Present article aims to investigate the effect of nano-clay content, foaming temperature and foaming time on the density and cell size of the PVC matrix foam. The cell size would affect the insulating and mechanical properties. The foaming temperature is set in three levels of 70, 80 and 90 °C, foaming time is set in three levels of 10, 20, and 30 s; and nano-clay is in content of 1, 3, and 5 wt%. Outputs consist the density and cell size, which affect impact the thermal conductivity, mechanical properties and the weight of the polymer foam. In addition the Least Absolute Shrinkage and Selection Operator (LASSO) regression method is employed in order to improve both the precision and generalization of the estimated foam density and cell size as functions of the MMT content, the foaming temperature and the foaming time. LASSO is found a suitable approach to predict the sample properties.