An alternative look at the linear regression model

Abstract An alternative look at the linear regression model is taken by proposing an original treatment of a full column rank (design) matrix. In such situation, Moore–Penrose inverse matrix can be obtained utilizing particular formula which applicable solely when to inverted columnwise partitioned into two matrices disjoint ranges. It turns out that this approach, besides simplifying derivations, provides novel insight some notions involved in and reduces computational costs needed obtain sought estimators. The paper contains also numerical example based on astronomical observations localization Polaris, demonstrating usefulness proposed approach.