Exam 13: Additional Topics in Regression Analysis

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 -Suppose you model the relationship as Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₅X₅ + β₆X₆.What effect does being a business student have on hours studying each week?

The range of the values of the Durbin-Watson statistic,d is:

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

If there is a positive correlation between the error terms from adjacent time-series observations,the computed Student's t statistic for the coefficient will be large.

Which of the following distributions is used in hypothesis testing to investigate the presence of heteroscedasticity?

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

Which of the following regression diagnostic tools is used to study the possible presence of multicollinearity?

Write a model specification and define the variables for a multiple regression model to predict the medical costs as a function of employment type indicated as: professional,technical,sales,and managerial,and a function of gender indicated as male and female.Be sure to include interactive terms.

Positive correlation leads to small values of d,with 0 being the lower limit.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following model: Y = β₀ + β₁X_1t + β₂X_2t + γ₃Y_t-1.Using a sample of 36 months,we estimate this model and obtain the following results: y_t = 1.33 + 17.6x_1t + 0.94x_2t + 0.39Y_t-1 -If X₁ were to increase by 1-unit in time t,by how much would we expect Y to change over all current and future time periods as a result of this increase?

Removing an independent variable that is highly correlated with one or more other independent variables will increase the variance of the coefficient estimate.

Suppose you were to run a regression of leisure travel expenditures by households on household income.We would expect that households with low incomes do not travel much.High-income households may or may not travel much,depending on the household's preferences for travel.The results from this regression will be subject to:

Suppose the following scatter plot shows the relationship between X and Y.How might you model Y?

From the regression results we calculate a Durbin-Watson test statistic of 2.68.What can we conclude about the possibility of autocorrelation in this model at α=0.05?

In regression equations,involving several independent variables,the multicollinearity problem arises from patterns of strong intercorrelations among the independent variables.

What problems can occur when the independent variables are correlated with each other?

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. -Compute an estimate of the autocorrelation coefficient if the evidence indicates that there was autocorrelation.

If the random errors in a model are independent,then the estimated standard errors for the coefficients are biased.

When the errors in a regression model are correlated,the coefficient estimates are biased and efficient.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following data for two variables,x and y.The independent variable x represents the amount of training time (in hours)for a salesperson starting a new car dealership to adjust fully,and the dependent variable y represents the weekly sales (in $1000s). -Develop a scatter diagram for the data.Does the scatter diagram suggest an estimated regression equation of the form = b₀ + b₁x + b₂x²? Explain.