Question 1

____________________ is a condition that exists when independent variables are correlated with one another.

Accepted Answer

The answer of ____________________ is a condition that exists when...

Question 2

In a multiple regression model, the following statistics are given: SSE = 100, R2 = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

Accepted Answer

A)  0.930 
B)  0.900 
C)  0.955 
D)  0.855 
A)  0.930 
B)  0.900 
C)  0.955 
D)  0.855

Question 3

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate s $\varepsilon$  = 0, and the coefficient of determination R2 = 1.

Accepted Answer

A) True 
 B)False

Question 4

In regression analysis, the total variation in the dependent variable y, measured by   , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Accepted Answer

A) True 
 B)False

Question 5

In multiple regression analysis, the ratio MSR/MSE yields the:

Accepted Answer

A)  t-test statistic for testing each individual regression coefficient. 
B)  F-test statistic for testing the validity of the regression equation. 
C)  coefficient of determination. 
D)  adjusted coefficient of determination. 
A)  t-test statistic for testing each individual regression coefficient. 
B)  F-test statistic for testing the validity of the regression equation. 
C)  coefficient of determination. 
D)  adjusted coefficient of determination.

Question 6

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

Accepted Answer

A) True 
 B)False

Question 7

Does it appear that the errors are normally distributed? Explain.

Accepted Answer

The histogram is slightly posi

Question 8

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted coefficient of determination. Then, the adjusted coefficient of determination is:

Accepted Answer

A)  0.385 
B)  0.877 
C)  0.591 
D)  0.736 
A)  0.385 
B)  0.877 
C)  0.591 
D)  0.736

Question 9

In a multiple regression analysis involving 4 independent variables and 30 data points, the number of degrees of freedom associated with the sum of squares for error, SSE, is 25.

Accepted Answer

A) True 
 B)False

Question 10

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y, then look for a change in the spread of the plotted values.

Accepted Answer

A) True 
 B)False

Question 11

In multiple regression analysis, the adjusted coefficient of determination is adjusted for the number of independent variables and the sample size.

Accepted Answer

A) True 
 B)False

Question 12

Student's Final Grade: A statistics professor investigated some of the factors that affect an individual student's final grade in her course. She proposed the multiple regression model   , where y is the final grade (out of 100 points), xS1U1B11S1U1B0 is the number of lectures skipped, xS1U1B12S1U1B0 is the number of late assignments, and xS1U1B13S1U1B0 is the midterm exam score (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below.
THE REGRESSION EQUATION IS       ANALYSIS OF VARIANCE
  
-Does this data provide enough evidence at the 1% significance level to conclude that the final grade and the midterm exam score are positively linearly related?

Accepted Answer

@#IMG-DLM& vs. @#IMG-DLM& Rejection region: t > t<sub>0.01,4

Question 13

In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations, the numerator and denominator degrees of freedom for the critical value of F are, respectively,

Accepted Answer

A)  5 and 30 
B)  6 and 29 
C)  5 and 24 
D)  6 and 25 
A)  5 and 30 
B)  6 and 29 
C)  5 and 24 
D)  6 and 25

Question 14

If multicollinearity exists among the independent variables included in a multiple regression model, then:

Accepted Answer

A)  the regression coefficients will be difficult to interpret. 
B)  the standard errors of the regression coefficients for the correlated independent variables will increase. 
C)  one or more of the coefficients may have the wrong sign. 
D)  All of these choices are true. 
A)  the regression coefficients will be difficult to interpret. 
B)  the standard errors of the regression coefficients for the correlated independent variables will increase. 
C)  one or more of the coefficients may have the wrong sign. 
D)  All of these choices are true.

Question 15

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)  None of these choices. 
A)  heteroscedasticity. 
B)  homoscedasticity. 
C)  multicollinearity. 
D)  None of these choices.

Question 16

A(n) ____________________ value of the F-test statistic indicates that the multiple regression model is valid.

Accepted Answer

The answer of A(n) ____________________ value of the F-test statistic...

Question 17

Real Estate Builder: A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below.
SUMMARY OUTPUT
   ANOVA
    
-Interpret the value of the Adjusted R-Square.

