Refer to Microcomputer components Problem 12.9. 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 ρ = .1, .2, ... ,1.0 and select from these the value of ρ that minimizes SSE.
b. From your estimate in part (a), obtain an estimate of the transformed regression function
c. Test whether any positive autocorrelation remains in the transformed regression model; use α = .05. 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 12.9a
e. Based on the results in parts (c) and (d), has the Hildreth-Lu procedure been effective here?
f. The value of industry production in month 17 will be $2.210 million. Predict the value of the firm's components used in month 17; employ a 95 percent prediction interval Interpret your interval.
g. Estimate ß1, with a 95 percent confidence interval. Interpret your interval
Problem 12.9
Microcomputer components. A staff analyst for a manufacturer of microcomputer components has compiled monthly data for the past 16 months on the value of industry production of processing units that use these components (X, in million dollars) and the value of the firm's components used (Y. in thousand dollars). The analyst believes that a simple linear regression relation is appropriate but anticipates positive autocorrelation. The data follow:
a. Fit a simple linear regression model by ordinary least squares and obtain the residuals. Also obtain s{bo} and s{b1}.
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 = .05. State the alternatives, decision rule, and conclusion. Is the residual analysis in part (b) in accord with the test result?