An alternative look at the linear regression model

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

Automated summary

An alternative perspective on the linear regression model is introduced, proposing a novel treatment of the model matrix with full column rank. By utilizing a specific formula, the Moore-Penrose inverse of the matrix can be obtained, simplifying derivations and providing fresh insights into certain aspects of the model. This approach also reduces computational costs required for obtaining estimators. The paper includes a numerical example based on astronomical observations to demonstrate the usefulness of the proposed approach.