Normal distribution
Assume that each data point, yk, has an error that is
independently random and distributed as a normal distribution, that is,

where σ2 is the variance, and
f(xk,p) is the expression that we want to fit.

The goal is to minimize the χ2 function:

where the weights are defined as: w≡1/σ2.
Consider the Taylor expansion of χ2:

Define the arrays
,
and
:

Linearize and the problem reduces to solving the matrix equation

Chi-square and weights
Hint for physicists
Degrees of freedom