Question 1

For the multiple regression model:   , if x 2 were to increase by 5, holding x 1 and x 3 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 2

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} Which of the independent variables in the model are significant at the 2% level?

Accepted Answer

Family inc

Question 3

Life Expectancy An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death ( y ), the average number of hours of exercise per week ( x 1), the cholesterol level ( x 2), and the number of points that the individual's blood pressure exceeded the recommended value ( x 3). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below. THE REGRESSION EQUATION IS y = 55.8 + 1.79 x 1 - 0.021 x 2 - 0.061 x 3 
   
 S = 9.47 R - Sq = 22.5% 
   {Life Expectancy Narrative} Interpret the coefficient b 1.

Accepted Answer

b ₁ = 1.79. This tells us for each additi

Question 4

Marc Anthony Concert At a recent Marc Anthony concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year. The following data were collected:   
 An Excel output follows:   {Marc Anthony Concert Narrative} Does it appear that heteroscedasticity is a problem? Explain.

Accepted Answer

The variance of the error vari

Question 5

Life Expectancy An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death ( y ), the average number of hours of exercise per week ( x 1), the cholesterol level ( x 2), and the number of points that the individual's blood pressure exceeded the recommended value ( x 3). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below. THE REGRESSION EQUATION IS y = 55.8 + 1.79 x 1 - 0.021 x 2 - 0.061 x 3   S = 9.47 R - Sq = 22.5% 
   {Life Expectancy Narrative} What is the adjusted coefficient of determination in this situation? What does this statistic tell you?

Accepted Answer

R ² adjusted is 0.160. This mea

Question 6

In a multiple regression model, the error variable e 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 7

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 8

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 9

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 10

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

Accepted Answer

A) 6.26 
B) 3.33 
C) 9.36 
D) 4.24 
A) 6.26 
B) 3.33 
C) 9.36 
D) 4.24

Question 11

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

Accepted Answer

A) F -test 
B) t -test 
C) z -test 
D) None of these choices. 
A) F -test 
B) t -test 
C) z -test 
D) None of these choices.

Question 12

Marc Anthony Concert At a recent Marc Anthony concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year. The following data were collected:   An Excel output follows:   {Marc Anthony Concert Narrative} Use the predicted values and the actual values of y to calculate the residuals.

Accepted Answer

The residu

Question 13

In a multiple regression model, the probability distribution of the error variable e 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 14

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), x 1 is the number of lectures skipped, x 2 is the number of late assignments, and x 3 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     S = 13.74 R - Sq = 30.0%   
 {Student's Final Grade Narrative} What is the coefficient of determination? What does this statistic tell you?

Accepted Answer

R ² = 0.30. This means that 30% of the va

Question 15

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 are the regression degrees of freedom that are missing from the output?

Accepted Answer

df = 3605.

Question 16

Marc Anthony Concert At a recent Marc Anthony concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year. The following data were collected:   An Excel output follows:   {Marc Anthony Concert Narrative} Does it appear that the errors are normally distributed? Explain.

Accepted Answer

The histogram is slightly posi

Question 17

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), x 1 is the number of lectures skipped, x 2 is the number of late assignments, and x 3 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     S = 13.74 R - Sq = 30.0%   {Student's Final Grade Narrative} What is the adjusted coefficient of determination? What does this statistic tell you?

Accepted Answer

R ² adjusted is 0.25. This means that 25%

Question 18

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 e  = 0, and the coefficient of determination R 2 = 1.

Accepted Answer

A) True 
 B)False

Question 19

A multiple regression model has the form   . The coefficient b 1 is interpreted as the change in the average value of y per unit change in ________ holding ________ constant.

Accepted Answer

Question 20

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.

For the multiple regression model: , if x ₂ were to increase by 5, holding x ₁ and x ₃ constant, the value of y will:

In a multiple regression model, the error variable e 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.

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 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:

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

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

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_e = 0, and the coefficient of determination R ² = 1.

A multiple regression model has the form . The coefficient b ₁ is interpreted as the change in the average value of y per unit change in holding constant.

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

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 Populat

Inference About Comparing Two Populat

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlat

Review of Statistical Inference

Filters

Exam 17: Multiple Regression

For the multiple regression model: , if x 2 were to increase by 5, holding x 1 and x 3 constant, the value of y will:

In a multiple regression model, the error variable e 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.

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 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:

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

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

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 e = 0, and the coefficient of determination R 2 = 1.

A multiple regression model has the form . The coefficient b 1 is interpreted as the change in the average value of y per unit change in ________ holding ________ constant.

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

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 Populat

Inference About Comparing Two Populat

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlat

Review of Statistical Inference

Filters

For the multiple regression model: , if x ₂ were to increase by 5, holding x ₁ and x ₃ constant, the value of y will:

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_e = 0, and the coefficient of determination R ² = 1.

A multiple regression model has the form . The coefficient b ₁ is interpreted as the change in the average value of y per unit change in holding constant.