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[Phys-L] linear least squares fitting : polynomials, Fourier series, et cetera




The linest(...) spreadsheet function is often used for finding a “trend line” ...
but it is capable of doing much more than that. I wrote up a web page discussing
the details.
http://www.av8n.com/physics/linear-least-squares.htm

*) It can find the coefficients of the best-fit quadratic.
An example of this is given in section 3.
*) It can also handle higher-order polynomials.
*) It can find the coefficients of the best-fit Fourier series.
An example of this is given in section 5.
*) More generally, it can fit to an arbitrary linear combination of basis
functions, using whatever basis functions you choose.

It must be emphasized that the fitted function is a linear combination
of the basis functions, but the basis functions do not need to be
linear functions of X.

There is also an example spreadsheet, including the quadratic and Fourier
examples.
http://www.av8n.com/physics/linear-least-squares.xls

======================

I mention it in this forum because anybody who wants to do physics needs
to be proficient with least-squares fitting. Fitting a straight trend-line
is the first baby step, and the non-straight examples discussed here are
the next step.

There is a whole lot more to the story, but these are some useful initial
steps in the right direction.

Also note that for many students, the barrier to using a spreadsheet is much
lower than the barrier to using an imperative computer language such as C++.

=======

The same web document
http://www.av8n.com/physics/linear-least-squares.htm
contains a digression that discusses "array constants" and also the
get.formula(...) function, both of which are useful and IMHO not as
widely known as they should be.