1 EXAMPLE 15. ROBUST REGRESSION: US POPULATION DATA 1 16:48 Sunday, December 30, 2001 The NLIN Procedure Iterative Phase Dependent Variable POP Method: Gauss-Newton Weighted Iter B0 B1 B2 SS 0 20450.4 -22.7806 0.00635 57.2648 1 20711.6 -23.0689 0.00643 31.3163 2 20889.8 -23.2640 0.00648 19.7945 3 20950.2 -23.3303 0.00650 16.7549 4 20966.8 -23.3486 0.00650 16.0573 5 20971.0 -23.3531 0.00650 15.8953 6 20972.0 -23.3542 0.00650 15.8572 7 20972.2 -23.3545 0.00650 15.8482 8 20972.3 -23.3545 0.00650 15.8460 9 20972.3 -23.3546 0.00650 15.8455 NOTE: Convergence criterion met. Estimation Summary Method Gauss-Newton Iterations 9 R 7.971E-6 PPC(B0) 1.511E-7 RPC(B0) 6.374E-7 Object 0.000032 Objective 15.84552 Observations Read 19 Observations Used 19 Observations Missing 0 Sum of Mean Approx Source DF Squares Square F Value Pr > F Regression 3 122572 40857.3 30014.8 <.0001 Residual 16 15.8455 0.9903 Uncorrected Total 19 122588 Corrected Total 18 59465.9 Approx Approximate 95% Confidence Parameter Estimate Std Error Limits B0 20972.3 309.6 20315.9 21628.6 B1 -23.3546 0.3299 -24.0539 -22.6553 B2 0.00650 0.000088 0.00632 0.00669 1 EXAMPLE 15. ROBUST REGRESSION: US POPULATION DATA 2 16:48 Sunday, December 30, 2001 The NLIN Procedure Approximate Correlation Matrix B0 B1 B2 B0 1.0000000 -0.9999035 0.9996131 B1 -0.9999035 1.0000000 -0.9999029 B2 0.9996131 -0.9999029 1.0000000 1 EXAMPLE 15. ROBUST REGRESSION: US POPULATION DATA 3 16:48 Sunday, December 30, 2001 Obs YEAR POP RBI SIGMA B R _WEIGHT_ 1 1790 3.929 -1.06728 2 4.685 0.53364 0.97422 2 1800 5.308 0.38694 2 4.685 0.19347 0.99659 3 1810 7.239 1.09250 2 4.685 0.54625 0.97300 4 1820 9.638 0.96538 2 4.685 0.48269 0.97888 5 1830 12.866 0.36659 2 4.685 0.18329 0.99694 6 1840 17.069 -0.55787 2 4.685 0.27894 0.99292 7 1850 23.191 -0.86400 2 4.685 0.43200 0.98307 8 1860 31.443 -0.34080 2 4.685 0.17040 0.99736 9 1870 39.818 -0.99528 2 4.685 0.49764 0.97756 10 1880 50.155 -0.98842 2 4.685 0.49421 0.97787 11 1890 62.947 0.17277 2 4.685 0.08638 0.99932 12 1900 75.994 0.28828 2 4.685 0.14414 0.99811 13 1910 91.972 2.03413 2 4.685 1.01706 0.90797 14 1920 105.710 0.23930 2 4.685 0.11965 0.99870 15 1930 122.775 0.47080 2 4.685 0.23540 0.99496 16 1940 131.669 -8.76937 2 4.685 4.38468 0.01540 17 1950 151.325 -8.54821 2 4.685 4.27410 0.02813 18 1960 179.323 -1.28571 2 4.685 0.64286 0.96270 19 1970 203.211 0.56610 2 4.685 0.28305 0.99271