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*From*: John Denker <jsd@av8n.com>*Date*: Tue, 28 Aug 2012 22:19:49 -0700

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.

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