from the desk of stinkpot

let’s say you’ve got 2 vectors (x,y) who are linearly related according to the relation: y = mx + b. you’d like to use matlab to find m and b.

this can be done with one line of linear algebra in matlab.

first, consider the equation y = mx + b: you can imagine rewriting this in linear algebra as [X_i 1_i]*[m b] = y_i, where _i denotes a vector with i items. If we let A = [m b], r = [X 1], and s = y, we have the familiar linear algebra form: Ar = s. To solve, all we need is A = r^-1*s.

In matlab-speak:

>> A = pinv([x ones(size(x))])*y

[note that since r is usually not square, we need to use matlab's pseudo-inverse function.]