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Remarks on fitting functions to data. (English)
PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 8, No. 4, 289-304 (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. (Authors’ abstract)
Classification: K85
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