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ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 26 Regression Analysis-Chapter 17

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Curve Fitting Often we are faced with the problem… what value of y corresponds to x=0.935?

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Curve Fitting Question 2 : Is it possible to find a simple and convenient formula that represents data approximately ? e.g. Best Fit ? Approximation

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Experimental Measurements Strain Stress

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Experimental Measurements Strain Stress

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BEST FIT CRITERIA Strain y Stress Error at each Point

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Best Fit => Minimize Error Best Strategy

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Best Fit => Minimize Error Objective: What are the values of a o and a 1 that minimize ?

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Least Square Approximation In our case Since x i and y i are known from given data

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Least Square Approximation 2 Eqtns 2 Unknowns

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Least Square Approximation

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Example

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Quantification of Error Average

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Quantification of Error Average

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Quantification of Error Average

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Quantification of Error Standard Deviation Shows Spread Around mean Value

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Quantification of Error

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“Standard Deviation” for Linear Regression

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Quantification of Error Better Representation Less Spread

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Quantification of Error Coefficient of Determination Correlation Coefficient

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Linearized Regression The Exponential Equation

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Linearized Regression The Power Equation

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Linearized Regression The Saturation-Growth-Rate Equation

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Polynomial Regression A Parabola is Preferable

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Polynomial Regression Minimize

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Polynomial Regression

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3 Eqtns 3 Unknowns

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Polynomial Regression Use any of the Methods we Learned

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Polynomial Regression With a 0, a 1, a 2 known the Total Error Standard Error Coefficient of Determination

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Polynomial Regression For Polynomial of Order m Standard Error Coefficient of Determination

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