Refer to McGill Company sales Problem 12.17. 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 (if 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 12.170.
e. Based on the results in parts (c) and (d), has the Hildreth-Lu procedure been effective here?
f. Industry sales for quarter 21 are expected to be $18 1.0 million. Predict the McGill Company sales for quarter 21, using a 90 percent prediction interval Interpret your interval.
g. Estimate ß1, with a 90 percent confidence interval Interpret your interval.
Problem 12.17
McGill Company sales. The data below show seasonally adjusted quarterly sales for the McGill Company (Y, in million dollars) and for the entire industry (X, in million dollars) for the most recent 20 quarters
a. Would you expect the autocorrelation parameter p to be positive. negative or zero here?
b. Fit a simple linear regression model by ordinary least squares and obtain the residuals. Also obtain 
d. Conduct a formal test for positive autocorrelation using α = .01. State the alternative decision rule. and conclusion. Is the residual analysis in part (c) in accord with the test result?