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Residential customers are the main users generally need a great quantity of natural gas in distribution systems, especially, in the wintry weather season since it is particularly consumed for cooking and space heating. Hence, it ought to be noninterruptible. Since distribution systems have a restricted ability for supply, reasonable planning and prediction through the whole year, especially in winter seasons, have emerged as vital. The Ridge Regression (RR) is formulated mainly to decrease collinearity results through shrinking the regression coefficients and reducing the impact in the model of variables. Conic multivariate adaptive regression splines ((C)MARS) model is constructed as an effective choice for MARS by using inverse problems, statistical learning, and multi-objective optimization theories. In this approach, the model complexity is penalized in the structure of RR and it is constructed a relaxation by utilizing continuous optimization, called Conic Quadratic Programming (CQP). In this study, CMARS and RR are applied to obtain forecasts of residential natural gas demand for local distribution companies (LDCs) that require short-term forecasts, and the model performances are compared by using some criteria. Here, our analysis shows that CMARS models outperform RR models. For one-day-ahead forecasts, CMARS yields a MAPE of about 4.8%, while the same value under RR reaches 8.5%. As the forecast horizon increases, it can be seen that the performance of the methods becomes worse, and for a forecast one week ahead, the MAPE values for CMARS and RR are 9.9% and 18.3%, respectively. [ABSTRACT FROM AUTHOR]