Editing Stimulus–response model (section)

==Mathematical formulation==

The object of a stimulus–response model 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'':<ref name="meyeretal2017">Meyer, A. F., Williamson, R. S., Linden, J. F., & Sahani, M. (2017). Models of neuronal stimulus-response functions: elaboration, estimation, and evaluation. ''Frontiers in systems neuroscience'', 10, 109.</ref>

: <math>\mathrm{E}(Y) = f(x)</math>

A common simplification assumed for such functions is linear, thus we expect to see a relationship like

: <math>\mathrm{E}(Y) = \alpha + \beta x.</math>

[[Statistical theory]] for [[linear model]]s has been well developed for more than fifty years, and a standard form of analysis called [[linear regression]] has been developed.