So I'm doing a simulation exercise where I had to make the error time be correlated with the independent variable X and see what happens to the empirical distribution. So I changed my code from this :
data samples;
do samp = 1 to 1000;
do t = 1 to 100;
u = rannor(1996)*5;
x = 100 + 3*rannor(6991);
y = 10 + 0.5*x + u;
output;
end;
end;
run;
to this:
data samples;
do samp = 1 to 1000;
do t = 1 to 100;
u = rannor(1996)*5;
x = 100 + 3*rannor(6991) + 0.3*u;
y = 10 + 0.5*x + u;
output;
end;
end;
run;
Then I'm supposed to figure out of the model satisfies the assumption that E(U|X) = 0. To do this I have to run a single regression using only the first sample by putting WHERE SAMP=1 after the proc reg statement. Then I have to pull out the residuals and the predicted values of Y. Then I need t do a proc contents on the staset and have X,Y, Yhat, u and uhat in it. Then I need to calculate the correlation between X and uhat. I'm so confused how to go about this. Here is all my code if you guys can please help, thanks.
data samples;
do samp = 1 to 1000;
do t = 1 to 100;
u = rannor(1996)*5;
x = 100 + 3*rannor(6991) + 0.3*u;
y = 10 + 0.5*x + u;
output;
end;
end;
run;
proc corr;
where samp=1;
var x y u;
run;
proc reg data=samples outest=bvalues outseb noprint;
by samp;
model y = x;
run;
data one two;
set bvalues;
if _type_ ='PARMS' then output one;
else if _type_ ='SEB' then output two;
run;
proc sql;
create table mystuff
as select one.intercept as b0hat, one.x as b1hat,
two.intercept as seb0, two.x as seb1
from one, two
where one.samp = two.samp;
quit;
proc means data=mystuff;
var b0hat b1hat;
run;
proc univariate data=mystuff noprint;
var b0hat b1hat;
histogram / normal;
run;
proc reg data=samples WHERE SAMP=1 noprint;
by samp;
model y = x;
run;
