The ordinary least square estimates of multiple regression parameters is characterized by low bias and large variance leading to poor performance in both prediction and interpretation of the regression model under study. Penalized regression techniques represented in ridge, lasso and elastic net were used to improve the ordinary least square estimates performance. Categorical regression algorithm provides efficient procedure for computing the regression coefficients of ridge, lasso, and elastic Net models. The statistical analysis was done on ten single nucleotide polymorphisms simulated data with strong linkage disequilibrium as predictors of a continuous phenotypic trait. The coefficients were 39%, 34%, 29% and 28% for ridge, elastic net, lasso and stepwise multiple regression methods, respectively. The current study finished that ridge regression followed by elastic net regression performed better than the other regression methods.