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:
|
t:
|
1
|
2
|
3
|
...
|
14
|
15
|
16
|
|
Xt
|
2.052
|
2.026
|
2.002
|
...
|
2.080
|
2.102
|
2.150
|
|
Yt:
|
102.9
|
101.5
|
100.8
|
...
|
104.8
|
105.0
|
107.2
|
a. Fit a simple linear regression model by ordinary least squares and obtain the residuals. Also obtain s{b0} 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?
(Kutner 502-503)
Kutner, Michael. Applied Linear Regression Models-Revised Edtion, 4th Edition. McGraw-Hill Learning Solutions, 37994. VitalBook file.