I have to change my code so that my error term no longer has a mean of zero, confused how?

[khalillx]

In my simulation exercise I have to change the error term in my code from 

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 

data samples;
do samp = 1 to 1000;
do t = 1 to 100;
u = 3 + rannor(1996)*5;
x = 100 + 3*rannor(6991);
y = 10 + 0.5*x + u;
output;
end;
end;
run;

Then I'm supposed to comment on the changes to the mean and variance of B1hat and B0hat. But the only thing that changed was the intercept's mean increased by 3. Not sure why. I thought a lot would change if I made the error code have a mean of 3 instead of a mean of zero. Am I doing something wrong with the code? The shape of the histogram for both B1hat and B0hat are still symmetric as well. I'm super confused.

[Reeza]

Do the algebra. Take your initial equation, plug in the changes and simplify the equation. https://www.reddit.com/r/statistics/comments/amg02y/what_happens_if_the_mean_of_the_error_term_u_is/...

[PaigeMiller]

You don't state that you are performing linear regression (are you?), but if you are, then the mean of the residuals is always zero. This is just plain old algebra, and there's no way to get any other mean of the residuals.