I am working on a data set with two time points and I am interested in the change from baseline. There are no differing treatment groups. First, I realize that this is most simply made using a paired t-test. However, I would like to adjust for baseline response.
My simple question is: Am I right to interpret the intercept term in the following model as the mean baseline adjusted change?
y= score at time2
x= score at time1
$\alpha$ = intercept
$$y - mean(x)= \alpha + \beta (x- mean(x))$$