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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.

*) 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


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
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.