The SAS System The REG Procedure Model: MODEL1 Dependent Variable: consume Number of Observations Read 69 Number of Observations Used 69 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 4.80557 2.40278 712.27 <.0001 Error 66 0.22264 0.00337 Corrected Total 68 5.02821 Root MSE 0.05808 R-Square 0.9557 Dependent Mean 1.76999 Adj R-Sq 0.9544 Coeff Var 3.28143 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 4.61171 0.15262 30.22 <.0001 income 1 -0.11846 0.10885 -1.09 0.2804 price 1 -1.23174 0.05024 -24.52 <.0001 The SAS System The REG Procedure Model: MODEL1 Dependent Variable: consume Durbin-Watson D 0.247 Number of Observations 69 1st Order Autocorrelation 0.852 The SAS System Plot of e*year. Legend: A = 1 obs, B = 2 obs, etc. | 0.15 + | | | | | A | 0.10 + A | AA | AA | A | A | AAA | A A 0.05 + A A | A | A A AA A R | A A e | AA B A s | B A A i | AA A d 0.00 + A A u | A A AA a | BA A l | A A A | A | A A AA | A -0.05 + A A | A | A | B A | A B | A A | -0.10 + | A | | | | A A | -0.15 + ---+---------+---------+---------+---------+-- 1860 1880 1900 1920 1940 year AR(3) Errors The AUTOREG Procedure Dependent Variable consume Ordinary Least Squares Estimates SSE 0.22264448 DFE 66 MSE 0.00337 Root MSE 0.05808 SBC -187.28786 AIC -193.99018 Regress R-Square 0.9557 Total R-Square 0.9557 Durbin-Watson 0.2470 Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 4.6117 0.1526 30.22 <.0001 income 1 -0.1185 0.1089 -1.09 0.2804 price 1 -1.2317 0.0502 -24.52 <.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 0.00323 1.000000 | |********************| 1 0.00275 0.852331 | |***************** | 2 0.00238 0.737127 | |*************** | 3 0.00202 0.627529 | |************* | Preliminary MSE 0.000880 Estimates of Autoregressive Parameters Standard Lag Coefficient Error t Value 1 -0.820472 0.125912 -6.52 2 -0.067388 0.162687 -0.41 3 0.034699 0.125912 0.28 AR(3) Errors The AUTOREG Procedure Yule-Walker Estimates SSE 0.04564309 DFE 63 MSE 0.0007245 Root MSE 0.02692 SBC -282.62851 AIC -296.03315 Regress R-Square 0.8124 Total R-Square 0.9909 Durbin-Watson 1.7332 Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 3.7940 0.2606 14.56 <.0001 income 1 0.2194 0.1436 1.53 0.1316 price 1 -1.1635 0.0746 -15.61 <.0001 AR(2) Errors The AUTOREG Procedure Dependent Variable consume Ordinary Least Squares Estimates SSE 0.22264448 DFE 66 MSE 0.00337 Root MSE 0.05808 SBC -187.28786 AIC -193.99018 Regress R-Square 0.9557 Total R-Square 0.9557 Durbin-Watson 0.2470 Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 4.6117 0.1526 30.22 <.0001 income 1 -0.1185 0.1089 -1.09 0.2804 price 1 -1.2317 0.0502 -24.52 <.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 0.00323 1.000000 | |********************| 1 0.00275 0.852331 | |***************** | 2 0.00238 0.737127 | |*************** | Preliminary MSE 0.000881 Estimates of Autoregressive Parameters Standard Lag Coefficient Error t Value 1 -0.819120 0.124905 -6.56 2 -0.038965 0.124905 -0.31 AR(2) Errors The AUTOREG Procedure Yule-Walker Estimates SSE 0.04567681 DFE 64 MSE 0.0007137 Root MSE 0.02672 SBC -286.81528 AIC -297.98581 Regress R-Square 0.8071 Total R-Square 0.9909 Durbin-Watson 1.7211 Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 3.7867 0.2615 14.48 <.0001 income 1 0.2152 0.1440 1.49 0.1400 price 1 -1.1565 0.0748 -15.46 <.0001 AR(1) Errors The AUTOREG Procedure Dependent Variable consume Ordinary Least Squares Estimates SSE 0.22264448 DFE 66 MSE 0.00337 Root MSE 0.05808 SBC -187.28786 AIC -193.99018 Regress R-Square 0.9557 Total R-Square 0.9557 Durbin-Watson 0.2470 Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 4.6117 0.1526 30.22 <.0001 income 1 -0.1185 0.1089 -1.09 0.2804 price 1 -1.2317 0.0502 -24.52 <.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 0.00323 1.000000 | |********************| 1 0.00275 0.852331 | |***************** | Preliminary MSE 0.000883 Estimates of Autoregressive Parameters Standard Lag Coefficient Error t Value 1 -0.852331 0.064870 -13.14 Yule-Walker Estimates SSE 0.04617817 DFE 65 MSE 0.0007104 Root MSE 0.02665 SBC -290.29919 AIC -299.23562 Regress R-Square 0.8084 Total R-Square 0.9908 Durbin-Watson 1.7899 AR(1) Errors The AUTOREG Procedure Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 3.8170 0.2595 14.71 <.0001 income 1 0.2050 0.1442 1.42 0.1600 price 1 -1.1610 0.0747 -15.54 <.0001