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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.
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