Stimulus-response model

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.