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For this reason, standard forms for exponential, in the case of analyzing the period of a pendulum as a function of its length. Practice to transform the data in such a way that the resulting line is a In fact, if the functional relationship between the two quantitiesīeing graphed is known to within additive or multiplicative constants, it is common The linear least squares fitting technique is the simplest and most commonly applied form of linear regression and providesĪ solution to the problem of finding the best fitting straight line throughĪ set of points. Noisy data points, the difference between vertical and perpendicular fits is quite When sums of vertical distances are used. In addition, the fitting technique can be easily generalized from a best-fit line Of the data points along the - and -axes to be incorporated simply, and also provides a much simplerĪnalytic form for the fitting parameters than would be obtained using a fit based

This provides a fitting function for the independent variable that estimates for a given (most often what an experimenter wants), allows uncertainties In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular May or may not be desirable depending on the problem at hand. Used, outlying points can have a disproportionate effect on the fit, a property which However, because squares of the offsets are Of the offset absolute values because this allows the residuals to be treated asĪ continuous differentiable quantity. The sum of the squares of the offsets is used instead A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of