Statistical Methods for Quality Improvement, Third Edition

CHAPTER 12

Linear Regression

Regression analysis is one of the two most widely used statistical procedures; the other is analysis of variance, which is covered in Chapter 13.

There are various procedures within the broad area of linear regression that have direct application in quality improvement work, and a regression approach is the standard way of analyzing data from designed experiments.

The word “regression” has a much different meaning outside the realm of statistics than it does within it; literally it means to revert back to a previous state or form. In the field of statistics, the word was coined by Sir Francis Galton (1822–1911) who observed that children's heights regressed toward the average height of the population rather than digressing from it. (This is essentially unrelated to the present-day use of regression, however.)

In this chapter we present regression as a statistical tool that can be used for (1) description, (2) prediction, and (3) estimation. A regression control chart is also illustrated.

12.1 SIMPLE LINEAR REGRESSION

In (univariate) regression there is always a single “dependent” variable, and one or more “independent” variables. For example, we might think of the number of nonconforming units produced within a particular company each month as being dependent on the amount of time that is devoted to maintaining control charts and using other statistical tools. In this case the amount of time (in minutes, say) would be the single independent variable. ...