This is an entry for The Encyclopedia of Statistics in Behavioral Science, to be published by Wiley in 2005. In regression analysis there are n observations yi on a dependent variable(also known as outcome or criterion) that are related to n corresponding observations xi on p independent variables (also known as inputs or predictors). Fitting regression models of some form or another is by far the most common uses of statistics in the sciences (crossref). Statistical theory tells us to assume that the observed outcomes yi are realizations of n random variables y i . We model the conditional expectation of y i given xi , or, to put it differently, we model the expected value of yi as a function of xi E(y i | xi ) = F(xi ), where the function F must be estimated from the data. Often the function F is known except for a small number of parameters. This defines parametric Date: July 18, 2004.