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

Which of these models are linear?

Example: Surface Tension Model

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

Nonlinear Regression: Mathcad - GENFIT

Nonlinear Regression Results

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

Linear Regression Results

Comparison nonlinear linear

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

Straight Line Model as Example

Fit a Line Through This Data

Least Squares

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

Problems with R 2

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

Residuals Should Be Normally Distributed

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

Parameter Confidence Level

Confidence Level of y

Multiple Linear Regression: Mathcad - Regress

Mathcad Regress Function

Results on Ycalc vs Y Plot

Residuals

R 2 Statistic

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

Confidence Level for Ycalc