Regression analysis diagnostic statistics

Regression analysis includes not only the estimation of model regression parameters, but also the calculation of goodness of fit and -> goodness of prediction statistics, regression diagnostics, residual analysis, and influence analysis [Atkinson, 1985]. 

Before leaving the subject of regression analysis, and in particular the use of PCR and PLS algorithms, it is instructive to examine some of the diagnostic statistics often available from their application. 

The basic principle of experimental design is to vary all factors concomitantly according to a randomised and balanced design, and to evaluate the results by multivariate analysis techniques, such as multiple linear regression or partial least squares. It is essential to check by diagnostic methods that the applied statistical model appropriately describes the experimental data. Unacceptably poor fit indicates experimental errors or that another model should be applied. If a more complicated model is needed, it is often necessary to add further experimental runs to correctly resolve such a model. 

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