15 Regression and Curve Fitting

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Regression analysis is the study of the relationship between one or several predictors (independent variables) and the response (dependent variable). To perform regression analysis on a dataset, a regression model is first developed. Then the best fit parameters are estimated using something like the least-square method. Finally, the quality of the model is assessed using one or more hypothesis tests.

From a mathematical point of view, there are two basic types of regression: linear and nonlinear. A model where the fit parameters appear linearly in the Least Squares normal equations is known as a "linear model"; otherwise it is "nonlinear". In many scientific experiments, the regression model has only one or two predictors, and the aim of regression is to fit a curve or a surface to the experimental data. So we may also refer to regression analysis as "curve fitting" or "surface fitting."

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