TABLE OF CONTENTS Regression is a family of curve-fitting methods for (1) predicting average response performance for new combinations of factors and (2) understanding which factor changes cause changes in average outputs. In this chapter, the uses of regression for prediction and performing hypothesis tests are described. Regression methods are perhaps the most widely used statistics or operations research techniques. Also, even though some people think of regression as merely the "curve fitting method" in Excel, the methods are surprisingly subtle with much potential for misuse (and benefit).
Some might call virtually all curve fitting methods "regression" but, more commonly, the term refers to a relatively small set of " linear regression" methods. In linear regression predictions increase like a first order polynomial in the coefficients. Models fit with terms like ? 32 x 1 2 x 4 are stilled called "linear" because the term is linear in ? 32, i.e., if the coefficient ? 32 increases, the predicted response increases proportionally. See Chapter 16 for a relatively thorough discussion of regression vs alternatives.
Note that standard screening using fractional factorials, response surface methods (RSM), and robust design using profit maximization (RDPM) methods are all based on regression analysis. Yet, regression modeling is relevant whether the response data is collected using a randomized experiment or, alternatively, if it is " on-hand" data from an observational study. In addressing on-hand data, primary challenges relate to preparing the data for analysis and determining which terms should...
