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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 $x$ amd the response $y$:
$y = f(x)$
The most common form assumed for such functions is linear, thus we expect to see a relationship like
$y = \alpha + \beta \cdot x$
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.

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