Linear model for data that follow gaussian distribution

Question

I have a question about linear regression. We have the linear regression of input data $(X,Y)=((x_1,y_1),(x_2,y_2)...(x_n,y_n))$ is $$F=aX+b$$ a,b are factors of the linear line, $y_i$ is {-1,1}. Given the probability ofx is normalization distribution $$p(X|Y=1 ;-1,a,b) is N(\mu,\sigma)$$ How to find a,b satisfy that $$L=\sum(Y-F)^2$$ is minimum Thank you so much. Could you suggest to me the paper about that issue