# clx2 multiple regression SAS output by linzhengnd

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```									                         clx2: Multiple regression example
Stat 404; Fall 2011

The following program was used to generate our second class example. The original
program is saved on the class website under examples as “clx2.” In addition to the
program, this handout contains the summary statistics as provided by “proc corr,”
and the multiple regression program, as specified by the proc statement in the SAS
program.

The SAS program

Data Clx2;
input y x1 x2;
X0=1;
Cards;
2 1 7
5 2 5
4 3 6
6 4 3
8 5 4
run;
proc print; var y x0 x1 x2; run;
proc means; var y x1 x2; run;
proc corr; var y x1 x2; run;
proc reg; model y=x1; run;
proc reg; model y=x2; run;
proc reg; model y=x1 x2/p r xpx i;
output out=out1 p=p1 r=r1; run;
proc plot; plot r1*p1; run;

The CORR Procedure

Simple Statistics

Variable          N        Mean      Std Dev        Sum       Minimum      Maximum

y                 5    5.00000       2.23607      25.00000    2.00000      8.00000
x1                5    3.00000       1.58114      15.00000    1.00000      5.00000
x2                5    5.00000       1.58114      25.00000    3.00000      7.00000

Pearson Correlation Coefficients, N = 5
Prob > |r| under H0: Rho=0

y            x1              x2

y           1.00000       0.91924      -0.84853
0.0272        0.0691

x1          0.91924       1.00000      -0.80000
0.0272                      0.1041

x2         -0.84853      -0.80000       1.00000
0.0691        0.1041
The REG Procedure

The sums of squares & cross-products

Model: MODEL1

Model Crossproducts X'X X'Y Y'Y

Variable      Intercept                       x1                  x2                   y

Intercept             5                       15               25                     25
x1                   15                       55               67                     88
x2                   25                       67              135                    113
y                    25                       88              113                    145

The inverse matrix, with parameter estimates on the right and in the last row, and
with the sums of squares due to error in the lower right corner:

X'X Inverse, Parameter Estimates, and SSE

Variable          Intercept                 x1               x2                  y

Intercept    16.311111111              -1.944444444      -2.055555556            4.3888888889
x1           -1.944444444               0.2777777778      0.2222222222           0.9444444444
x2           -2.055555556               0.2222222222      0.2777777778           0.444444444
y             4.3888888889              0.9444444444      -0.444444444           2.3888888889

The resulting prediction equation with associated t-tests:

Parameter Estimates

Parameter         Standard
Variable        DF              Estimate            Error       t Value        Pr > |t|

Intercept          1             4.38889         4.41392           0.99             0.4248
x1                 1             0.94444         0.57601           1.64             0.2428
x2                 1            -0.44444         0.57601          -0.77             0.5211

And the resulting ANOVA table with associated F-test:

Analysis of Variance

Sum of              Mean
Source                      DF          Squares            Square      F Value           Pr > F

Model                        2         17.61111           8.80556         7.37           0.1194
Error                        2          2.38889           1.19444
Corrected Total              4         20.00000

Root MSE                    1.09291       R-Square        0.8806
Dependent Mean              5.00000       Adj R-Sq        0.7611
Coeff Var                  21.85813

```
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