Data Analyzing by Attention to Weighted Multicollinearity in Logistic Regression Applicable in Industrial Data

Abstract

The Middle East’s largest industrial complex produces flat steel sheets with specific properties such as low thickness, high strength and suitable formability in order to reduce the vehicle weight and fuel consumption and prevention of environmental pollution. The aim of this study is to investigate the effect of some important explanatory variables on suitable formability of manufacturing steel sheets according to primary data set. Existence or lack of existence of crack on steel sheet is considered as a binary response variable. It is determined by bending test with the angle of zero degree. Existence of multicollinearity between mentioned explanatory variables has an effect on the probability of crack existence. Because of special condition of the response variable, which is binary, the suitable regression is logistic, and correction techniques based on least squares do not work. Developments in weighted multicollinearity diagnostics are used to assess maximum likelihood logistic regression parameter estimates. Then principal component, a biased estimation method, is used in a way that it has additional scaling parameter which can accommodate a spectrum of explanatory variable standardizations. After that, by this scale parameter α, other biased estimation methods such as partial least squares, ridge and Stein are explained. They can considerably reduce the variance of the parameter estimation.