Probabilistic Design for Optimization and Robustness for Engineers

11 Binary logistic regression

11.1 Introduction

In the conversion of end-customer requirements into functional requirements and ultimately to design requirements, we need to establish linking relationships between explanatory input and response output variables. As discussed in Chapter 6 on desirability, these response outputs may include numerical measures such as customer satisfaction, usability, performance, and cost or categorical outputs such as will purchase versus will not purchase or has versus does not have features (binary outcomes). To meet desirability goals for response outputs, we must identify critical explanatory input variables along with settings or a range of settings.

A recurring challenge in establishing useful linking relationships is that they may change, possibly even from a linear to a quadratic relationship, depending on the range of the explanatory variable. To illustrate, consider the square footage of homes. Suppose several houses in a particular area with similar characteristics are selected, and the square footage versus selling price is compared. Here, you might find the following relationship as shown in Figure 11.1.

Figure 11.1 Home price versus square footage.

In the first region of the figure, the relationship between square footage and price appears fairly flat. Then, we have a range in which there is a fairly steep linear relationship. ...