We already know that using the criterion of either
- minimizing sum of residuals OR
- minimizing sum of the absolute value of residuals
is BAD as either of the criteria do not give a unique line. Visit these notes for an example where these criteria are shown to be inadequate.
So we use minimizing the sum of the squares of the residuals as the criterion. How can we show that this criterion gives a unique line?
The proof is given below as image files because the proof is equation intensive. I made a better resolution pdf file also.
This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com