Regression with Autocorrelated Errors U.S. Wine Consumption and Adult Population –

Data Description Y=U.S. Annual Wine Consumption (Millions of Gallons) X=U.S. Adult Population (Millions of People) Years – (Post Prohibition) Model:

Ordinary Least Squares Regression

Covariance Structure (q=1)

Generalized Least Squares (q=1)

Estimated GLS (q=1)

Estimated GLS (q=1) – Wine/Population Data

Estimated GLS (General q) - I

Estimated GLS (General q) - II

SAS Proc Autoreg Output The AUTOREG Procedure Dependent Variable wine Ordinary Least Squares Estimates SSE DFE 67 MSE 2366 Root MSE SBC AIC Regress R-Square Total R-Square Durbin-Watson Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept <.0001 adpop <.0001 Estimates of Autocorrelations Lag Covariance Correlation | |********************| | |******************* |

SAS Proc Autoreg Output Preliminary MSE Estimates of Autoregressive Parameters Standard Lag Coefficient Error t Value Yule-Walker Estimates SSE DFE 66 MSE Root MSE SBC AIC Regress R-Square Total R-Square Durbin-Watson Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept <.0001 adpop <.0001