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.