We analyze the problem of simultaneous support recovery and estimation of the coefficient vector ($\beta^* $) in a linear model with independent and identically distributed Normal errors. We apply the penalized least square estimator based on non-convex penalties of stochastic gates (STG) [YLNK20] to estimate the coefficients. Considering Gaussian design matrices we show that under reasonable conditions on dimension and sparsity of $\beta^* $ the STG based estimator converges to the true data generating coefficient vector and also detects its support set with high probability. We propose a new projection based algorithm for linear models setup to improve upon the existing STG estimator that was originally designed for general non-linear models. Our new procedure outperforms many classical estimators for support recovery in synthetic data analysis.