is the unexplained error term that is supposed to comprise independent and identically distributed Gaussian variables.
The statistician Sir David Cox has said, "How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis".
[2] Specification error occurs when the functional form or the choice of independent variables poorly represent relevant aspects of the true data-generating process.
In the example given above relating personal income to schooling and job experience, if the assumptions of the model are correct, then the least squares estimates of the parameters
Hence specification diagnostics usually involve testing the first to fourth moment of the residuals.
[5] Building a model involves finding a set of relationships to represent the process that is generating the data.
One approach is to start with a model in general form that relies on a theoretical understanding of the data-generating process.
The purpose of the comparison is to determine which candidate model is most appropriate for statistical inference.
Common criteria for comparing models include the following: R2, Bayes factor, and the likelihood-ratio test together with its generalization relative likelihood.