Question 1

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  True

Question 2

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  True

Question 3

Discuss two indicators that can be found in an analysis that suggest multicollinearity is present.

Accepted Answer

A good indicator of multicollinearity is a large F-statistic,but small t-statistics.A related 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 significant.Another clue is when a regression coefficient exhibits the wrong sign.Or when an independent variable is added or deleted,the regression coefficients for the other variables change drastically.

Question 4

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} Is there enough evidence at the 5% significance level to infer that the model is useful in predicting length of life?

Accepted Answer

@#IMG-DLM& @#IMG-DLM& At least one β_i is not equal to zero. R

Question 5

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 6

A multiple regression model has the form   .The coefficient b1 is interpreted as the change in the average value of y per unit change in ________ holding ________ constant.

Accepted Answer

Question 7

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} Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per week and the age at death are linearly related?

Accepted Answer

@#IMG-DLM& Rejection region: | t | > t_0.005,36≈ 2.724 Test

Question 8

Multiple regression has four requirements for the error variable.One is that the probability distribution of the error variable is ____________________.

Accepted Answer

The answer of Multiple regression has four requirements for the...

Question 9

A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

Accepted Answer

A) True 
 B)False

Question 10

The coefficient of determination ranges from:

Accepted Answer

A) 1.0 to ∞. 
B) 0.0 to 1.0. 
C) 1.0 to k,where k is the number of independent variables in the model. 
D) 1.0 to n,where n is the number of observations in the dependent variable. 
A) 1.0 to ∞. 
B) 0.0 to 1.0. 
C) 1.0 to k,where k is the number of independent variables in the model. 
D) 1.0 to n,where n is the number of observations in the dependent variable.

Question 11

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 following values for the level of significance is the smallest for which all explanatory variables are significant individually: α = .01,.05,.10,or .15?

Accepted Answer

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

Question 12

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −dL,we conclude that positive first-order autocorrelation exists.

Accepted Answer

A) True 
 B)False

Question 13

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 14

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d L or d > 4 −dL,where dL and dU are the critical values of d,we conclude that autocorrelation exists.

Accepted Answer

A) True 
 B)False

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

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is ____________________ with a mean of ____________________.

Accepted Answer

normal; ze

Question 17

If the Durbin-Watson statistic has a value close to 4,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 18

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate sε 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 19

Consider the following statistics of a multiple regression model: Total variation in y = 1000,SSE = 300,n = 50,and k = 4.
a.Determine the standard error of estimate.
b.Determine the coefficient of determination.
c.Determine the F-statistic.

Accepted Answer

a. sε = 2.

Question 20

A high correlation between two independent variables is an indication of ____________________.

Accepted Answer

The answer of A high correlation between two independent variables...

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

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.

Discuss two indicators that can be found in an analysis that suggest multicollinearity is present.

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 has the form .The coefficient b₁ is interpreted as the change in the average value of y per unit change in holding constant.

Multiple regression has four requirements for the error variable.One is that the probability distribution of the error variable is ____________________.

A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

The coefficient of determination ranges from:

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −d_L,we conclude that positive first-order autocorrelation exists.

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.

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d < d_L or d > 4 −d_L,where d_L and d_U are the critical values of d,we conclude that autocorrelation exists.

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

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is with a mean of .

If the Durbin-Watson statistic has a value close to 4,which assumption is violated?

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

Consider the following statistics of a multiple regression model: Total variation in y = 1000,SSE = 300,n = 50,and k = 4. a.Determine the standard error of estimate. b.Determine the coefficient of determination. c.Determine the F-statistic.

A high correlation between two independent variables is an indication of ____________________.

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

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

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.

Discuss two indicators that can be found in an analysis that suggest multicollinearity is present.

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 has the form .The coefficient b1 is interpreted as the change in the average value of y per unit change in ________ holding ________ constant.

Multiple regression has four requirements for the error variable.One is that the probability distribution of the error variable is ____________________.

A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

The coefficient of determination ranges from:

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −dL,we conclude that positive first-order autocorrelation exists.

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.

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d < dL or d > 4 −dL,where dL and dU are the critical values of d,we conclude that autocorrelation exists.

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

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is ____________________ with a mean of ____________________.

If the Durbin-Watson statistic has a value close to 4,which assumption is violated?

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

Consider the following statistics of a multiple regression model: Total variation in y = 1000,SSE = 300,n = 50,and k = 4. a.Determine the standard error of estimate. b.Determine the coefficient of determination. c.Determine the F-statistic.

A high correlation between two independent variables is an indication of ____________________.

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

A multiple regression model has the form .The coefficient b₁ is interpreted as the change in the average value of y per unit change in holding constant.

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 −d_L,we conclude that positive first-order autocorrelation exists.

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.

If the value of the Durbin-Watson test statistic,d,satisfies the inequalities d < d_L or d > 4 −d_L,where d_L and d_U are the critical values of d,we conclude that autocorrelation exists.

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is with a mean of .

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