SAS PROGRAMMING
                                           HANDOUT #25

     PROC IML is a interactive matrix language that contains lots of matrix functions,
SAS functions, and various programming statements.   This handout uses PROC IML to
perform usual linear regression.



DATA DRAPER;
 INPUT X1 X2 X3 X4 Y;
CARDS;
7 26 6 60 78.5
1 29 15 52 74.3
11 56 8 20 104.3
11 31 8 47 87.6
7 52 6 33 95.9
11 55 9 22 109.2
3 71 17 6 102.7
1 31 22 44 72.5
2 54 18 22 93.1
21 47 4 26 115.9
1 40 23 34 83.8
11 66 9 12 113.3
10 68 8 12 109.4

PROC IML;
 USE DRAPER;
 READ ALL INTO XX;                         *this makes a matrix out of a data set;
 Y=XX[,5];  N=NROW(XX);  R=NCOL(XX);
 ONE=SHAPE(1,N,1);
 X=ONE||XX[,1:4];
 BETA=INV(X`*X)*X`*Y;
 SIGMA=SQRT((Y-X*BETA)`*(Y-X*BETA)/(N-R));
 SE=SIGMA*SQRT(VECDIAG(INV(X`*X)));
 TVALUE=BETA/SE;
 PVALUE=(1-PROBT(ABS(TVALUE),N-R))*2;
 FINAL=BETA||SE||TVALUE||PVALUE;
 PRINT FINAL (|colname={ESTIMATE SE TVALUE PVALUE}
              rowname={INTERCPT X1 X2 X3 X4} FORMAT=8.4|);

 CREATE LAST FROM FINAL;                   *this creates a SAS data set from a matrix;
 APPEND FROM FINAL;

PROC PRINT DATA=LAST;
RUN;
PROC REG DATA=DRAPER;
 MODEL Y=X1 X2 X3 X4;
RUN;

                          FINAL    ESTIMATE       SE   TVALUE   PVALUE

                          INTERCPT  62.4054  70.0710   0.8906   0.3991
                          X1         1.5511   0.7448   2.0827   0.0708
                          X2         0.5102   0.7238   0.7049   0.5009
                          X3         0.1019   0.7547   0.1350   0.8959
                          X4        -0.1441   0.7091  -0.2032   0.8441


                      OBS        COL1      COL2       COL3        COL4

                        1      62.4054    70.0710     0.89060    0.39913
                        2       1.5511     0.7448     2.08266    0.07082
                        3       0.5102     0.7238     0.70486    0.50090
                        4       0.1019     0.7547     0.13503    0.89592
                        5      -0.1441     0.7091    -0.20317    0.84407