Question 1

In a multiple regression model, the error variable   is assumed to have a mean of:

Accepted Answer

A) -1.0 
B)  0.0 
C)  1.0 
D)  None of these choices. 
A) -1.0 
B)  0.0 
C)  1.0 
D)  None of these choices.

Question 2

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
  
-{Student's Final Grade Narrative} Interpret the coefficient b1.

Accepted Answer

b₁ = -3.18.This tells us that for each ad

Question 3

In a multiple regression analysis involving 50 observations and 5 independent variables, the total variation in y is 475 and SSE = 71.25.Then, the coefficient of determination is 0.85.

Accepted Answer

A) True 
 B)False

Question 4

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 5

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate  are both small, the coefficient of determination R2 is close to 1, and the value of the test statistic F is large.

Accepted Answer

A) True 
 B)False

Question 6

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
    
-{Real Estate Builder Narrative} What minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home?

Accepted Answer

The answer of Real Estate Builder
A real estate builder wishes...

Question 7

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

Accepted Answer

The answer of An adverse effect of multicollinearity is that...

Question 8

For the multiple regression model:   , if x2 were to increase by 5, holding x1 and x3 constant, the value of y will:

Accepted Answer

A)  increase by 5. 
B)  increase by 75. 
C)  decrease on average by 5. 
D)  decrease on average by 75. 
A)  increase by 5. 
B)  increase by 75. 
C)  decrease on average by 5. 
D)  decrease on average by 75.

Question 9

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 10

In a multiple regression model, the probability distribution of the error variable   is assumed to be:

Accepted Answer

A)  normal. 
B)  non-normal. 
C)  positively skewed. 
D)  negatively skewed. 
A)  normal. 
B)  non-normal. 
C)  positively skewed. 
D)  negatively skewed.

Question 11

In reference to the equation   , the value 0.12 is the average change in y per unit change in x1, when x2 is held constant.

Accepted Answer

A) True 
 B)False

Question 12

A multiple regression model has the form:   .As x2 increases by one unit, holding x1 constant, then the value of y will increase by:

Accepted Answer

A)  7.25 units 
B)  6 units on average 
C)  2 units 
D)  None of these choices 
A)  7.25 units 
B)  6 units on average 
C)  2 units 
D)  None of these choices

Question 13

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson d statistic should be near ____________________.

Accepted Answer

The answer of If the residuals in a regression analysis...

Question 14

To use the Durbin-Watson test to test for positive first-order autocorrelation, the null hypothesis will be H0: ____________________ (there is/there is no) first-order autocorrelation.

Accepted Answer

Question 15

If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

Accepted Answer

A)  Homoscedasticity. 
B)  Normality of the errors. 
C)  Independence of errors. 
D)  None of these choices. 
A)  Homoscedasticity. 
B)  Normality of the errors. 
C)  Independence of errors. 
D)  None of these choices.

Question 16

In testing the significance of a multiple regression model with three independent variables, the null hypothesis is   .

Accepted Answer

A) True 
 B)False

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
    
-{Real Estate Builder Narrative} What is the predicted house size for an individual earning an annual income of $40,000, having a family size of 4, and having 13 years of education?

Accepted Answer

The answer of Real Estate Builder
A real estate builder wishes...

Question 18

In a multiple regression analysis involving 40 observations and 5 independent variables, the following statistics are given: Total variation in y = 350 and SSE = 50.Then, the coefficient of determination is:

Accepted Answer

A)  0.8408 
B)  0.8571 
C)  0.8469 
D)  0.8529 
A)  0.8408 
B)  0.8571 
C)  0.8469 
D)  0.8529

Question 19

The coefficient of determination R2 measures the proportion of variation in y that is explained by the explanatory variables included in the model.

Accepted Answer

A) True 
 B)False

Question 20

A multiple regression equation includes 5 independent variables, and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is:

Accepted Answer

A)  81% 
B)  90% 
C)  86% 
D)  about 16% 
A)  81% 
B)  90% 
C)  86% 
D)  about 16%

In a multiple regression model, the error variable is assumed to have a mean of:

In a multiple regression analysis involving 50 observations and 5 independent variables, the total variation in y is 475 and SSE = 71.25.Then, the coefficient of determination is 0.85.

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.

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate are both small, the coefficient of determination R² is close to 1, and the value of the test statistic F is large.

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

For the multiple regression model: , if x₂ were to increase by 5, holding x₁ and x₃ constant, the value of y will:

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

In a multiple regression model, the probability distribution of the error variable is assumed to be:

In reference to the equation , the value 0.12 is the average change in y per unit change in x₁, when x₂ is held constant.

A multiple regression model has the form: .As x₂ increases by one unit, holding x₁ constant, then the value of y will increase by:

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson d statistic should be near ____________________.

To use the Durbin-Watson test to test for positive first-order autocorrelation, the null hypothesis will be H₀: ____________________ (there is/there is no) first-order autocorrelation.

If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

In testing the significance of a multiple regression model with three independent variables, the null hypothesis is .

In a multiple regression analysis involving 40 observations and 5 independent variables, the following statistics are given: Total variation in y = 350 and SSE = 50.Then, the coefficient of determination is:

The coefficient of determination R² measures the proportion of variation in y that is explained by the explanatory variables included in the model.

A multiple regression equation includes 5 independent variables, and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is:

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

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

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Filters

Exam 17: Multiple Regression

In a multiple regression model, the error variable is assumed to have a mean of:

In a multiple regression analysis involving 50 observations and 5 independent variables, the total variation in y is 475 and SSE = 71.25.Then, the coefficient of determination is 0.85.

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.

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate are both small, the coefficient of determination R2 is close to 1, and the value of the test statistic F is large.

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

For the multiple regression model: , if x2 were to increase by 5, holding x1 and x3 constant, the value of y will:

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

In a multiple regression model, the probability distribution of the error variable is assumed to be:

In reference to the equation , the value 0.12 is the average change in y per unit change in x1, when x2 is held constant.

A multiple regression model has the form: .As x2 increases by one unit, holding x1 constant, then the value of y will increase by:

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson d statistic should be near ____________________.

To use the Durbin-Watson test to test for positive first-order autocorrelation, the null hypothesis will be H0: ____________________ (there is/there is no) first-order autocorrelation.

If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

In testing the significance of a multiple regression model with three independent variables, the null hypothesis is .

In a multiple regression analysis involving 40 observations and 5 independent variables, the following statistics are given: Total variation in y = 350 and SSE = 50.Then, the coefficient of determination is:

The coefficient of determination R2 measures the proportion of variation in y that is explained by the explanatory variables included in the model.

A multiple regression equation includes 5 independent variables, and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is:

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

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

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Filters

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate are both small, the coefficient of determination R² is close to 1, and the value of the test statistic F is large.

For the multiple regression model: , if x₂ were to increase by 5, holding x₁ and x₃ constant, the value of y will:

In reference to the equation , the value 0.12 is the average change in y per unit change in x₁, when x₂ is held constant.

A multiple regression model has the form: .As x₂ increases by one unit, holding x₁ constant, then the value of y will increase by:

To use the Durbin-Watson test to test for positive first-order autocorrelation, the null hypothesis will be H₀: ____________________ (there is/there is no) first-order autocorrelation.

The coefficient of determination R² measures the proportion of variation in y that is explained by the explanatory variables included in the model.