REMARKS ON FITTING FUNCTIONS TO DATA
Bernd Rossa, Dick Pulskamp, Danny Otero · PRIMUS · 1998
Data abounds in nature and everyday life, and follows a great variety of patterns. Different patterns are modeled by different families of functions, and several function-families have corresponding transformations which change the pattern they represent into a linear one. Some of the newer texts in precalculus and calculus, as well as widely-used calculators, seem to suggest that the “goodness of fit” be based on how well the transformed data fits a linear pattern, using the correlation coefficient of the transformed data as a measure. However, the various transformations distort the discrepancy between data and model; therefore, the goodness of fit of various models to a data set must be evaluated in the data space rather than a transformed space.