Least-squares computations

Given a set of n observations of k variables, xij , i=1, 2, ..., n, j=1, 2, ..., k, the least-squares coefficients, bj , j=1, 2, ..., k and intercept b0, in fitting a linear model can be found by solving the set of (k + 1) ‘normal’ equations:-

∑ yi = nb0 + b1

∑ xi1 + . . . + bk

∑ xik

∑ xi1yi = b0

∑ xi1 + b1

∑ x2i1 + ... + bk

∑ xi1xik

∑ xi2yi = b0

∑ xi2 + b1

∑ xi2xi1 + ... + bk

∑ xi2xik

... = ...