Trigonometric regression?

Question

Mathematics

It is necessary to construct regression equations of the form y = a = b*sin(x). I can't find information about this anywhere. Is it really necessary to simply make the replacement t = sin (x), find the coefficients with the usual least squares, then return the sine back? How very simple.

Answer 1

Quite right. In general, least squares regression is extremely easy to derive for any formula of the form
y = A1 f1(x) + A2 f2(x) + … + Am fm(x)
provided that m pairs (x1, y1) .. are given. .(xm, ym). Unknown - A1…Am.
A little more complicated, we must remember the theory of matrices - for N > m pairs.