Comparison of regression analysis and neural network models based on heteroscedasticity

Abstract

A feed forward backpropagation neural network (FFBN) was suggested for this study with the focus on a new developed model called feed forward backpropagation neural network performance over a filtered data by clustering algorithm based on robust measure (FFBNFDCARM). The new developed model was tested with five (5) different data sets obtained from the UCI machine learning repository data link. The performance functions of the evaluating metrics of mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and the mean absolute percentage error (MAPE) were used to relate the performance of the developed model with regression analysis when the data tends to deviate from the assumption of homoscedastic relation. Heteroscedasticity in regression analysis is a problem that usually arises when there is unequal variance in the analysis. One of the classical regression theories that deal with the problem of heteroscedasticity is the weighted least square (WLS) regression. A feed forward backpropagation neural network is introduced in order to deal with the problem of heteroscedasticity in this study. We proposed a clustering based algorithm using the robust estimates of location and dispersion matrix that helps in preserving the error assumption of linear regression. The relationship shows that, results obtained from the developed model gives a better performance when related to the weighted least square regression as well as the standalone feed forward backpropagation neural network for all the data sets considered. MATLAB R2014 (a) software and R i386 version 3.3.0 software were used for the analysis of this study and the results were presented.