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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.

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Regression Analysis

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  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

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