1. 525201 Statistics and Numerical Method Part I: Statistics Week VI: Empirical Model 1/2555 สมศักดิ์ ศิวดำรงพงศ์ somsaksi@sut.ac.th 1

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4. 6-2 Simple Linear Regression Least Square Estimation 4

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6. Simple Linear Regression 6

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8. Residual 8

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11. General Regression Analysis: Salt Conc. (y) versus Roadway area (x) Salt Conc. (y) = 2.67655 + 17.5467 Roadway area (x) Term Coef SE Coef T P Constant 2.6765 0.868004 3.0836 0.006 Roadway area (x) 17.5467 0.934630 18.7739 0.000 S = 1.79066 R-Sq = 95.14% R-Sq(adj) = 94.87% PRESS = 70.9737 R-Sq(pred) = 94.03% 11

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

14. 6-3 Multiple Regression 14

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

16. Multiple Regression 16

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19. Regression Analysis: Pull Strengt versus Wire Length, Die Height ( The regression equation is Pull Strength (y) = 2.26 + 2.74 Wire Length (x1) + 0.0125 Die Height (x2) Predictor Coef SE Coef T P Constant 2.264 1.060 2.14 0.044 Wire Length (x1) 2.74427 0.09352 29.34 0.000 Die Height (x2) 0.012528 0.002798 4.48 0.000 S = 2.28805 R-Sq = 98.1% R-Sq(adj) = 97.9% 19

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