Proof of Regression Formulae

Think of an arbitrary line as being given by:

Now look at the sum of the squares of the residuals of the n points:

Use the definitions of , , and .Also use the fact that and . Then the above sum of squares becomes

Because squares are always non-negative, this sum is minimized when and . In other words, the line minimizing the sum of the squares of the residuals is

in agreement with our usual formulas.

-- Main.ahb2 - 26 Sep 2007

+