I have a linear regression problem of the form
z ~ x + y + b where
x are continuous variables and
b is categorical with two levels
B. The information if a sample is
b=B got lost for all samples. However I've always got pairs of data from which I know that one of them is
A, the other one
B (in total 27 pairs). I just don't know which is which.
I want to determine if
b is a significant factor to the model and compare the strength of its effect to
So far I've been thinking about a Monte Carlo simulation randomly assigning the classes and then doing the regression analysis and evaluating the p-value and the effect strength. I will end up with a distribution of these variables. Will their median then be the most probable p-value and effect strength? I'm not sure about this. Are there better strategies?