Refer to Advertising agency Problem 12.13. Assume that regression model (12.1) is applicable.
a. Use the Hildreth-Lu procedure to obtain a point estimate of the autocorrelation parameter. Do a search at the values p = .1, .2, ... , 1.0 and select from these the value of p that minimizes SSE.
b. Based on your estimate in part (a), obtain an estimate of the transformed regression function (12.17). Also obtain 
c. Test whether any positive autocorrelation remains in the transformed regression model; use α = .01. State the alternatives, decision rule, and conclusion.
d. ,Restate the estimated regression function obtained in part (b) in terms of the original .variables. Also obtain s{bo} and s{b1}. Compare the estimated regression coefficients obtained with the Hildreth-Lu procedure and their estimated standard deviations with those obtained with ordinary least squares in Problem 12.13a.
e. Based on the results in parts (c) and (d), has the Hildreth-Lu procedure been effective here?
f. Staff time in month 21 is expected to be 3.625 thousand hours. Predict the amount of billings in constant dollars for month 21, using a 99 percent prediction interval. Interpret your interval.
g. Estimate ß1 with a 99 percent confidence interval. Interpret your interval.
Problem 12.13
Advertising agency. The managing partner of an advertising agency is interested in the possibility of making accurate predictions of monthly billings. Monthly data on amount of billings (Y. in thousands of constant dollars) and on number of hours of staff time (X, in thousand hours) for the 20 most recent months follow. A simple linear regression model is believed to be appropriate. but positively autocorrelated error terms may be present.
a. Fit a simple linear regression model by ordinary least squares and obtain the residuals. Also obtain s{bo} and s{bi}.
b. Plot the residuals against time and explain whether you find any evidence of positive autocorrelation.
c. Conduct a formal test for positive autocorrelation using α = .01. State the alterative, decision rule. and conclusion. b the residual analysis in part (b) in accord with the test result?