Laboratory 1



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;

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.

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