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Regression with Autocorrelated Errors
U.S. Wine Consumption and Adult Population – 1934-2002
Data Description
• Y=U.S. Annual Wine Consumption (Millions of Gallons)
• X=U.S. Adult Population (Millions of People)• Years – 1934-2002 (Post Prohibition)• Model:
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Regression StatisticsMultiple R 0.965612383R Square 0.932407274Adjusted R Square 0.931398427Standard Error 48.64438813Observations 69
ANOVAdf SS MS F Significance F
Regression 1 2186985.91 2186985.91 924.23 0.0000Residual 67 158540.53 2366.28Total 68 2345526.43
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept -347.9736 21.9895 -15.8245 0.0000 -391.8649 -304.0824apop_m 4.3092 0.1417 30.4012 0.0000 4.0263 4.5921
present isation Autocorrel
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SAS Proc Autoreg Output The AUTOREG Procedure Dependent Variable wine Ordinary Least Squares Estimates SSE 158540.525 DFE 67 MSE 2366 Root MSE 48.64439 SBC 738.318203 AIC 733.84999 Regress R-Square 0.9324 Total R-Square 0.9324 Durbin-Watson 0.1199
Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 -347.9736 21.9895 -15.82 <.0001 adpop 1 4.3092 0.1417 30.40 <.0001
Estimates of Autocorrelations Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 2297.7 1.000000 | |********************| 1 2147.9 0.934807 | |******************* |
SAS Proc Autoreg Output
Preliminary MSE 289.8
Estimates of Autoregressive Parameters Standard Lag Coefficient Error t Value 1 -0.934807 0.043717 -21.38
Yule-Walker Estimates SSE 18516.1612 DFE 66 MSE 280.54790 Root MSE 16.74956 SBC 596.454422 AIC 589.752103 Regress R-Square 0.5702 Total R-Square 0.9921 Durbin-Watson 1.6728
Standard Approx Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -347.2297 74.0420 -4.69 <.0001 adpop 1 4.2540 0.4546 9.36 <.0001
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