Employee salaries. A group of high-technology companies agreed to share employee salary information in an effort to establish salary ranges for technical positions in research and development. Data obtained for each employee included current salary (Y), a coded variable indicating highest academic degree obtained (1 = bachelor's degree, 2 = master's degree; 3 = doctoral degree), years of experience since last degree (X3), and the number of persons currently supervised (X4). The data follow.
a. Create two indicator variables for highest degree attained:
b. Regress Yon XI. X2. X3 and X4, using a first-order model and ordinary least squares obtain the residuals. and plot them against Y. What does the residual plot suggest?
c. Divide the cases into two groups, placing the 33 cases with the smallest fitted values
. into group I and the other 32 cases into group 2. Conduct the Brown-Forsythe test fi I constancy of the error variance, using α = .0 I. State the decision rule and conclusion.
d. Plot the absolute residuals against X3 and against X4. What do these plots suggest about the relation between the standard deviation of the error term and X3 and X4?
e. Estimate the standard deviation function by regressing the absolute residuals against X3 and X4 In first-order form, and then calculate the estimated weight for each case using (11.16a)
f. Using the estimated weights, obtain the weighted least squares lit of the regression model Are the weighted least squares estimates of the regression coefficients similar to the one' obtained with ordinary least squares in part (b)?
h. Iterate the steps in parts (e) and (f) one more time. Is there a substantial change in the estimated regression coefficients? If so, what should you do?