1. ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 25 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 Total Error

7. Best Fit => Minimize Error Not a Good Choice Not a Unique Best Fit

8. Best Fit => Minimize Error Try Absolute Not a Good Choice Not a Unique Best Fit

9. Best Fit => Minimize Error Best Strategy

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

11. Least Square Approximation What x minimizes f(x)? Remember:

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

13. Least Square Approximation

16. 2 Eqtns 2 Unknowns

17. Least Square Approximation

18. Example xyxyx2x2 10.5 1a1=0.839 22.554a0=0.0714 3269 4416 53.517.525 6636 75.538.549 2824119.5140

19. Example

21. Quantification of Error Average

22. Quantification of Error Average

23. Quantification of Error Average

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

25. Quantification of Error

26. “Standard Deviation” for Linear Regression

27. Quantification of Error Better Representation Less Spread

28. Quantification of Error Coefficient of Determination Correlation Coefficient

29. Linearized Regression

32. Homework 17.4 17.7 17.8 17.11