nag_regsn_ridge (g02kbc) Example Program Results
Number of parameters used = 4
Effective number of parameters (NEP):
Ridge
Coeff. NEP
0.0000 4.0000
0.0020 3.2634
0.0040 3.1475
0.0060 3.0987
0.0080 3.0709
0.0100 3.0523
0.0120 3.0386
0.0140 3.0278
0.0160 3.0189
0.0180 3.0112
0.0200 3.0045
0.0220 2.9984
0.0240 2.9928
0.0260 2.9876
0.0280 2.9828
0.0300 2.9782
Parameter Estimates (Original scalings)
Ridge
Coeff. Intercept 1 2 3
0.0000 117.0847 4.3341 -2.8568 -2.1861
0.0020 22.2748 1.4644 -0.4012 -0.6738
0.0040 7.7209 1.0229 -0.0242 -0.4408
0.0060 1.8363 0.8437 0.1282 -0.3460
0.0080 -1.3396 0.7465 0.2105 -0.2944
0.0100 -3.3219 0.6853 0.2618 -0.2619
0.0120 -4.6734 0.6432 0.2968 -0.2393
0.0140 -5.6511 0.6125 0.3222 -0.2228
0.0160 -6.3891 0.5890 0.3413 -0.2100
0.0180 -6.9642 0.5704 0.3562 -0.1999
0.0200 -7.4236 0.5554 0.3681 -0.1916
0.0220 -7.7978 0.5429 0.3779 -0.1847
0.0240 -8.1075 0.5323 0.3859 -0.1788
0.0260 -8.3673 0.5233 0.3926 -0.1737
0.0280 -8.5874 0.5155 0.3984 -0.1693
0.0300 -8.7758 0.5086 0.4033 -0.1653
Variance Inflation Factors
Ridge
Coeff. 1 2 3
0.0000 708.8429 564.3434 104.6060
0.0020 50.5592 40.4483 8.2797
0.0040 16.9816 13.7247 3.3628
0.0060 8.5033 6.9764 2.1185
0.0080 5.1472 4.3046 1.6238
0.0100 3.4855 2.9813 1.3770
0.0120 2.5434 2.2306 1.2356
0.0140 1.9581 1.7640 1.1463
0.0160 1.5698 1.4541 1.0859
0.0180 1.2990 1.2377 1.0428
0.0200 1.1026 1.0805 1.0105
0.0220 0.9556 0.9627 0.9855
0.0240 0.8427 0.8721 0.9655
0.0260 0.7541 0.8007 0.9491
0.0280 0.6832 0.7435 0.9353
0.0300 0.6257 0.6969 0.9235
Prediction error criterion
Ridge
Coeff. 1 2 3 4 5
0.0000 8.0368 7.6879 6.1503 7.3804 8.6052
0.0020 7.5464 7.4238 6.2124 7.2261 8.2355
0.0040 7.5575 7.4520 6.2793 7.2675 8.2515
0.0060 7.5656 7.4668 6.3100 7.2876 8.2611
0.0080 7.5701 7.4749 6.3272 7.2987 8.2661
0.0100 7.5723 7.4796 6.3381 7.3053 8.2685
0.0120 7.5732 7.4823 6.3455 7.3095 8.2695
0.0140 7.5734 7.4838 6.3508 7.3122 8.2696
0.0160 7.5731 7.4845 6.3548 7.3140 8.2691
0.0180 7.5724 7.4848 6.3578 7.3151 8.2683
0.0200 7.5715 7.4847 6.3603 7.3158 8.2671
0.0220 7.5705 7.4843 6.3623 7.3161 8.2659
0.0240 7.5694 7.4838 6.3639 7.3162 8.2645
0.0260 7.5682 7.4832 6.3654 7.3162 8.2630
0.0280 7.5669 7.4825 6.3666 7.3161 8.2615
0.0300 7.5657 7.4818 6.3677 7.3159 8.2600
Key:
1 Leave one out cross-validation
2 Generalised cross-validation
3 Unbiased estimate of variance
4 Final prediction error
5 Bayesian information criterion