Least-squares theory based on general distributional assumptions with an application to the incomplete observations problem (Q1058794)

The linear regression model \(y=\beta^ Tx+\epsilon\) is reanalyzed. Taking the modest position that \(\beta^ Tx\) is an approximation of the ''best'' predictor of y we derive the asymptotic distribution of b and \(R^ 2\), under mild assumptions. The method of derivation yields an easy answer to the estimation of \(\beta\) from a data set which contains incomplete observations, where the incompleteness is random.