Multiple linear regression allows modeling a dependent variable as a linear combination of multiple independent variables. The REG procedure in SAS can be used to perform multiple linear regression. It allows selection of independent variables using forward, backward, or stepwise selection methods. An example demonstrates generating simulated data with multiple independent variables and a dependent variable, then using the REG procedure with forward selection to identify a best fitting regression model.

1. REG procedure:
Multiple linear regression
2013.03.21

2. Outline
• Regression with more than one variables
• Model selection

3. Syntax
PROC REG <options> ;
MODEL dependents=<regressors> < / options > ;
RUN;
Y= X1 X2 X3 / selection=forward (backward, stepwise)

4. Example
data example;
do i=1 to 500; proc reg corr;
x1=100+20*rannor(20130321); model y=x1 x2 x3 x4/pcorr1
x2=50+20*rannor(20130321); pcorr2;
x3=(x1+x2)+5*rannor(20130321); plot residual.*predicted.;
x4=exp(3*rannor(20130321)); run;
e=20*rannor(20130321);
y=x1+3*x2+2*x3+e;
output;
end
;

5. Output

6. Output: figures

7. Example
proc reg corr;
model y=x1 x2 x3 x4/pcorr1 pcorr2 selection=forward;
plot residual.*predicted.;
run;

8. Forward selection

9. Summary

10. Stepwise & backward selection

11. Example 2
Data;
…
X5=x1*x2;
…
;
proc reg corr;
model y=x1 x2 x3 x4 x5/pcorr1 pcorr2 selection=forward;
plot residual.*predicted.;
run;

12. Selection result