I have two groups of customers. One received a promotion another did not. I want to determine the effect of the promotion. I created a simple linear regression with a dummy variable for weekend.
$test = control + weekend$
This returned an R-Squared of .72 when applied to the pre-intervention data.
When I applied the regression to the post data I looked at the residuals and ran a two-sided T-test to see if they were statistically significantly different from 0.
I was able to reject the null. Now I have a 95% CI for the residuals of 1,000,000 and 1,300,00 and a mean of 1,100,000. My question is, can I conclude that these are unbiased estimators of the effect of the intervention? Or is the interpretation more complicated since the data comes from the residuals of a model with an R-Squared less than 1?