Regression and Model Building
Statisticians, like artists, have the bad habit of falling in love with their models.
(Attributed to George Box)
Regression has already been encountered in earlier chapters. In this chapter regression modelling is examined in more detail. In terms of the process model shown earlier in Figure 1.3, regression methods enable the models to be built in terms of linking process inputs (Xs) to process performance measures (Ys) via functional relationships of the form Y = f(X). The links between regression models and design of experiments will be established. Scenarios in which the response variable is categorical will be dealt with under the heading of logistic regression. The Minitab facilities for the creation, analysis and checking of regression models will be exemplified.
10.1 Regression with a Single Predictor Variable
In Section 3.2.1 reference was made to data on the diameter (Y, mm) of machined automotive components and the temperature (X, °C) of the coolant supplied to the machine at the time of production. Given that the target diameter is 100 mm, a scatterplot indicated the possibility of improving the process through controlling the coolant temperature, thereby leading to less variability in the diameter of the components. Use of Graph > Scatterplot . . . and the With Regression option yielded the scatterplot in Figure 10.1, with the addition of the least squares regression line modelling the linear relationship between diameter ...