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 <math>f</math> between the stimulus <math>x</math> amd the response <math>y</math>:

<math>y = f(x)</math>

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

<math>y = \alpha + \beta \cdot 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.