525201 Statistics and Numerical Method Part I: Statistics Week VI: Empirical Model 1/2555 สมศักดิ์ ศิวดำรงพงศ์ 1.

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Presentation transcript:

Statistics and Numerical Method Part I: Statistics Week VI: Empirical Model 1/2555 สมศักดิ์ ศิวดำรงพงศ์ 1

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6-2 Simple Linear Regression Least Square Estimation 4

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Simple Linear Regression 6

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Residual 8

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General Regression Analysis: Salt Conc. (y) versus Roadway area (x) Salt Conc. (y) = Roadway area (x) Term Coef SE Coef T P Constant Roadway area (x) S = R-Sq = 95.14% R-Sq(adj) = 94.87% PRESS = R-Sq(pred) = 94.03% 11

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Correlation and Regression The sample correlation coefficient between X and Y is between [-1,1] 13

6-3 Multiple Regression 14

Multiple Regression The least squares function is given by The least squares estimates must satisfy 15

Multiple Regression 16

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Regression Analysis: Pull Strengt versus Wire Length, Die Height ( The regression equation is Pull Strength (y) = Wire Length (x1) Die Height (x2) Predictor Coef SE Coef T P Constant Wire Length (x1) Die Height (x2) S = R-Sq = 98.1% R-Sq(adj) = 97.9% 19

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