Statistical and Numerical Computing
Published Online: 15 SEP 2006
Copyright © 2002 John Wiley & Sons, Ltd
Encyclopedia of Environmetrics
How to Cite
Lee, A. J. and Seber, G. A. 2006. Residuals. Encyclopedia of Environmetrics. 5.
- Published Online: 15 SEP 2006
Many scientific problems involve modeling the relationship between variables. Regression analysis is concerned with modeling the behavior of a variable Y (the response or dependent variable) in terms of a set x1, …, xp of explanatory variables (also called covariates, regressors, and independent variables). The model takes the form E(Y) = f (x1, , xp; β) where f is one of a ‘sensible’ family of functions, and β is a parameter vector which must be estimated from the data. We also need to postulate the statistical distribution of y for a fixed covariate vector x = (x1, …, xp)T. The assumed form of f is tentative and we need various diagnostic checks to assess its suitability. To do this, we need a measure of the discrepancy between each datum y and the ‘fitted value’ ŷ predicted by the model. These measures are known as residuals. The precise form of the residual depends on the type of data (continuous data, counts, binary data) and the form of the model.