Accepted Answer

The Adjusted R-Square is 0.748

Question 18

The least squares method requires that the variance   of the error variable$\varepsilon$ is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

Accepted Answer

A)  heteroscedasticity. 
B)  homoscedasticity. 
C)  influential observation. 
D)  non-independence of $\varepsilon$. 
A)  heteroscedasticity. 
B)  homoscedasticity. 
C)  influential observation. 
D)  non-independence of $\varepsilon$.

Question 19

The problem of multicollinearity arises when the:

Accepted Answer

A)  dependent variables are highly correlated with one another. 
B)  independent variables are highly correlated with one another. 
C)  independent variables are highly correlated with the dependent variable. 
D)  None of these choices. 
A)  dependent variables are highly correlated with one another. 
B)  independent variables are highly correlated with one another. 
C)  independent variables are highly correlated with the dependent variable. 
D)  None of these choices.

Question 20

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s $\varepsilon$  are both large, the coefficient of determination R2 is close to 0, and the value of the test statistic F is large.

Accepted Answer

A) True 
 B)False

____________________ is a condition that exists when independent variables are correlated with one another.

In a multiple regression model, the following statistics are given: SSE = 100, R² = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate s _{$\varepsilon$} = 0, and the coefficient of determination R² = 1.

In regression analysis, the total variation in the dependent variable y, measured by , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

In multiple regression analysis, the ratio MSR/MSE yields the:

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

Does it appear that the errors are normally distributed? Explain.

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted coefficient of determination. Then, the adjusted coefficient of determination is:

In a multiple regression analysis involving 4 independent variables and 30 data points, the number of degrees of freedom associated with the sum of squares for error, SSE, is 25.

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y, then look for a change in the spread of the plotted values.

In multiple regression analysis, the adjusted coefficient of determination is adjusted for the number of independent variables and the sample size.

In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations, the numerator and denominator degrees of freedom for the critical value of F are, respectively,

If multicollinearity exists among the independent variables included in a multiple regression model, then:

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

A(n) ____________________ value of the F-test statistic indicates that the multiple regression model is valid.

The problem of multicollinearity arises when the:

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both large, the coefficient of determination R² is close to 0, and the value of the test statistic F is large.

What Is Statistics

Graphical and Tabular Descriptive Techniques

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations, Part 1

Inference About Comparing Two Populations, Part 2

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Review of Statistical Inference

Filters

Exam 17: Multiple Regression

____________________ is a condition that exists when independent variables are correlated with one another.

In a multiple regression model, the following statistics are given: SSE = 100, R2 = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate s ε\varepsilonε = 0, and the coefficient of determination R2 = 1.

In regression analysis, the total variation in the dependent variable y, measured by , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

In multiple regression analysis, the ratio MSR/MSE yields the:

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

Does it appear that the errors are normally distributed? Explain.

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted coefficient of determination. Then, the adjusted coefficient of determination is:

In a multiple regression analysis involving 4 independent variables and 30 data points, the number of degrees of freedom associated with the sum of squares for error, SSE, is 25.

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y, then look for a change in the spread of the plotted values.

In multiple regression analysis, the adjusted coefficient of determination is adjusted for the number of independent variables and the sample size.

In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations, the numerator and denominator degrees of freedom for the critical value of F are, respectively,

If multicollinearity exists among the independent variables included in a multiple regression model, then:

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

A(n) ____________________ value of the F-test statistic indicates that the multiple regression model is valid.

The least squares method requires that the variance of the error variable ε\varepsilonε is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

The problem of multicollinearity arises when the:

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s ε\varepsilonε are both large, the coefficient of determination R2 is close to 0, and the value of the test statistic F is large.

What Is Statistics

Graphical and Tabular Descriptive Techniques

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations, Part 1

Inference About Comparing Two Populations, Part 2

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Review of Statistical Inference

Filters

In a multiple regression model, the following statistics are given: SSE = 100, R² = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate s _{$\varepsilon$} = 0, and the coefficient of determination R² = 1.

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both large, the coefficient of determination R² is close to 0, and the value of the test statistic F is large.