Question 1

In a multiple regression model, the values of the random error term   are assumed to:

Accepted Answer

A)  be independent 
B)  have a mean of 0, and a common variancefor any set of the predictor variables 
C)  be normally distributed 
D)  all of these are required assumptions 
E)  none of these 
A)  be independent 
B)  have a mean of 0, and a common variancefor any set of the predictor variables 
C)  be normally distributed 
D)  all of these are required assumptions 
E)  none of these

Question 2

Suppose that one equation has 3 explanatory variables and an F-ratio of 52. Another equation has 5 explanatory variables and an F-ratio of 40. The first equation will always be considered a better model.

Accepted Answer

A) True 
 B)False

Question 3

Which of the following is an advantage of using stepwise regression compared to just entering all the independent variables at one time?

Accepted Answer

A)  There are no advantages of using stepwise regression over entering all the variables at one time. 
B)  Stepwise regression allows us to observe the effects of multicollinearity more early than when all variables are entered at one time. 
C)  Stepwise regression will generally produce a model with larger value for the coefficient of determination. 
D)  All of these. 
E)  None of these. 
A)  There are no advantages of using stepwise regression over entering all the variables at one time. 
B)  Stepwise regression allows us to observe the effects of multicollinearity more early than when all variables are entered at one time. 
C)  Stepwise regression will generally produce a model with larger value for the coefficient of determination. 
D)  All of these. 
E)  None of these.

Question 4

A regression model of the form   is called a third-order polynomial model.

Accepted Answer

A) True 
 B)False

Question 5

To check out whether the regressions assumption involving normality of the error terms (residuals), it is appropriate to construct a normal probability plot. If this plot forms a straight line from the lower left-hand corner to the upper right-hand corner, the error terms may be assumed to be normally distributed.

Accepted Answer

A) True 
 B)False

Question 6

Which of the following statements is true?

Accepted Answer

A)  It is appropriate to compute a correlation coefficient for the relationship between a dummy variable and a dependent variable. 
B)  If a qualitative variable has m categories, you should use m - 1 dummy variables to incorporate the qualitative variable into a regression model. 
C)  Dummy variables are used to incorporate qualitative variables into a regression model. 
D)  All of these. 
E)  None of these. 
A)  It is appropriate to compute a correlation coefficient for the relationship between a dummy variable and a dependent variable. 
B)  If a qualitative variable has m categories, you should use m - 1 dummy variables to incorporate the qualitative variable into a regression model. 
C)  Dummy variables are used to incorporate qualitative variables into a regression model. 
D)  All of these. 
E)  None of these.

Question 7

In multiple regression, a large value of the test statistic F indicates that most of the variation in y is unexplained by the regression equation and that the model is useless. A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

Accepted Answer

A) True 
 B)False

Question 8

Quantitative predictor variables are entered into a regression model through indicator variables.

Accepted Answer

A) True 
 B)False

Question 9

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Accepted Answer

A) True 
 B)False

Question 10

Which of the following correctly describes a multiple-regression ANOVA test?

Accepted Answer

A)  It is a test of the significance of individual coefficients, rather than of the overall significance of the regression model. 
B)  It amounts to testing the hypothesis that none of the true regression coefficients is zero and that, therefore, all of the independent predictors help explain the variation of the dependent variable. 
C)  It is a test of the overall significance of a regression, rather than a test of the significance of individual coefficients. 
D)  It is a test of the significance of individual coefficients, rather than of the overall significance of the regression model and it is a test of the overall significance of a regression, rather than a test of the significance of individual coefficients. 
E)  None of these. 
A)  It is a test of the significance of individual coefficients, rather than of the overall significance of the regression model. 
B)  It amounts to testing the hypothesis that none of the true regression coefficients is zero and that, therefore, all of the independent predictors help explain the variation of the dependent variable. 
C)  It is a test of the overall significance of a regression, rather than a test of the significance of individual coefficients. 
D)  It is a test of the significance of individual coefficients, rather than of the overall significance of the regression model and it is a test of the overall significance of a regression, rather than a test of the significance of individual coefficients. 
E)  None of these.

Question 11

In a regression model involving 40 observations, the following estimated regression model was obtained:   . For this model, the following statistics are given: SSR = 501 and SSE = 99. Then, the value of MSR is:

Accepted Answer

A)  12.525 
B)  33 
C)  167 
D)  15 
E)  18.52 
A)  12.525 
B)  33 
C)  167 
D)  15 
E)  18.52

Question 12

Multicollinearity is present when there is a high degree of correlation between the dependent variable and all the independent variables included in the model.

Accepted Answer

A) True 
 B)False

Question 13

A coefficient of multiple correlation is denoted by   and equals the proportion of the total variation in the values of the dependent variable, y that is explained by the estimated multiple regression of y on   ,   , and possibly additional independent variable (   , and so on).

Accepted Answer

A) True 
 B)False

Question 14

In a multiple regression model, the adjusted   value measures the explained variation in the dependent variable after taking into account the relationship between the sample size and the number of independent variables in the model.

