Chapters authored
Fitting Models to Data: Residual Analysis, a Primer
The aim of this chapter is to show checking the underlying assumptions (the errors are independent, have a zero mean, a constant variance and follows a normal distribution) in a regression analysis, mainly fitting a straight‐line model to experimental data, via the residual plots. Residuals play an essential role in regression diagnostics; no analysis is being complete without a thorough examination of residuals. The residuals should show a trend that tends to confirm the assumptions made in performing the regression analysis, or failing them should not show a tendency that denies them. Although there are numerical statistical means of verifying observed discrepancies, statisticians often prefer a visual examination of residual graphs as a more informative and certainly more convenient methodology. When dealing with small samples, the use of the graphic techniques can be very useful. Several examples taken from scientific journals and monographs are selected dealing with linearity, calibration, heteroscedastic data, errors in the model, transforming data, time‐order analysis and non‐linear calibration curves.
Part of the book: Uncertainty Quantification and Model Calibration