Fitting Experimental Data Using the Method of Least Squares

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Abstract
With a view toward facilitating proper use of computer curve-fitting programs, the method of least squares for fitting smooth curves to experimental data is discussed. The distinction between the problem when the functional form of the data is known, and when it is not known, is emphasized. For the latter case, the usual procedure of using an expansion having M linear coefficients to represent the functional form is considered. In making such a fit, care must be exercised in choosing M. Although the least-squares sum decreases as M is increased (tending to zero as M approaches N, the number of data points), the resulting fit is not necessarily a better representation of the data. It is shown that, in the extreme case where M=N, the least-squares fit is identical to a linear expansion which is constrained to pass through every point, and such a fit is, of course, meaningless. Tests for the statistical significance of fits are discussed.

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