Cleansing of inconsistent sample in linear regression model based on rough sets theory

The linear regression model is one of the most common and easiest algorithms used in machine learning for predictive analysis purposes. However, this model performs well under strict assumptions such as the number of observations, the linearity of variables, multicollinearity, homoskedasticity, reliability of measurement, and normality. Besides, there is no consideration to date for handling and cleansing inconsistent samples in the data sets. These samples may significantly influence the performance of multiple linear regression in terms of these assumptions and several aspects, such as adjusted R-square, intercept-slopes, exogenous variables, and the accuracy of prediction. In this paper, the data reduction strategy of rough sets was employed to remove and clean these types of samples, boosting the performance of the linear regression models. This strategy was evaluated by examining three different effects; adjusted R-square, slopes-intercepts, and mean square error of the regression model. Simulated data and simple modeling problems were used to determine the effects of these three aspects. The secondary data sets were collected from various domains to examine the proposed rough-regression model. The simulation results showed that the data reduction strategy is exceedingly effective to boost the performance of the multiple linear regression in the three aspects above. In the implementation, these aspects also performed better than before data reduction. The results from both simulations and implementations demonstrate that the data reduction of rough sets is a viable strategy in cleansing of the inconsistent samples in the linear regression models. Thus, the proposed rough regression model is effectively proven to support the data analysis of surveys or cross-sectional studies, especially when the stated aspects are not well fulfilled. Therefore, the surveys are not needed to be repeated and reconsidered by researchers.