1 / 30

Regression Analysis

Regression Analysis. RLR. 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. Linear Regression.

darci
Download Presentation

Regression Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Regression Analysis 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. Statistical Analysis of Regression Straight Line Model as Example

  14. Fit a Line Through This Data

  15. Least Squares

  16. How “Good” is the Fit? • What is the R2 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 R2

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

  19. Residuals Should Be Normally Distributed

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

  21. Parameter Confidence Level

  22. Confidence Level of y

  23. Multiple Linear Regression in Mathcad

  24. Multiple Linear Regression: Mathcad - Regress

  25. Mathcad Regress Function

  26. Results on Ycalcvs Y Plot

  27. Residuals

  28. R2 Statistic

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

  30. Confidence Level for Ycalc

More Related