 6 7 1 } \\\hline \boldsymbol { x } _ { 1 } & - 0.18019 & 0.141949 & - 1.26939 & 0.208391 \\\hline \mathbf { x } _ { 2 } & 0.268156 & 0.260643 & 1.028828 & 0.307005 \\\hline \boldsymbol { x } _ { 3 } & - 2.31068 & 0.962056 & - 2.40182 & 0.018896 \\\hline \mathbf { x } _ { 4 } & - 0.50579 & 0.270872 & - 1.86725 & 0.065937 \\\hline \boldsymbol { x } _ { 5 } & \mathbf { 2 . 3 2 9 5 1 3 } & 0.940321 & 2.47736 & 0.015584 \\\hline\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \text { SS } & \text { ME } & F & p \text {-value } \\\hline \text { Repression } & 5 & 279.358 & 55.8716 & 4.423755 & \mathbf { 0 . 0 0 1 5 3 2 } \\\hline \text { Residual } & 67 & 846.2036 & 12.6299 & & \\\hline \text { Total } & 72 & 1125.562 & & & \\\hline\end{array}$$ $$\begin{array} { | c | c | c | } \hline R = 0.498191 & R ^ { 2 } = 0.248194 & \text { Adj } R ^ { 2 } = 0.192089 \\\hline \mathrm { s } _ { \mathrm { e } } = 3.553858 & n = 73 & \\\hline\end{array}$$ Which of the following conclusions can be drawn from the above results?

A)All the independent variables in the regression are significant at 5% level.
B)Commuting distance is a highly significant (<1%)variable in explaining absenteeism.
C)Age of the employees tends to have a very significant (<1%)effect on absenteeism.
D)This model explains a little over 49% of the variability in absenteeism data.
E)A single-parent household employee is expected to be absent fewer days, all other variables held constant, compared to one who is not a single-parent household.

Question 72

An "all possible regressions" search of a data set containing 8 independent variables will produce ______ regressions.

A)8
B)15
C)256
D)64
E)255

Question 73

Suppose a company is interested in understanding the effect of age and sex on the likelihood a customer will purchase a new product.The data analyst intends to run a logistic regression on her data.Which of the following variable(s)will the analyst need to code as 0 or 1 prior to performing the logistic regression analysis?

A)age and gender
B)age and purchase status
C)age
D)purchase status
E)sex and purchase status Gender is no longer considered dichotomous

Question 74

Inspection of the following table of t values for variables in a multiple regression analysis reveals that the first independent variable entered by the forward selection procedure will be ___________. $$\begin{array} { | l | r | r | r | r | r | r | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\\hline y & 1 & & & & & \\\hline x _ { 1 } & - 0.1661 & 1 & & & & \\\hline x _ { 2 } & 0.231849 & - 0.51728 & 1 & & & \\\hline x _ { 3 } & 0.423522 & - 0.22264 & - 0.00734 & 1 & & \\\hline x _ { 4 } & - 0.33227 & 0.028957 & - 0.49869 & 0.260586 & 1 & \\\hline x _ { 5 } & 0.199796 & - 0.20467 & 0.078916 & 0.207477 & 0.023839 & 1 \\\hline\end{array}$$

A)x₂
B)x₃
C)x₄
D)x₅
E)x₁

Question 75

An "all possible regressions" search of a data set containing 7 independent variables will produce ______ regressions.

A)13
B)127
C)48
D)64
E)97

Question 76

Large correlations between two or more independent variables in a multiple regression model could result in the problem of ________.

A)multicollinearity
B)autocorrelation
C)partial correlation
D)rank correlation
E)non-normality

Question 77

Which of the following iterative search procedures for model-building in a multiple regression analysis reevaluates the contribution of variables previously include in the model after entering a new independent variable?

A)Backward elimination
B)Stepwise regression
C)Forward selection
D)All possible regressions
E)Backward selection

Question 78

A useful technique in controlling multicollinearity involves the use of _________.

A)variance inflation factors
B)a backward elimination procedure
C)a forward elimination procedure
D)a forward selection procedure
E)all possible regressions

Question 79

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. $$\begin{array} { | c | c | c | c | c | c | c | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\\hline y & 1 & & & & & \\\hline x _ { 1 } & 0.854168 & 1 & & & & \\\hline x _ { 2 } & - 0.11828 & - 0.00383 & 1 & & & \\\hline x _ { 3 } & - 0.12003 & - 0.08499 & - 0.14523 & 1 & & \\\hline x _ { 4 } & 0.525901 & 0.118169 & - 0.14876 & 0.050042 & 1 & \\\hline x _ { 5 } & - 0.18105 & - 0.07371 & 0.995886 & - 0.14151 & - 0.16934 & 1 \\\hline\end{array}$$

A)x₁ and x₂
B)x₁ and x₅
C)x₃ and x₄
D)x₂ and x₅
E)x₃ and x₅

Question 80

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. $$\begin{array} { | c | r | c | c | c | c | c | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\\hline y & 1 & & & & & \\\hline x _ { 1 } & - 0.08301 & 1 & & & & \\\hline x _ { 2 } & 0.236745 & - 0.51728 & 1 & & & \\\hline x _ { 3 } & 0.155149 & - 0.22264 & - 0.00734 & 1 & & \\\hline x _ { 4 } & 0.022234 & - 0.58079 & 0.884216 & 0.131956 & 1 & \\\hline x _ { 5 } & 0.4808 & - 0.20467 & 0.078916 & 0.207477 & 0.103831 & 1 \\\hline\end{array}$$

A)x₁ and x₅
B)x₂ and x₃
C)x₄ and x₂
D)x₄ and x₃
E)x₄ and y