Nonlinear Regression: Screencast
Discusses assumption in nonlinear regression (NLR) and uses data for vapor pressure versus temperature to fit to an Antoine equation. Discusses how to evaluate NLR results.
We suggest you list the important points in this screencast as a way to increase retention.
Important Equations:
\[R^2=1-\frac{SS}{SS_{mean}}\]
where \(R^2\) is R-squared, a measure of goodness of fit of model
\(SS\) = sum of squares of residuals
residual = measured value -calculated value
\(SS_{mean}\) = sum of squares of (measured value – mean)
mean = average value of the dependent variable measured
degrees of freedom = number of measurements – number of parameters
Arrhenius expression format from regression to determine activation energy
\[k = k_{0}e^{-\frac{E}{R}(\frac{1}{T}-\frac{1}{T_{0}})}\]
where \(k\) = rate constant
\(k_{0}\) = rate constant at temperature \(T_{0}\)
\(E\) = activation energy
\(R\) = gas constant
\(T\) = temperature (K)
\(T_{0}\) = temperature in middle of temperature range where data obtained