Department of Mathematics
Correlation
and Predictability - Applications in Manufacturing.
Stefan Pittner
Northeastern University
The problem of predicting a dependent numerical variable from an independent variable (or several independent variables) is generally approached with methods from approximation theory. In this talk it is demonstrated that establishing the predictability of a numerical variable is, however, mainly a problem of statistics. The importance of the predictability problem is demonstrated with an application in manufacturing process control. It is shown how existing concepts in statistics, such as statistical dependence, the Pearson correlation coefficient and the Spearman rank correlation coefficient, can be used for the evaluation of the predictability of a numerical variable. The merits and drawbacks of the concepts are discussed. Next, a nonparametric correlation measure called g-correlation coefficient is derived. The idea behind g-correlation is to replace the function approximation concept of predictability by a classification concept. The g-correlation concept allows one to detect (a) any monotonic relationship between the dependent and the independent variable and (b) a classification procedure in situations where accurate predictions are not possible. A method is proposed to estimate g-correlation from a set of samples for the variables under consideration. It is also sketched how g-correlation can be extended to more than one independent variable using Fisher linear discriminant functions. Results of the application of different correlation coefficients in a manufacturing application show that g-correlation has a central role among all standard concepts of correlation.
All interested persons are welcome.
The talk will be accessible to upper class students.