The settlement and compressibility magnitude of the major clayey and marly sediments in Tebessa area (N-E of Algeria) depends on several geotechnical parameters such as compression Cc and recompression Cs indices. The aim of this study was to investigate the parameters related to soil compressibility through tools of statistical analysis, which save time in comparison to multiply repeated laboratory tests. The study also adopted the principal component analysis (PCA) method to eliminate a number of uncorrelated variables that have no influence on the compressibility magnitude, or their impact is insignificant. The highest mean correlation coefficients were obtained for different contributing parameters. Multiple regression analysis has been performed to obtain the best fit model of the output Cc parameter taking into account the best correlation by adding parameters as regressors to reach the highest coefficient of regression R2. The final obtained model of the present case study gives the best fit model with R2 of 0.92 which is a better value compared to different published models in the literature (R2 of 0.7 as maximum). The chosen input parameters using PCA combined with multiple regression analysis allow identifying the most important input parameters that noticeably affect the soil compression index, and provide with the best model for estimating the Cc index.