In practice it may happen that a first-try econometric model is not appropriate because it violates one or more of the key assumptions that are needed to obtain valid results. In case there is something wrong with the variables, such as measurement error or strong collinearity, we may better modify the estimation method or change the model. In the present chapter we deal with endogeneity, which can, for example, be caused by measurement error, and which implies that one or more regressors are correlated with the unknown error term. This is of course not immediately visible because the errors are not known beforehand and are estimated jointly with the unknown parameters. Endogeneity can thus happen when a regressor is measured with error, and, as we see, when the data are aggregated at too low a frequency. Another issue is called multicollinearity, in which it is difficult to disentangle (the statistical significance of) the separate effects. This certainly holds for levels and squares of the same variable. Finally, we deal with the interpretation of model outcomes.

Using linear regression requires assumptions that must be met.The criteria for using regression is discussed including the need for the dependent variable to be interval and to have a linear relationship with the independent variable(s).Omitting relevant variables and problems are discussed, along with explaining the importance of the error term in a regression.Detecting multicollinearity in the R Commander is illustrated, along with implications of and solutions for multicollinearity.The effects of heteroscedasticity are discussed with an illustration of it.

Multiple linear regression generalizes straight line regression to allow multiple explanatory (or predictor) variables, in this chapter under the normal errors assumption. The focus may be on accurate prediction. Or it may, alternatively or additionally, be on the regression coefficients themselves. Simplistic interpretations of coefficients can be grossly misleading. Later chapters elaborate on the ideas and methods developed in this chapter, applying them in new contexts. The attaching of causal interpretations to model coefficients must be justified both by reference to subject area knowledge and by careful checks to ensure that they are not artefacts of the correlation structure. There is attention to regression diagnostics, to assessment, and comparison of models. Variable selection strategies can readily over-fit. Hence the importance of training/test approaches and cross-validation. The potential is demonstrated for errors in x to seriously bias regression coefficients. Strong multicollinearity leads to large variance inflation factors.

Between 1937 and 1943, Douglas and several younger coauthors developed an approach to estimating the Cobb–Douglas regression with cross section data, applying it to industry-level data from the US, Australia, and Canada. This research is described in detail. Over this period claims made by the Douglas team about the meaning of an estimated Cobb–Douglas regression and its relationship to neoclassical theory evolved and never really reached a settled state. During this period, Douglas and his coauthors also responded to Horst Mendershausen's forceful critique of Douglas's work with the regression. Mendershausen pointed to a number of problems in Douglas’s data and methods, concluding that his results did not represent a stable, causal relationship between inputs and output and that his regression method was an unreliable tool for estimation of a production function. Douglas and his associates developed detailed responses to Mendershausen’s critique, and after going back and forth with Mendershausen for a few years, Douglas essentially declared victory and moved on. This debate is analyzed, and possible reasons that Mendershausen’s criticisms did not have more influence are offered.