What is the criteria for choosing β values according to ordinary least squares?

Answer 1

y= Xß + µ so µ'µ=(y-Xß)'(y-Xß)

so minimize this by choosing beta to satisfy ∂µ'µ/∂ß = 0

or X'Y-X'Xß = 0 or X'Xß=X'Y or (X'X)^-1(X'X)ß=(X'X)^-1X'Y which is the OLS estimator