Exam 13: Additional Topics in Regression Analysis

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 -Briefly discuss what is meant by the "dummy variable trap".

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 -Suppose that the true linear model for a process was Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ and you incorrectly estimated the model y = α + α₁X₂.Discuss the bias that results from using the second model.

Kurt is trying to regress a model that studies market prices between similar products from different companies.During his study he realized that one of the independent variables,the competitor's price,was causing multicollinearity issues with the model.If Kurt removes the variable from the model,which of the following statistical phenomenon could affect Kurt's model?

The model y_t = 8 + 2.1x_t + 0.25y_t-1 is estimated using regression analysis applied to time-series data.What is the effect of a 1-unit increase in x in period (t + 1)?

Consider the following model: Y_t = β₀ + β₁x_1t + β₂x_2t + β₃₃x_3t + γ₄Y_t-1.Suppose we increase X₁ by one unit in time period t with all other independent variables in the model held fixed.What is the total expected increase in the dependent variable over all current and future time periods?

In a regression model such as y = β₀ + β₁X₁ + β₂X₂ + ε,if changes in x₁ and x₂ happen simultaneously,the model is said to be affected by:

When measuring experimental outcomes,a(n)________ variable represents a variable whose effect is crucial in estimating using minimum variance.

Which of the following is true of the value of the Durbin-Watson statistic,d,when there is positive correlation?

Write the model specification and define the variables for a multiple regression model to predict earnings as a function of age and level of education: high school graduate,college graduate,master degree or doctorate degree.

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 -With advertising held fixed,what would be the expected impact over time of a $1 increase in disposable income per student on clothing expenditure?

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 negative first-order autocorrelation given that: Durbin-Watson Statistic d = 1.75,n = 20,k = 2,and α = 0.01.

If the Durbin-Watson statistic has a value close to 0 or 4,which assumption is violated?

Explain what is meant by autocorrelated errors.What effects does autocorrelation have on the results of a regression?

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

The estimated standard deviation of the slope coefficients is influenced directly by the spread of the independent variables and the correlations between independent variables.

If the Durbin-Watson statistic,d,is found to be 2,which of the following would be considered true?

The model y_t = 12 + 2.4x_t + 0.5y_t-1 is estimated using regression analysis applied to time-series data.What is the effect of a 1-unit increase in x in period (t + 2)?

The coefficients can be easily estimated if the independent variables are perfectly correlated.

Suppose that the estimated regression equation of a College of Business graduates is given by: = 32,000 + 4,000x + 1,800D,where y is the starting salary,x is the grade point average and D is a dummy variable which takes the value of 1 if the student is a finance major and 0 if not.An accountancy major graduate with a 3.5 grade point average would have an average starting salary of:

Which of the following is the similarity between how heteroscedasticity and autocorrelations occur?