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