What happens when data are fitted to the wrong equation?

Abstract

In many problems of data analysis it is necessary to fit the data to a mathematical equation. Random errors of measurement will be responsible for deviations between the data and the equation, but superimposed on this there may be deviations that result from the equation being an inadequate description of the system from which the data were obtained. Plots of the residual (i.e. the difference between the experimental and calculated values of the dependent variable) against each of the experimental variables have been previously used to detect a misfit between the data and the equation. In the present paper, we show that the shape of the residual plots may be used as a guide in choosing a more appropriate equation. In addition, residual plots give useful information on the error structure of the data, and hence the weighting factors that should be used in the analysis.