1. RLR

2. Purpose of Regression Fit data to model Known model based on physics P* = exp[A - B/(T+C)] Antoine eq. Assumed correlation y = a + b*x1+c*x2 Use model Interpolate Extrapolate (use extreme caution) Identify outliers Identify trends in data

3. Linear Regression There are two classes of regressions Linear Non-linear “Linear” refers to the parameters Sensitivity coefficients of linear models contain no model parameters.

4. Which of these models are linear?

5. Example: Surface Tension Model

6. Issue 1: Nonlinear vs. Linear Regression Nonlinear model Linearized model

7. Nonlinear Regression: Mathcad - GENFIT

8. Nonlinear Regression Results

9. Linear Regression: Mathcad - Linfit Does the linear regression Redefine the dependent variable Defines the independent variables

10. Linear Regression Results

11. Comparison nonlinear linear

12. Issue 2: How many parameters? Linear regressions with 2, 3,4, and 5 parameters

13. Straight Line Model as Example

14. Fit a Line Through This Data

15. Least Squares

16. How “Good” is the Fit? 1. What is the R 2 value  Useful statistic, but not definitive  Does tell you how well model fits the data  Does not tell you that the model is correct  Tells you how much of the distribution about the mean is described by the model

17. Problems with R 2

18. How “Good” is the Fit? 2. Are residuals random

19. Residuals Should Be Normally Distributed

20. How “Good” is the Fit? 3. Find Confidence Interval

21. Parameter Confidence Level

22. Confidence Level of y

24. Multiple Linear Regression: Mathcad - Regress

25. Mathcad Regress Function

26. Results on Ycalc vs Y Plot

27. Residuals

28. R 2 Statistic

29. Confidence Level for Parameters n is number of points, kk is number of independent variables

30. Confidence Level for Ycalc