Exam 13: Additional Topics in Regression Analysis

The correlation between errors far apart in time is relatively strong.

Which of the following is not an indicator of multicollinearity?

For which of the following values of the Durbin-Watson statistic,d,would negative correlation be concluded?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that a regression was run with three independent variables and 30 observations.The Durbin-Watson statistic was 0.64. -Test the hypothesis that there was no autocorrelation versus the alternative of positive autocorrelation in errors.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: You are interested in determining the number of hours that college students spend studying each week.You identify the following variables: Y = number of hours spent studying each week X₁= 1 if the student is a freshman,0 otherwise X₂ = 1 if the student is a sophomore,0 otherwise X₃ = 1 if the student is a junior,0 otherwise X₄ = 1 if the student is a senior,0 otherwise X₅ = 1 if the student is a business major,0 otherwise X₆ = 1 if the student is an arts and sciences major,0 otherwise X₇ = 1 if the student is an engineering major,0 otherwise -Which of the following regression models would work for the indicators provided?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A market researcher is interested in the average amount of money spent per year by college students on clothing.From 25 years of annual data,the following estimated regression was obtained through least squares: y_t = 48.75 + + + where the numbers in parentheses below the coefficients are the coefficient standard errors,and y = Expenditure per student,in dollars,on clothes x₁ = Disposable income per student,in dollars,after the payment of tuition,fees,and room and board. x₂ = Index of advertising,aimed at the student market,on clothes -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

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An economist is in the process of developing a model to predict the price of gold.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₃ + ε.A random sample of 20 daily observations was taken.The computer output is shown below. THE REGRESSION EQUATION IS y = 115.6 + 22.3x₁ + 14.7x₂ - 1.36x₁x₂ S = 20.9 R-Sq = 55.4% ANALYSIS OF VARIANCE -Interpret the coefficient b₁.

The Durbin-Watson test is used to detect:

Suppose that the sample regression equation of a model is = 10 + 2x₁ + 3x₂ - x₁x₂.If we examine the relationship between x₁ and y for four different values of x₂,we observe that the:

Suppose we want to estimate the model Y = β₀ + β₁x_1t + β₂x_2t + β₃x_3t + β₄x_4t + ε.There is reason to believe,however,that the error term is autocorrelated.How can we estimate the parameters for this regression?

From the regression results we calculate a Durbin-Watson test statistic of 1.53.What can we conclude about the possibility of autocorrelation in this model at α = 0.05?

When time-series data are analyzed,the error term represents the effect of the independent variables on the dependent variables.

Which of the following tests can be used to test autocorrelation?

What does the following plot of residuals from a regression analysis suggest?

If the value of the Durbin-Watson statistic d satisfies the inequality d_L ≤ d ≤ d_U ,where d_L and d_U are the critical values for d,then the test for positive first-order autocorrelation is inconclusive.

Suppose a scatter plot of your data between X and Y looks as shown below.How might you model Y?

Suppose you are interested in examining the determinants of earnings.You have information on the age of the individual as well as their level of education: high school graduate,college graduate or graduate degree.Let Y = earnings,X₁ = age,X₂ = 1 if the person has only a high school degree and 0 otherwise,X₃ = 1 if the person has a college degree and 0 otherwise,X₄ = 1 if the person has a graduate degree and 0 otherwise.Which of the following model specifications would work for this data?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A market researcher is interested in the average amount of money spent per year by college students on clothing.From 25 years of annual data,the following estimated regression was obtained through least squares: y_t = 48.75 + + + where the numbers in parentheses below the coefficients are the coefficient standard errors,and y = Expenditure per student,in dollars,on clothes x₁ = Disposable income per student,in dollars,after the payment of tuition,fees,and room and board. x₂ = Index of advertising,aimed at the student market,on clothes -Test at the 5% level,against the obvious one-sided alternative,the null hypothesis that,all else being equal,advertising does not affect expenditures on clothes in this market.

When all the coefficient student t statistics are small,indicating no individual effect,and yet the overall F statistic indicates a strong effect for the total regression model,the model is said to be affected by:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: You are interested in examining the factors that determine the average length of stay in a hospital across states.You collect data on the following variables: Y = statewide average hospital stay X₁ = median state income X₂ = 1 if the state is in the Northeast,0 otherwise X₃ = 1 if the state is in the South,0 otherwise X₄ = 1 if the state is in the Midwest,0 otherwise X₅ = 1 if the state is in the West,0 otherwise -You run the following regression Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄.What is the additional length of stay that can be attributed to being from a state in the South?