Accepted Answer

A) True 
 B)False

Question 15

Suppose a regression analysis based on the model   with 15 observations produced SSE = 3.55,   = 13.131, and   = 125.1. Hence, the proportion of the total variability in y that is accounted for by   and   is:

Accepted Answer

A)  0.2704 
B)  0.7296 
C)  0.9688 
D)  0.0312 
E)  0.1032 
A)  0.2704 
B)  0.7296 
C)  0.9688 
D)  0.0312 
E)  0.1032

Question 16

In order to test the validity of a multiple regression model involving 4 predictor variables and 25 observations, the numerator and denominator degrees of freedom (   , respectively) for the critical value of F are:

Accepted Answer

A)  4 and 20 
B)  4 and 25 
C)  20 and 4 
D)  25 and 4 
E)  3 and 21 
A)  4 and 20 
B)  4 and 25 
C)  20 and 4 
D)  25 and 4 
E)  3 and 21

Question 17

In multiple regression analysis, which of the following is a clue that multicollinearity is present?

Accepted Answer

A)  The value ofis large, indicting a good fit, but the individual t - tests are nonsignificant. 
B)  The signs of the regression coefficients are contrary to what we would intuitively expect the contributions of those variables would be. 
C)  A matrix of correlations, generated by computer, shows which predictor variables are highly correlated with each other and with the response variable y. 
D)  All of these. 
E)  None of these. 
A)  The value ofis large, indicting a good fit, but the individual t - tests are nonsignificant. 
B)  The signs of the regression coefficients are contrary to what we would intuitively expect the contributions of those variables would be. 
C)  A matrix of correlations, generated by computer, shows which predictor variables are highly correlated with each other and with the response variable y. 
D)  All of these. 
E)  None of these.

Question 18

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Accepted Answer

A) True 
 B)False

Question 19

Having a large number of predictors in a regression model guarantees that the model fit is good.

Accepted Answer

A) True 
 B)False

Question 20

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Accepted Answer

A) True 
 B)False

In a multiple regression model, the values of the random error term are assumed to:

Suppose that one equation has 3 explanatory variables and an F-ratio of 52. Another equation has 5 explanatory variables and an F-ratio of 40. The first equation will always be considered a better model.

Which of the following is an advantage of using stepwise regression compared to just entering all the independent variables at one time?

A regression model of the form is called a third-order polynomial model.

Which of the following statements is true?

Quantitative predictor variables are entered into a regression model through indicator variables.

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Which of the following correctly describes a multiple-regression ANOVA test?

In a regression model involving 40 observations, the following estimated regression model was obtained: . For this model, the following statistics are given: SSR = 501 and SSE = 99. Then, the value of MSR is:

Multicollinearity is present when there is a high degree of correlation between the dependent variable and all the independent variables included in the model.

A coefficient of multiple correlation is denoted by and equals the proportion of the total variation in the values of the dependent variable, y that is explained by the estimated multiple regression of y on , , and possibly additional independent variable ( , and so on).

In a multiple regression model, the adjusted value measures the explained variation in the dependent variable after taking into account the relationship between the sample size and the number of independent variables in the model.

Suppose a regression analysis based on the model with 15 observations produced SSE = 3.55, = 13.131, and = 125.1. Hence, the proportion of the total variability in y that is accounted for by and is:

In order to test the validity of a multiple regression model involving 4 predictor variables and 25 observations, the numerator and denominator degrees of freedom ( , respectively) for the critical value of F are:

In multiple regression analysis, which of the following is a clue that multicollinearity is present?

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Having a large number of predictors in a regression model guarantees that the model fit is good.

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Linear Regression and Correlation

Analysis of Categorical Data

Nonparametric Statistics

Filters

Exam 13: Multiple Regression Analysis

In a multiple regression model, the values of the random error term are assumed to:

Suppose that one equation has 3 explanatory variables and an F-ratio of 52. Another equation has 5 explanatory variables and an F-ratio of 40. The first equation will always be considered a better model.

Which of the following is an advantage of using stepwise regression compared to just entering all the independent variables at one time?

A regression model of the form is called a third-order polynomial model.

Which of the following statements is true?

Quantitative predictor variables are entered into a regression model through indicator variables.

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Which of the following correctly describes a multiple-regression ANOVA test?

In a regression model involving 40 observations, the following estimated regression model was obtained: . For this model, the following statistics are given: SSR = 501 and SSE = 99. Then, the value of MSR is:

Multicollinearity is present when there is a high degree of correlation between the dependent variable and all the independent variables included in the model.

A coefficient of multiple correlation is denoted by and equals the proportion of the total variation in the values of the dependent variable, y that is explained by the estimated multiple regression of y on , , and possibly additional independent variable ( , and so on).

In a multiple regression model, the adjusted value measures the explained variation in the dependent variable after taking into account the relationship between the sample size and the number of independent variables in the model.

Suppose a regression analysis based on the model with 15 observations produced SSE = 3.55, = 13.131, and = 125.1. Hence, the proportion of the total variability in y that is accounted for by and is:

In order to test the validity of a multiple regression model involving 4 predictor variables and 25 observations, the numerator and denominator degrees of freedom ( , respectively) for the critical value of F are:

In multiple regression analysis, which of the following is a clue that multicollinearity is present?

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Having a large number of predictors in a regression model guarantees that the model fit is good.

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Linear Regression and Correlation

Analysis of Categorical Data

Nonparametric Statistics

Filters