For the following multiple regression model: ,a unit increase in x1,holding x2 and x3 constant,results in:

A) a decrease of 3 units on average in the value of y. B) an increase of 8 units in the value of y. C) an increase of 3 units on average in the value of y. D) None of these choices. A) a decrease of 3 units on average in the value of y. B) an increase of 8 units in the value of y. C) an increase of 3 units on average in the value of y. D) None of these choices.

Test the hypotheses H0: no first-order autocorrelation vs.H1: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

d L = 0.97 and d U = 1.41 The decision is ma

Exam 17: Multiple Regression

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.

(True/False)

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Question 81

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

(Multiple Choice)

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Question 82

If the Durbin-Watson statistic d has values smaller than 2,this indicates

(Multiple Choice)

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Question 83

In a multiple regression analysis involving 6 independent variables,the total variation in y is 900 and SSR = 600.What is the value of SSE?

(Multiple Choice)

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Question 84

When an explanatory variable is dropped from a multiple regression model,the adjusted coefficient of determination can increase.

(True/False)

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Question 85

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

(Short Answer)

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Question 86

For the following multiple regression model: ,a unit increase in x₁,holding x₂ and x₃ constant,results in:

(Multiple Choice)

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Question 87

When an explanatory variable is dropped from a multiple regression model,the coefficient of determination can increase.

(True/False)

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Question 88

The Durbin-Watson statistic,d,is defined as ,where e_i is the residual at time period i.

(True/False)

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Question 89

If the value of the Durbin-Watson statistic d is small (d < 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

(Short Answer)

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Question 90

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:

(Multiple Choice)

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Question 91

Because of multicollinearity,the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable,when in fact they are.

(True/False)

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Question 92

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 the regression model as a whole is significant: α = .00005,.001,.01,and .05?

(Short Answer)

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Question 93

Three predictor variables are being considered for use in a linear regression model.Given the correlation matrix below,does it appear that multicollinearity could be a problem?

(Essay)

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Question 94

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} Suppose the builder wants to test whether the coefficient on income is significantly different from 0.What is the value of the relevant t-statistic?

(Short Answer)

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Question 95

How do you go about checking for multicollinearity?

(Essay)

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Question 96

Test the hypotheses H₀: no first-order autocorrelation vs.H₁: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

(Essay)

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Question 97

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

(True/False)

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Question 98

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α = .05,n = 20,and there are two independent variables in the model,the critical values for the test are d_L = __________ and d_U = __________,respectively.

(Short Answer)

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Question 99

A multiple regression model involves 10 independent variables and 30 observations.If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs.≠ 0)the critical value will be:

(Multiple Choice)

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Question 100

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Exam 17: Multiple Regression

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.

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

If the Durbin-Watson statistic d has values smaller than 2,this indicates

In a multiple regression analysis involving 6 independent variables,the total variation in y is 900 and SSR = 600.What is the value of SSE?

When an explanatory variable is dropped from a multiple regression model,the adjusted coefficient of determination can increase.

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

For the following multiple regression model: ,a unit increase in x1,holding x2 and x3 constant,results in:

When an explanatory variable is dropped from a multiple regression model,the coefficient of determination can increase.

The Durbin-Watson statistic,d,is defined as ,where ei is the residual at time period i.

If the value of the Durbin-Watson statistic d is small (d < 2),this indicates a(n)____________________ (positive/negative)first-order autocorrelation exists.

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:

Because of multicollinearity,the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable,when in fact they are.

Three predictor variables are being considered for use in a linear regression model.Given the correlation matrix below,does it appear that multicollinearity could be a problem?

How do you go about checking for multicollinearity?

Test the hypotheses H0: no first-order autocorrelation vs.H1: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

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

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α = .05,n = 20,and there are two independent variables in the model,the critical values for the test are dL = __________ and dU = __________,respectively.

A multiple regression model involves 10 independent variables and 30 observations.If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs.≠ 0)the critical value will be:

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

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For the following multiple regression model: ,a unit increase in x₁,holding x₂ and x₃ constant,results in:

The Durbin-Watson statistic,d,is defined as ,where e_i is the residual at time period i.

Test the hypotheses H₀: no first-order autocorrelation vs.H₁: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α = 0.01.

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

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α = .05,n = 20,and there are two independent variables in the model,the critical values for the test are d_L = __________ and d_U = __________,respectively.