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Ho Chi Minh City University of Technology Faculty of Geology & Petroleum Engineering Modeling & Simulation Division Presenter: Dr. Do Quang Khanh Email: doquangkhanh@yahoo.com Website: www.hcmut.edu.vn CURVE FITTING (REGRESSION) HCMUT Least Squares Dr. Do Quang Khanh 2 HCMUT Least Squares Sum of Squares as a measure of “how good the fit is”. (Other possible measures: Sum of Abs Deviations) Other requirements:  Smoothness,  Least number of parameters,  Extrapolati
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  Ho Chi Minh City University of Technology Faculty of Geology & Petroleum Engineering Modeling & Simulation Division Presenter: Dr. Do Quang Khanh Email: doquangkhanh@yahoo.com Website: www.hcmut.edu.vn CURVE FITTING (REGRESSION)  HCMUT Least Squares Dr. Do Quang Khanh 2  HCMUT Least Squares  Sum of Squares as a measure of “how good the fit is”. (Other possible measures: Sum of Abs Deviations)  Other requirements:  Smoothness,  Least number of parameters,  Extrapolating power, etc.  Two basic cases  Model is based on “first principles”  Model is just a convenient vehicle Dr. Do Quang Khanh 3  HCMUT Least Squares and its Num. Aspects  Two parameters or more to find?  If two parameters  Is it in straight line form? ã“Linear regression”  Or can we transform it into straight line form? ã“Pseudo-linear regression:” Transformation to straight-line form  More than two parameters (linear): Generalized least squares  Nonlinear least squares: Gauss-Newton-Marquardt Dr. Do Quang Khanh 4
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