EXAMPLE 6. SERIALLY CORRELATED ERRORS: EXPENDITURE DATA 1 15:09 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 6395.17034 6395.17034 402.34 <.0001 Error 18 286.10716 15.89484 Corrected Total 19 6681.27750 Root MSE 3.98683 R-Square 0.9572 Dependent Mean 243.47500 Adj R-Sq 0.9548 Coeff Var 1.63747 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 -154.95464 19.88340 -7.79 <.0001 X 1 2.30180 0.11475 20.06 <.0001 EXAMPLE 6. SERIALLY CORRELATED ERRORS: EXPENDITURE DATA 2 15:09 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Durbin-Watson D 0.326 Number of Observations 20 1st Order Autocorrelation 0.752 EXAMPLE 6. SERIALLY CORRELATED ERRORS: EXPENDITURE DATA 3 15:09 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Dep Var Predicted Std Error Std Error Student Obs Y Value Mean Predict Residual Residual Residual 1 214.6000 211.7217 1.8168 2.8783 3.549 0.811 2 217.7000 216.0951 1.6303 1.6049 3.638 0.441 3 219.6000 219.7780 1.4800 -0.1780 3.702 -0.0481 4 227.2000 223.9212 1.3210 3.2788 3.762 0.872 5 230.9000 226.9136 1.2151 3.9864 3.797 1.050 6 233.3000 231.5172 1.0724 1.7828 3.840 0.464 7 234.1000 232.4379 1.0476 1.6621 3.847 0.432 8 232.3000 235.6604 0.9729 -3.3604 3.866 -0.869 9 233.7000 237.5018 0.9399 -3.8018 3.874 -0.981 10 236.5000 240.0338 0.9078 -3.5338 3.882 -0.910 11 238.7000 245.3279 0.8963 -6.6279 3.885 -1.706 12 243.2000 250.3919 0.9559 -7.1919 3.871 -1.858 13 249.4000 254.7653 1.0543 -5.3653 3.845 -1.395 14 254.3000 257.2973 1.1268 -2.9973 3.824 -0.784 15 260.9000 259.8293 1.2081 1.0707 3.799 0.282 16 263.3000 261.9009 1.2801 1.3991 3.776 0.371 17 265.6000 263.0518 1.3219 2.5482 3.761 0.677 18 268.2000 265.1234 1.3998 3.0766 3.733 0.824 19 270.4000 266.9648 1.4718 3.4352 3.705 0.927 20 275.6000 269.2666 1.5646 6.3334 3.667 1.727 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | |* | 0.086 2 | | | 0.020 3 | | | 0.000 4 | |* | 0.047 5 | |** | 0.056 6 | | | 0.008 7 | | | 0.007 8 | *| | 0.024 9 | *| | 0.028 10 | *| | 0.023 11 | ***| | 0.077 12 | ***| | 0.105 13 | **| | 0.073 14 | *| | 0.027 15 | | | 0.004 16 | | | 0.008 EXAMPLE 6. SERIALLY CORRELATED ERRORS: EXPENDITURE DATA 4 15:09 Tuesday, August 14, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y Output Statistics Cook's Obs -2-1 0 1 2 D 17 | |* | 0.028 18 | |* | 0.048 19 | |* | 0.068 20 | |*** | 0.272 Sum of Residuals 0 Sum of Squared Residuals 286.10716 Predicted Residual SS (PRESS) 346.61946 EXAMPLE 6. SERIALLY CORRELATED ERRORS: EXPENDITURE DATA 5 15:09 Tuesday, August 14, 2001 The AUTOREG Procedure Dependent Variable Y Ordinary Least Squares Estimates SSE 286.107155 DFE 18 MSE 15.89484 Root MSE 3.98683 SBC 115.961689 AIC 113.970224 Regress R-Square 0.9572 Total R-Square 0.9572 Durbin-Watson 0.3259 Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 -154.9546 19.8834 -7.79 <.0001 X 1 2.3018 0.1148 20.06 <.0001 Estimates of Autocorrelations Lag Covariance Correlation 0 14.3054 1.000000 1 10.7646 0.752489 Estimates of Autocorrelations Lag -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 0 | |********************| 1 | |*************** | Preliminary MSE 6.2051 Estimates of Autoregressive Parameters Standard Lag Coefficient Error t Value 1 -0.752489 0.159735 -4.71 EXAMPLE 6. SERIALLY CORRELATED ERRORS: EXPENDITURE DATA 6 15:09 Tuesday, August 14, 2001 The AUTOREG Procedure Yule-Walker Estimates SSE 94.7508078 DFE 17 MSE 5.57358 Root MSE 2.36084 SBC 97.6903646 AIC 94.7031678 Regress R-Square 0.9024 Total R-Square 0.9858 Durbin-Watson 1.2601 Standard Approx Variable DF Estimate Error t Value Pr > |t| Intercept 1 -158.2802 32.1269 -4.93 0.0001 X 1 2.3273 0.1856 12.54 <.0001 EXAMPLE 6. SERIALLY CORRELATED ERRORS: EXPENDITURE DATA 7 15:09 Tuesday, August 14, 2001 The ARIMA Procedure Name of Variable = YRES Mean of Working Series -0.11748 Standard Deviation 2.173416 Number of Observations 20 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 4.723738 1.00000 | |********************| 1 1.384450 0.29308 | . |****** . | 2 0.729899 0.15452 | . |*** . | 3 1.157981 0.24514 | . |***** . | 4 -0.633916 -.13420 | . ***| . | 5 0.410983 0.08700 | . |** . | "." marks two standard errors Inverse Autocorrelations Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 1 -0.41025 | .********| . | 2 0.14361 | . |*** . | 3 -0.29667 | . ******| . | 4 0.31738 | . |****** . | 5 -0.15071 | . ***| . | Partial Autocorrelations Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 1 0.29308 | . |****** . | 2 0.07507 | . |** . | 3 0.19941 | . |**** . | 4 -0.29637 | . ******| . | 5 0.20969 | . |**** . |