Re:Ask HN: What is your favorite equation?
by harpocrates on Saturday December 24, 2016 @01:19AM
(#13248860)
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
[1] https://isites.harvard.edu/fs/docs/icb.topic515975.files/OLS...
Re:Ask HN: What is your favorite equation?
by latenightcoding on Saturday December 24, 2016 @01:33AM
(#13248886)
Or watch this video:
https://www.youtube.com/watch?v=Y_Ac6KiQ1t0
One of my favourite math lectures.
used to find the line of best fit.
The first time I saw it I was in high school and I was watching Andrew Ng's machine learning class for the first time. My Math background was not the best and I didn't fully understand it until a couple of years later when I took MIT's free online course on linear algebra (OCW 18.06)