Interpolation Equation

[Albert Chan]

Linear regression line minimize Mean Squared Error (MSE)
For 2 points, it is the same as the secant line. (MSE = 0)

Proof: from secant line, we can get regression line formula.

a * x1 + b = y1      ... (1)
a * x2 + b = y2      ... (2)

(1) * x1 + (2) * x2:

a * (x1²+x2²) + b * (x1+x2) = (y1*x1 + y2*x2)      ... (3)

(1) + (2):

a * (x1+x2) + 2 * b = (y1+y2)      ... (4)

(3) and (4) are exactly n=2 linear regression formula.