Laboratory 5
Regression Assumptions & Multicollinearity
Assumption Checking
Random sampling to get X1 (n=30) and E (n=30) from a normal distribution
population, N (0,1). Let X2 = X1*X1; X3 = X1*X1*X1; Y1= X1 + X2 + X3 + E;
Y2= X1 + X2 + X3 + E². Please run the following SAS program to fit the regression
models Y1= X1 X2 X3 and Y2= X1 X2 X3. Check the assumption of multiple
regression by examining and plotting the residuals. Report and interpret the
results (both testing and graphs) for model Y2= X1 X2 X3
SAS program
title1 '*********************************************';
title2 'Assumption Checking by Henian Chen 2002-09-03';
title3 '*********************************************';
data assumption;
do i=1 to 100;
x1=rannor(0);
x2=(rannor(0))**2;
x3=(rannor(0))**3;
e=rannor(0);
y1=x1+x2+x3+e;
y2=x1+x2+x3+e**2;
output;
end;
proc reg;
model y1=x1 x2 x3/r;
plot student.*x1;
plot npp.*residual.;
output out=reg1 r=resd1;
model y2=x1 x2 x3/r;
plot student.*x1;
plot npp.*residual.;
output out=reg2 r=resd2;
data reg;
set reg1 reg2;
proc univariate normal;
var resd1 resd2;
run;
Applied Epidemiologic Analysis – P8400
Page 1
Lab5: Regression Assumptions & Multicollinearity
Henian Chen
Fall 2002
Collinearity
Random sampling to get X1 (n=30) from a normal distribution population,
N (8,2²), and e (n=30) from another normal distribution population, N (0,1).
Let X2 = 2X1 + e; Y = 3X1 + 1 + e. Please run the following SAS program to fit
the regression models Y= X1 , Y= X2 , and Y= X1 X2. Why is X2 significant in
model Y= X2, but not in model Y= X1 X2 ? Please run this program 10 times.
Make a table to record the parameter estimate, SE, and P value of the final
model for each model y=x1 x2/selection=forward. What did you learn
from this computer experiment by comparing the β and SE?
SAS program
title1 '*****************************************';
title2 ''Collinearity by Henian Chen 2002-08-26';
title3 '*****************************************';
data collinearity;
do i=1 to 30;
x1=rannor(0)*2+8;
x2=rannor(0)+x1*2;
y=rannor(0)+x1*3+1;
output;
end;
proc reg;
model y=x1;
model y=x2;
model y=x1 x2/collin collinoint vif tol;
run;
proc reg;
model y=x1 x2/selection=forward;
run;
We will practice Case-Control Analysis and Logistic regression in the next week’s
laboratory. Please bring the dataset ‘case-control978.dat’, and the SAS program
‘case-control978.sas’ for labs 6 & 7.
Applied Epidemiologic Analysis – P8400
Page 2
Lab5: Regression Assumptions & Multicollinearity
Henian Chen
Fall 2002