The stimulus-response model describes a statistical unit as making a quantitative response to a quantitative stimulus administered by the researcher. The object of this kind of research is to establish a mathematical function that describes the relation f between the stimulus x and the expected value (or other measure of location) of the response Y:

$E(Y)\; =\; f(x)$

The most common form assumed for such functions is linear, thus we expect to see a relationship like

$E(Y)\; =\; alpha\; +\; beta\; x.$

Statistical theory for linear models has been well developed for more than fifty years, and a standard form of analysis called linear regression has been developed.