For the interested: take `B` to be the matrix minimizing `(Y - XB)'(Y - XB)` (the least squares aka the "best fit"), then `B = (X'X)^-1 X'Y`. Proof: Since `B`

For the interested: take `B` to be the matrix minimizing `(Y - XB)'(Y - XB)` (the least squares aka the "best fit"), then `B = (X'X)^-1 X'Y`. Proof: Since `B` is a minimum, the derivative of the expression minimized wrt `B` must be zero (the "derivative" is taken in the matrix sense here). 0 = d/dB [ (Y - XB)'(Y - XB) ] = d/dB [ Y′Y − Y′XB − B′X′Y + B′X′XB ] = d/dB [ Y′Y − 2Y′XB + B′X′XB ] Y′XB and B′X′Y are just scalars :) = − 2Y′X + 2′X′XB Solving for `B` you get the result. [1] https://isites.harvard.edu/fs/docs/icb.topic515975.files/OLSDerivation.pdf https://isites.harvard.edu/fs/docs/icb.topic515975.files/OLS...