This paper aims to identity the significant impact factors (IFs) of the residential electricity consumption level (RECL) and to better understand the influence mechanism of IFs on RECL. The analysis of influence mechanism is commonly through regression model where feature selection must first be performed to pick out non-redundant IFs that is highly correlated with RECL. In contrast to the existing studies, this study recognizes the problem that majority feature selection methods (e.g., step regression) are limited to the identification of linear relationships and proposes a novel wrapper feature selection (WFS) method to address this issue. The WFS is based on genetic algorithm (GA) and multinomial logistic regression (MLR). GA is a searching algorithm used to generate different feature subsets (FSs) that consist of several IFs. MLR is a modeling algorithm used to score these FSs. Further, maximal information coefficient (MIC) is utilized to verify the validity of WFS for selecting IFs. Finally, MLR based explanatory model is established to excavate the relationship between selected IFs and RECL. The results of Ireland dataset based case study show that WFS can identify the significant and non-redundant IFs that are linearly or nonlinearly related to RECL. The details about how selected IFs affect RECL are also provided via the explanatory model. Such research can provide useful guidance for a wide range of stakeholders including local governments, electric power companies, and individual households.