Regression Analysis

Regression analysis aims to determine the best global representation of experimental data for applications in design and analysis of a complex engineering system. Regression analysis or curve fitting consists in arriving at a relationship that may exist between two or more variables. In the context of experiments, the variables represent cause(s) effect relationship, with a particular measured quantity depending on other measured quantities. This chapter discusses linear regression, polynomial regression, non-linear regression, multiple linear regression and segmented regression in detail. Goodness of fit of a model to data may be judged by looking at either the correlation coefficient or the index of correlation. Another test that is usually made consists of the X2 test. Regression analysis is based on the argument that the errors with respect to the regression line are normally distributed. This is the basis for the least square analysis that is employed to estimate the fit parameters.