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For the trigonometric data fit, the data should represent a periodic function,
and the x data should be scaled so that values between 0 and 1 are proportional
to 2 Pi radians (or 360 degrees).
For both types of regression, the choice of degree and the evaluation of the
fit's quality depend on judgments that are left up
to the user. It is well known about this class of regression method that an
effort to squeeze more correlation out of the algorithm than the data can
support will produce an
out-of-control function that, although it fits the data points, wanders
wherever it pleases between those points. Therefore, a good correlation
coefficient is not enough to assure a well-behaved or meaningful function. The
decision about the result's appropriateness is left entirely to the user.
The optimal fit is that in which the degree of the equation is equal to the
number of data pairs minus one.
For those seeking a standard two-element linear regression, select polynomial
type fit and degree 1
below, and for the standard form:
, b corresponds to be the first parameter listed in the results window below,
and m to the
second.
To change data, simply type in the new data below, then press "Solve." To change the degree of the equation, press one of the provided arrow buttons.
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Polynomial/Trig Regression Data Fit
For the trigonometric option, this is the resulting regression series:
