Statistical model specification

In statistics, model specification is part of the process of building a statistical model: specification consists of selecting an appropriate functional form for the model and choosing which variables to include. For example, given personal income y {\displaystyle y} together with years of schooling s {\displaystyle s} and on-the-job experience x {\displaystyle x} , we might specify a functional relationship y = f ( s , x ) {\displaystyle y=f(s,x)} as follows: ln ⁡ y = ln ⁡ y 0 + ρ s + β 1 x + β 2 x 2 + ε {\displaystyle \ln y=\ln y_{0}+\rho s+\beta _{1}x+\beta _{2}x^{2}+\varepsilon } where ε {\displaystyle \varepsilon } is the unexplained error term that is supposed to comprise independent and identically distributed Gaussian variables.

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