Automation of Multiple Linear Regression Analysis Using Neural Networks

Abstract

Statistical regression analysis is a powerful tool that can be used to model relationships between variables in a statistical data set. Also, regression analysis is a widely used technique in the statistical data analysis. Regression analysis needs an expert knowledge on the subject Statistics. But most of the people, who need regression analysis to be done for their existing data, do not have enough background knowledge on Statistics. Due to this reason, they are required to get an assistantship from a statistician. Even though enough statistical software packages are available for regression analysis, the person who is operating that software is also expected to have knowledge on Statistics for selection of suitable variables, selection of suitable transformations, interpretation of results etc. This is a great disadvantage for most of those people. So far few attempts have been made to automate regression analysis using neural networks (NN). But all of those attempts have been made to get improved regression estimates using neural networks rather than addressing the above problem. This project focuses on how neural networks can be used to automate regression analysis and simplify the regression estimation process.

The primary goal of this project is fitting a statistically significant multiple linear regression model for a given data set. This project introduces a neural network model for multiple linear regression analysis. The proposed neural network architecture is capable of recognizing linearly related covariate (independent) variables or possible transformations for covariate variables that converts non-linear relationships into a linear form with the response variable. Then this NN model will reduce the number of covariates in the proposed regression model by applying principle component analysis. Principle component analysis would also be useful for eliminating multicollinearity of the regression model. Finally the NN model will estimate parameters of the regression model using backpropagation algorithm. This model can be used for multiple linear regression analysis by any person who doesn’t have good statistical background knowledge