Variable selection is a contentious issue that has spawned a variety of methods for finding the optimum regression equation with the fewest parameters. There are better linear independence features in the matrices of systems that are indeterminately compatible when using the RRQR (Rank-Revealing QR factorization) algorithm. An advantage of the RRQR technique is that it can be used to select variables with higher linear independence when determining the rank of a matrix. The RRQR decomposition with restricted pivot and an empirical model selection criterion such as Mallows' Cp are described in this paper. This procedure's benefits can be shown in two different scenarios, ‘QR' and ‘RRQR' decompositions.