Lecture_05_Polynomial_Regression

Lecture_05_Polynomial_Regression - EGR 102 Introduction to...

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1 EGR 102 Lecture 5 1 EGR 102 Introduction to Engineering Modeling Curve Fitting Polynomial Regression Chapter 14.1 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill EGR 102 Lecture 5 2 Curve Fitting ± Describes techniques to fit curves to discrete data to obtain intermediate estimates. ± There are two general approaches to curve fitting: ± Data exhibit a significant degree of scatter ± Derive a single curve that represents the general trend of the data. ± Data is very precise ± Pass a curve or a series of curves through each of the points. ± In engineering, two types of applications are encountered: ± Trend analysis ± Predicting values of dependent variable may include extrapolation beyond data points or interpolation between data points. ± Hypothesis testing ± Comparing existing mathematical model with measured data.
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2 EGR 102 Lecture 5 3 Variable Data Example (a) Data with significant error (b) Polynomial fit oscillating beyond the range of the data (c) Linear fit EGR 102 Lecture 5 4 ± Arithmetic mean: The sum of the individual data points ( y i ) divided by the number of points ( n ). ± Standard deviation: The most common measure of a spread for a sample.
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Lecture_05_Polynomial_Regression - EGR 102 Introduction to...

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