Studying the Additive Residuals

Summary

This chapter is an introduction to the analysis of the residuals, the residuals being what is left over, in the sample, when the value of the dynamic center is removed from all data points.

This analysis is important because:

• 1. the idea for selecting a formula type, for adding parameters, etc. was based on a tentative for reducing these residuals;

• 2. studying the residuals may reveal problems about the data;

• 3. studying the residuals may suggest new formula, to look for other cost drivers, in order to improve the formula;

• 4. all we can do to estimate the quality of a specific cost model is based on the values of the residuals;

• 5. the confidence we may have about an estimate is highly correlated to these values.

Studying the residuals is therefore an important step in building a specific model.

This chapter, after redefining what we call “residuals”, investigates first the classical approach with the most important — meaning those you are probably to use often — residuals: the additive ones. It shows that the simple display of these residuals is important as it can reveal interesting features, such as new (undetected up to now) outliers, a bad choice for the formula, or a trend in their values.

It then mentions the question of homoscedasticity and the sign test, to be used in particular circumstances.

The study of the residuals in the bilinear case, so often presented in most manuals, is developed. We mention the autocorrelation problem, even if it is rather rare in the cost domain, except if a wrong formula type was selected.

An interesting comment, mentioned by Mosteller and Tukey [43], allows, when a trend — even modest — in the residuals is apparent, to considerably improve the predictive capacity of the formula.

Multiplicative residuals are afterwards studied.

Eventually the modern approach based on the Bootstrap — and sometimes on the Jackknife — is briefly presented. It allows for using a more realistic, in the cost domain, distribution of the residuals and for computing the absolute minimum cost for doing something.

It also allows for using different metrics, among which the median is especially interesting.