Standard Article

Residuals

Statistical and Numerical Computing

  1. Alan J. Lee,
  2. George A.F. Seber

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.var039

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Lee, A. J. and Seber, G. A. 2006. Residuals. Encyclopedia of Environmetrics. 5.

Author Information

  1. University of Auckland, New Zealand

Publication History

  1. Published Online: 15 SEP 2006

Abstract

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.