A novel Levenberg-Marquardt like second-order algorithm for tuning the Parzen window σ in a Radial Basis Function (Gaussian) kernel. Each attribute has its own sigma parameter. The values of the optimized σ are then used as a gauge for variable selection. Kernel Partial Least Squares (K-PLS) model is applied to several benchmark data sets to estimate effectiveness of second-order sigma tuning procedure for an RBF kernel. The variable subset selection method based on these sigma values is then compared with different feature selection procedures such as random forests and sensitivity analysis. The sigma-tuned RBF kernel model outperforms K-PLS and SVM models with a single sigma value. K-PLS models also compare favorably with Least Squares Support Vector Machines (LS-SVM), epsilon-insensitive Support Vector Regression and traditional PLS. Sigma tuning and variable selection is applied to industrial magnetocardiograph data for detection of ischemic heart disease from measurement of magnetic field around the heart.