Carmona, L., "Regression Analysis: A Geometric Perspective," SAE Technical Paper 2017-36-0074, 2017.
Regression analysis is perhaps one of the most widely used statistical tools in six-sigma projects. The reason for its popularity is that it provides a formal evaluation of the relationship between one dependent variable and one or more predictors. The ordinary least squares (OLS), which is a method for estimating the parameters of the linear regression model, has some numerical properties that can be easily understood by looking at them in a geometric manner. In this paper, we discuss the fundamentals of both simple and multiple regression analysis from a geometric perspective. This approach offers an intuitive understanding of some concepts that otherwise would require a background in statistical mathematics and differential calculus. One of the topics covered in this paper is multicollinearity, whose consequences are not well understood by many practitioners. A practical example drawn from the automotive industry (body exterior quality) is used to clarify the basic notions that appear throughout the paper. This example consists of a regression analysis made over a sample of vehicles in an attempt to explain the level of customer's complaints regarding side door closing effort (dependent variable) by the actual closing effort measured in a laboratory using a standard procedure (independent variable). It is well known that closing effort, in turn, is also highly correlated with the compression load deflection (CLD) of the door seals, meaning that including both variables as predictors in the same model would produce unreliable estimates of the parameters. Unfortunately, many quality engineers disregard the effects of multicollinearity when they perform this kind of analysis. This paper is intended to draw attention to these issues in a user-friendly way.