Lack of fit in linear regression considering errors in both axes

Testing for lack of fit of the experimental points to the regression line is an important step in linear regression. When lack of fit exists, standard deviations for both regression line coefficients are overestimated, and this gives rise, for instance, to confidence intervals that are too large. If these confidence intervals are then used in hypothesis tests, bias may not be detected so there is a greater probability of committing a β error. In this paper, we present a statistical test, which analyses the variance of the residuals from the regression line whenever the data to be handled have errors in both axes. The theoretical expressions developed were validated by applying the Monte Carlo simulation method to two real and nine simulated data sets. Two other real data sets were used to provide examples of application.