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

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

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

4. Experimental Measurements Strain Stress

5. Experimental Measurements Strain Stress

6. BEST FIT CRITERIA Strain y Stress Error at each Point

7. Best Fit => Minimize Error Best Strategy

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

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

10. Least Square Approximation 2 Eqtns 2 Unknowns

11. Least Square Approximation

12. Example

14. Quantification of Error Average

15. Quantification of Error Average

16. Quantification of Error Average

17. Quantification of Error Standard Deviation Shows Spread Around mean Value

18. Quantification of Error

19. “Standard Deviation” for Linear Regression

20. Quantification of Error Better Representation Less Spread

21. Quantification of Error Coefficient of Determination Correlation Coefficient

22. Linearized Regression The Exponential Equation

23. Linearized Regression The Power Equation

24. Linearized Regression The Saturation-Growth-Rate Equation

25. Polynomial Regression A Parabola is Preferable

26. Polynomial Regression Minimize

27. Polynomial Regression

28. 3 Eqtns 3 Unknowns

29. Polynomial Regression Use any of the Methods we Learned

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

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