If I have the model Y= B_0 + B_1X+ U

and both Y and X are dummy variables and I'm ask to find the OLS estimators for B0 and B1, are there any differences to how I would approach this compared to if it were a regular model?

I would still be trying to minimize the sum of the squared residuals, so I would take the derivative of u^2 WRT to B_0 and B_1 and set them each equal to zero, but in this case since both y and X can only take on values of 1 and 0 how would that work?

thanks!