The performances of two biased estimators for the general linear regression model under conditions of collinearity are examined and a new proposed ridge parameter is introduced. Using Mean Square Error (MSE) and Monte Carlo simulation, the resulting estimator’s performance is evaluated and compared with the Ordinary Least Square (OLS) estimator and the Hoerl and Kennard (1970a) estimator. Results of the simulation study indicate that, with respect to MSE criteria, in all cases investigated the proposed estimator outperforms both the OLS and the Hoerl and Kennard estimators.