The inhibition of mild steel corrosion in 1 M HCl by 17 furan derivatives was investigated experimentally using potentiodynamic polarization measurements. The furan derivatives inhibit the mild steel corrosion. The experimental inhibition efficiency (IE) was used in a Quantitative Structure-Activity Relationship (QSAR) study. Dragon software was used to calculate the molecular descriptors. Penalized multiple linear regression (PMLR) was applied as a variable selection method using three penalties namely, ridge, LASSO, and elastic net. A number of 8 and 38 significant molecular descriptors were selected by LASSO and elastic net methods, respectively. The most significant descriptors namely, PJI3, P_VSA_s_4, Mor16u, MATS3p, and PDI were selected by both LASSO and elastic net methods. The elastic net results show low mean-squared error of the training set (MSEtrain) of 0.0004 and test set (MSEtest) of 5.332. The results confirm that the penalized multiple linear regression based on elastic net penalty is the most effective method to deal with high dimensional data