Question 1

Which of the following methods is used to help assess whether the regression model meets the assumption of having normally distributed residuals?

Accepted Answer

A)  Develop a normal probability plot of the residuals. 
B)  Develop a histogram of the residuals. 
C)  Develop a normal probability plot of the population means. 
D)  Both develop a normal probability plot of the residuals and develop a histogram of the residuals. 
E)  Neither develop a normal probability plot of the residuals nor develop a histogram of the residuals. 
A)  Develop a normal probability plot of the residuals. 
B)  Develop a histogram of the residuals. 
C)  Develop a normal probability plot of the population means. 
D)  Both develop a normal probability plot of the residuals and develop a histogram of the residuals. 
E)  Neither develop a normal probability plot of the residuals nor develop a histogram of the residuals.

Question 2

Which of the following statements is false?

Accepted Answer

A)  An adjusted coefficient of multiple determination, denoted by(adj.), is adjusted for the degrees of freedom. 
B)  An estimated partial-regression coefficient gives the partial change in Y for a unit change in that independent variable, while holding other independent variables constant. 
C)  The coefficient of multiple determination takes on values between 0 and 1, inclusive. 
D)  A coefficient of multiple correlation, denoted by R, 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 variables (, and so on). 
E)  None of these statements is false. 
A)  An adjusted coefficient of multiple determination, denoted by(adj.), is adjusted for the degrees of freedom. 
B)  An estimated partial-regression coefficient gives the partial change in Y for a unit change in that independent variable, while holding other independent variables constant. 
C)  The coefficient of multiple determination takes on values between 0 and 1, inclusive. 
D)  A coefficient of multiple correlation, denoted by R, 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 variables (, and so on). 
E)  None of these statements is false.

Question 3

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

Accepted Answer

A)  heteroscedasticity 
B)  homoscedasticity 
C)  multicollinearity 
D)  causality 
E)  collinearity 
A)  heteroscedasticity 
B)  homoscedasticity 
C)  multicollinearity 
D)  causality 
E)  collinearity

Question 4

What is the effect of multicollinearity on the estimated regression coefficients?

Accepted Answer

The adverse effect of multicol

Question 5

In testing the significance of a multiple regression model in which there are three independent variables, the null hypothesis is   .

Accepted Answer

A) True 
 B)False

Question 6

A multiple regression model has the form   . The coefficient   is interpreted as the change in y per unit change in   .

Accepted Answer

A) True 
 B)False

Question 7

An estimated partial-regression coefficient is the coefficient of a dependent variable in an estimated multiple-regression equation.

Accepted Answer

A) True 
 B)False

Question 8

In a multiple regression model, the regression coefficients are calculated such that the quantity   is minimized.

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

Assume you are considering including two additional qualitative variables into a regression model. The first variable has 4 categories, and the second variable has 4 categories as well. Given this information, how many indicator variables will be incorporated into the model?

Accepted Answer

A)  8 
B)  7 
C)  6 
D)  5 
E)  4 
A)  8 
B)  7 
C)  6 
D)  5 
E)  4

Question 11

In a simple linear regression problem, the following pairs of   are given: (6.75, 7.42), (8.96, 8.06), (10.30, 11.65), and (13.24, 12.15). Then, the sum of squares for error is:

Accepted Answer

A)  39.2500 
B)  -0.0300 
C)  4.2695 
D)  39.2800 
A)  39.2500 
B)  -0.0300 
C)  4.2695 
D)  39.2800

Question 12

An estimated partial-regression coefficient gives the partial change in y for a unit change in that independent variable, while holding other independent variables constant.

Accepted Answer

A) True 
 B)False

Question 13

A dummy or indicator variable is a dependent variable whose values are either 0.0 or 1.0.

Accepted Answer

A) True 
 B)False

Question 14

If stepwise procedure is used, a variable selected at an earlier step can be removed from the model if, in the presence of other variables, it no longer contributes significantly to explaining the variation in the dependent variable y.

Accepted Answer

A) True 
 B)False

Question 15

Given MSR = 345 and MSE = 431.25, the value of the F-statistic:

Accepted Answer

A)  equals .894 
B)  equals 1.25 
C)  equals .80 
D)  equals .43 
E)  cannot be computed without additional information 
A)  equals .894 
B)  equals 1.25 
C)  equals .80 
D)  equals .43 
E)  cannot be computed without additional information

Question 16

A chemist was interested in examining the effects of four chemicals on a chemical process yield. Let   , i = 1, 2, 3, 4, represent the effects of the four chemicals, respectively and y be the process yield. The chemist's first instinct was to include each of the chemicals in the equation in a linear fashion. After the initial analysis, the chemist decided to remove chemicals 2 and 3 from the model.
Complete model:   Reduced model:     Use the statistical software output above to test whether the reduced model is adequate at the 0.05 level of significance.
Test Statistic:
F = ______________
Reject Region:
Reject   if F > ______________
Conclusion: ______________
There ______________ evidence to indicate that at least one of   or   is not 0.
The reduced model ______________ adequate.

Accepted Answer

1.2136; 6.94; Do not

Question 17

If you wish to develop a multiple regression model that includes a qualitative variable; education status, in which the following categories exist: no degree, high school diploma, junior college degree, bachelor degree, and graduate degree, you need to code the categories as 1, 2, 3, 4, and 5.

