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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:

<math>E(Y) = f(x)</math>

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

<math>E(Y) = \alpha + \beta x.</math>

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.