Definition: A regression function describes the relationship between dependent variable Y
and explanatory variable(s) X. One might estimate the regression function
m() in the econometric model
Yi = m(Xi) + ei
where the ei are the residuals or errors. As presented that is a nonparametric or semiparametric model, with few assumptions about m(). If one were to assume also that m(X) is linear in X one would get to a standard linear regression model:
Yi = (Xi)b + ei
where the vector b could be estimated.
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