Accepted Answer

A) True 
 B)False

Question 18

Multiple linear regression is an extension of simple linear regression to allow for more than one dependent variable.

Accepted Answer

A) True 
 B)False

Question 19

In stepwise regression procedure, the independent variable with the largest F-statistic, or equally with the smallest p-value, is chosen as the first entering variable. The standard, also called the F-to-enter, is usually set at F equals:

Accepted Answer

A)  4 
B)  2 
C)  5 
D)  0 
E)  1 
A)  4 
B)  2 
C)  5 
D)  0 
E)  1

Question 20

Typical symptoms of the presence of multicollinearity include:

Accepted Answer

A)  the estimated regression coefficients to vary substantially from sample to sample ; this fact raises their standard errors; hence, theis unlikely to be greater than 2, or statistically significant 
B)  the estimated regression coefficients change greatly in value as independent variables are dropped from or added to the regression equation 
C)  the signs of the estimated regression coefficients are nonsensical; they are negative when common sense suggests positive signs and vice versa 
D)  all of these and more 
E)  none of these 
A)  the estimated regression coefficients to vary substantially from sample to sample ; this fact raises their standard errors; hence, theis unlikely to be greater than 2, or statistically significant 
B)  the estimated regression coefficients change greatly in value as independent variables are dropped from or added to the regression equation 
C)  the signs of the estimated regression coefficients are nonsensical; they are negative when common sense suggests positive signs and vice versa 
D)  all of these and more 
E)  none of these

Which of the following methods is used to help assess whether the regression model meets the assumption of having normally distributed residuals?

Which of the following statements is false?

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

What is the effect of multicollinearity on the estimated regression coefficients?

In testing the significance of a multiple regression model in which there are three independent variables, the null hypothesis is .

A multiple regression model has the form . The coefficient is interpreted as the change in y per unit change in .

An estimated partial-regression coefficient is the coefficient of a dependent variable in an estimated multiple-regression equation.

In a multiple regression model, the regression coefficients are calculated such that the quantity is minimized.

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

Assume you are considering including two additional qualitative variables into a regression model. The first variable has 4 categories, and the second variable has 4 categories as well. Given this information, how many indicator variables will be incorporated into the model?

In a simple linear regression problem, the following pairs of are given: (6.75, 7.42), (8.96, 8.06), (10.30, 11.65), and (13.24, 12.15). Then, the sum of squares for error is:

An estimated partial-regression coefficient gives the partial change in y for a unit change in that independent variable, while holding other independent variables constant.

A dummy or indicator variable is a dependent variable whose values are either 0.0 or 1.0.

If stepwise procedure is used, a variable selected at an earlier step can be removed from the model if, in the presence of other variables, it no longer contributes significantly to explaining the variation in the dependent variable y.

Given MSR = 345 and MSE = 431.25, the value of the F-statistic:

If you wish to develop a multiple regression model that includes a qualitative variable; education status, in which the following categories exist: no degree, high school diploma, junior college degree, bachelor degree, and graduate degree, you need to code the categories as 1, 2, 3, 4, and 5.

Multiple linear regression is an extension of simple linear regression to allow for more than one dependent variable.

In stepwise regression procedure, the independent variable with the largest F-statistic, or equally with the smallest p-value, is chosen as the first entering variable. The standard, also called the F-to-enter, is usually set at F equals:

Typical symptoms of the presence of multicollinearity include:

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

Which of the following methods is used to help assess whether the regression model meets the assumption of having normally distributed residuals?

Which of the following statements is false?

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

What is the effect of multicollinearity on the estimated regression coefficients?

In testing the significance of a multiple regression model in which there are three independent variables, the null hypothesis is .

A multiple regression model has the form . The coefficient is interpreted as the change in y per unit change in .

An estimated partial-regression coefficient is the coefficient of a dependent variable in an estimated multiple-regression equation.

In a multiple regression model, the regression coefficients are calculated such that the quantity is minimized.

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

Assume you are considering including two additional qualitative variables into a regression model. The first variable has 4 categories, and the second variable has 4 categories as well. Given this information, how many indicator variables will be incorporated into the model?

In a simple linear regression problem, the following pairs of are given: (6.75, 7.42), (8.96, 8.06), (10.30, 11.65), and (13.24, 12.15). Then, the sum of squares for error is:

An estimated partial-regression coefficient gives the partial change in y for a unit change in that independent variable, while holding other independent variables constant.

A dummy or indicator variable is a dependent variable whose values are either 0.0 or 1.0.

If stepwise procedure is used, a variable selected at an earlier step can be removed from the model if, in the presence of other variables, it no longer contributes significantly to explaining the variation in the dependent variable y.

Given MSR = 345 and MSE = 431.25, the value of the F-statistic:

If you wish to develop a multiple regression model that includes a qualitative variable; education status, in which the following categories exist: no degree, high school diploma, junior college degree, bachelor degree, and graduate degree, you need to code the categories as 1, 2, 3, 4, and 5.

Multiple linear regression is an extension of simple linear regression to allow for more than one dependent variable.

In stepwise regression procedure, the independent variable with the largest F-statistic, or equally with the smallest p-value, is chosen as the first entering variable. The standard, also called the F-to-enter, is usually set at F equals:

Typical symptoms of the presence of multicollinearity include:

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