Question 1

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

Accepted Answer

A) True 
 B)False

Question 2

In multiple regression,the standard error of estimate is defined by   ,where n is the sample size and k is the number of independent variables.

Accepted Answer

A) True 
 B)False

Question 3

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   ​   ​ ​ S = 13.74 R−Sq = 30.0% ​ ANALYSIS OF VARIANCE   ​ ​
-{Student's Final Grade Narrative} Does this data provide enough evidence to conclude at the 5% significance level that the final grade and the number of skipped lectures are linearly related?

Accepted Answer

@#IMG-DLM& Rejection region: | t | > t_0.025,46≈ 2.014 Test

Question 4

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   ​   ​ ​ S = 13.74 R−Sq = 30.0% ​ 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 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 (xS1U1B11S1U1B0),the cholesterol level (xS1U1B12S1U1B0),and the number of points that the individual's blood pressure exceeded the recommended value (xS1U1B13S1U1B0).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 + 1.79xS1U1B11S1U1B0− 0.021xS1U1B12S1U1B0− 0.061xS1U1B13S1U1B0   ​ S = 9.47 ​ R−Sq = 22.5% ANALYSIS OF VARIANCE   ​ ​
-{Life Expectancy Narrative} What is the coefficient of determination? What does this statistic tell you?

Accepted Answer

R² = 0.225.This means that 22.5% of the v

Question 6

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 7

Which of the following statements regarding multicollinearity is not true?

Accepted Answer

A) It exists in virtually all multiple regression models. 
B) It is also called collinearity and intercorrelation. 
C) It is a condition that exists when the independent variables are highly correlated with the dependent variable. 
D) All of these choices are true. 
A) It exists in virtually all multiple regression models. 
B) It is also called collinearity and intercorrelation. 
C) It is a condition that exists when the independent variables are highly correlated with the dependent variable. 
D) All of these choices are true.

Question 8

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) 0.992 
B) 0.900 
C) 0.955 
D) 0.855 
A) 0.992 
B) 0.900 
C) 0.955 
D) 0.855

Question 9

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA     ​ ​
-{Real Estate Builder Narrative} One individual in the sample had an annual income of $10,000,a family size of 1,and an education of 8 years.This individual owned a home with an area of 1,000 square fee (House = 10.00).What is the residual (in hundreds of square feet)for this data point?

Accepted Answer

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

Question 10

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 11

Test the hypotheses H0: There is no first-order autocorrelation vs.H1: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

Accepted Answer

d_L = 1.29 and d_U = 1.78 The decision is ma

Question 12

In a multiple regression analysis involving k independent variables and n data points,the number of degrees of freedom associated with the sum of squares for error is:

Accepted Answer

A) k− 1 
B) n−k 
C) n− 1 
D) n−k− 1 
A) k− 1 
B) n−k 
C) n− 1 
D) n−k− 1

Question 13

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA     ​ ​
-{Real Estate Builder Narrative} Which of the independent variables in the model are significant at the 2% level?

Accepted Answer

Family inc

Question 14

In a multiple regression analysis,there are 20 data points and 4 independent variables,and the sum of the squared differences between observed and predicted values of y is 180.The standard error of estimate will be:

Accepted Answer

A) 9.000 
B) 6.708 
C) 3.464 
D) 3.000 
A) 9.000 
B) 6.708 
C) 3.464 
D) 3.000

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

Accepted Answer

The answer of One clue to the presence of multicollinearity...

Question 17

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 sε = 0,and the coefficient of determination R2 = 1.

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

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 20

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

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

In multiple regression,the standard error of estimate is defined by ,where n is the sample size and k is the number of independent variables.

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,

Which of the following statements regarding multicollinearity is not true?

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:

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

Test the hypotheses H₀: There is no first-order autocorrelation vs.H₁: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

In a multiple regression analysis involving k independent variables and n data points,the number of degrees of freedom associated with the sum of squares for error is:

In a multiple regression analysis,there are 20 data points and 4 independent variables,and the sum of the squared differences between observed and predicted values of y is 180.The standard error of estimate will be:

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

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

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 sε = 0,and the coefficient of determination R² = 1.

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

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.

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

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

Model Building

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

Exam 17: Multiple Regression

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

In multiple regression,the standard error of estimate is defined by ,where n is the sample size and k is the number of independent variables.

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,

Which of the following statements regarding multicollinearity is not true?

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:

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

Test the hypotheses H0: There is no first-order autocorrelation vs.H1: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

In a multiple regression analysis involving k independent variables and n data points,the number of degrees of freedom associated with the sum of squares for error is:

In a multiple regression analysis,there are 20 data points and 4 independent variables,and the sum of the squared differences between observed and predicted values of y is 180.The standard error of estimate will be:

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

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

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 sε = 0,and the coefficient of determination R2 = 1.

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

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.

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

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

Model Building

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

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:

Test the hypotheses H₀: There is no first-order autocorrelation vs.H₁: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and α = 0.05.

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 sε = 0,and the coefficient of determination R² = 1.