RIDGE REGRESSION FOR LONGLEY DATA USING SYSTAT'S MATRIX MODULE
SAT 3/13/99 9:27:46 AM SYSTAT VERSION 7.0.1 COPYRIGHT (C) 1997, SPSS INC. Welcome to SYSTAT! >matrix Current program limits: Number of MATRICES = 15. Number of row and column NAMES = 230. Number of NUMERIC data elements = 4100 (32800 bytes). Number of CHARACTER data elements = 1100 (13200 bytes). >USE 'C:\SYSTAT7\DATA\LONGLEY.SYD' SYSTAT Rectangular file C:\SYSTAT7\DATA\LONGLEY.SYD, created Tue Feb 18, 1986 at 13:56:00, contains variables: DEFLATOR GNP UNEMPLOY ARMFORCE POPULATN TIME TOTAL ********** Active Matrix: LONGLEY ********** >format 11 7 >mat y = longley(;total) ********** Active Matrix: Y ********** >mat x = longley(;deflator..time) ********** Active Matrix: X ********** >mat y = colzsc(y) ********** Active Matrix: Y ********** >mat x = colzsc(x) ********** Active Matrix: X ********** >mat xpx = trp(x)*x/(nrow(x)-1) ********** Active Matrix: XPX ********** >mat xpy = trp(x)*y/(nrow(x)-1) ********** Active Matrix: XPY ********** >sho xpx Matrix: XPX DEFLATOR GNP UNEMPLOY ARMFORCE POPULATN DEFLATOR 1.0000000 0.9915892 0.6206334 0.4647442 0.9791634 GNP 0.9915892 1.0000000 0.6042609 0.4464368 0.9910901 UNEMPLOY 0.6206334 0.6042609 1.0000000 -0.1774206 0.6865515 ARMFORCE 0.4647442 0.4464368 -0.1774206 1.0000000 0.3644163 POPULATN 0.9791634 0.9910901 0.6865515 0.3644163 1.0000000 TIME 0.9911492 0.9952735 0.6682566 0.4172451 0.9939528 TIME DEFLATOR 0.9911492 GNP 0.9952735 UNEMPLOY 0.6682566 ARMFORCE 0.4172451 POPULATN 0.9939528 TIME 1.0000000 ********** Active Matrix: XPX ********** >sho xpy Matrix: XPY DEFLATOR 0.9708985 GNP 0.9835516 UNEMPLOY 0.5024981 ARMFORCE 0.4573074 POPULATN 0.9603906 TIME 0.9713295 ********** Active Matrix: XPY ********** >mat beta = inv(xpx)*xpy ********** Active Matrix: BETA ********** >sho beta Matrix: BETA DEFLATOR 0.0462820 GNP -1.0137463 UNEMPLOY -0.5375426 ARMFORCE -0.2047407 POPULATN -0.1012211 TIME 2.4796644 ********** Active Matrix: BETA ********** >mat ridge = i(6) ********** Active Matrix: RIDGE ********** >mat betar = inv(xpx+ridge#0.01)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.02)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.03)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.04)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.05)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.06)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.07)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.08)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat betar = inv(xpx+ridge#0.09)*xpy ********** Active Matrix: BETAR ********** >mat beta = beta||betar ********** Active Matrix: BETA ********** >mat beta = trp(beta) ********** Active Matrix: BETA ********** >mat ridge = [0.0; 0.01; 0.02; 0.03; 0.04; 0.05; 0.06; 0.07; 0.08;, >0.09] ********** Active Matrix: RIDGE ********** >colname ridge = ridge ********** Active Matrix: RIDGE ********** >mat beta = beta||ridge ********** Active Matrix: BETA ********** >show beta Matrix: BETA DEFLATOR GNP UNEMPLOY ARMFORCE POPULATN TIME 0.0462820 -1.0137463 -0.5375426 -0.2047407 -0.1012211 2.4796644 0.2243909 0.3384163 -0.3012889 -0.1203120 0.0900342 0.5684712 0.2554418 0.3389921 -0.2794636 -0.1027295 0.1713698 0.4314136 0.2631998 0.3346829 -0.2623944 -0.0895991 0.2023704 0.3776147 0.2651152 0.3298206 -0.2474496 -0.0784852 0.2177420 0.3480589 0.2649235 0.3250096 -0.2339612 -0.0686880 0.2262858 0.3289198 0.2638317 0.3203945 -0.2216270 -0.0598886 0.2312827 0.3152458 0.2623252 0.3160117 -0.2102638 -0.0519009 0.2342336 0.3048190 0.2606278 0.3118634 -0.1997416 -0.0445991 0.2359194 0.2964941 0.2588520 0.3079400 -0.1899598 -0.0378905 0.2367841 0.2896178 RIDGE 0.0 0.0100000 0.0200000 0.0300000 0.0400000 0.0500000 0.0600000 0.0700000 0.0800000 0.0900000 ********** Active Matrix: BETA ********** >format >save beta Matrix: BETA has been saved. ********** Active Matrix: BETA ********** >use beta SYSTAT Rectangular file beta.SYD, created Sat Mar 13, 1999 at 09:28:56, contains variables: DEFLATOR GNP UNEMPLOY ARMFORCE POPULATN TIME RIDGE ********** Active Matrix: BETA ********** >plot deflator..time*ridge/overlay line xmin=-0.01 xmax=0.1 ymin=-1.1 ymax=2.5, > stick xlim=0 xlabel='Ridge Factor', > ylim=0 ylabel='Estimate of Beta'
Last modified 13 April 1999