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Communications of the ACM

Communications of the ACM

A short method for measuring error in a least-squares power series

When fitting a curve to a set of points by means of a least-squares powers series, it is frequently desirable to obtain also a measure of the total error of the curve. Such error is most often measured by the size of the residual sum of squares and, while it is not infrequent for computer programs to provide this error sum along with the coefficients of the power series, in every case we have so far found this sum has been obtained by evaluating the series at every data point. This procedure requires that either the data be read through the machine a second time after the determination of the coefficients or that every data point be stored in the memory of the computer.

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