settings produces the same formulas and same results. The only difference is the interpretation and the assumptions which have to be imposed in order for the method to give meaningful results. The choice of the applicable framework depends mostly on the nature of data in hand, and on the inference task which has to be performed. One of the lines of difference in interpretation is whether to treat the regressors as random variables, or as predefined constants. In the first case (random design) the regressors xi are random and sampled together with the yi's from some population, as in an observational study. This approach allows for more natural study of the asymptotic properties of the estimators. In the other interpretation (fixed design), the regressors X are treated as known constants set by a design, and y is sampled conditionally on the values of X as in an experiment. For practical purposes, this distinction is often unimportant, since estimation and inference is carried out while conditioning on X. All results stated in this article are within the random design framework. Classical linear regression model The classical model focuses on the "finite sample" estimation and inference, meaning that the number of observations n is fixed. This contrasts with the other approaches, which study the asymptotic behavior of OLS, and in which the number of observations is allowed to grow to infinity. Correct specification. The linear functional form must coincide with the form of the actual data-generating process. Strict exogeneity. The errors in the regression should have conditional mean zero: The immediate consequence of the exogeneity assumption is that the errors have mean zero: , and that the regressors are uncorrelated with the errors: . The exogeneity assumption is critical for the OLS theory. If it holds then the regressor variables are called exogenous. If it doesn't, then those regressors that are correlated with the error term are called endogenous, and the OLS estimator becomes biased. In such case the method of instrumental variables may be used to carry out inference. No linear dependence. The regressors in X must all be linearly independent. Mathematically, this means that the matrix X must have full column rank almost surely: Usually, it is also assumed that the regressors have finite moments up to at least the second moment. Then the matrix is finite and positive semi-definite. When this assumption is violated the regressors are called linearly