Question

What is the general formate for the equation of a least-squares regression line?

Answer 1

Equation for least-squares linear regression:

`y = m x + b`

where
`m = (sum(x_iy_i) - (sum x_i sum y_i)/n)/(sum x_i^2 -((sum x_i)^2)/n)`

and
`b = (sum y_i - m sum x_i)/n`

for a collection of `n` pairs `(x_i,y_i)`

This looks horrible to evaluate (and it is, if you are doing it by hand); but using a computer (with, for example, a spreadsheet with columns :`y, x, xy, and x^2`) it isn't too bad.