Excel ModelingNon Linear Regression

Anchored By:

Renu Rao

Kaveh Saba

Features of Solver

Solver can optimize the value in the target cell by varying the adjustable cells.

Cells are related by a given model equation, which is then used to find predicted values.

NonLinear Regression

Two-variable nonlinear regression 3 components:

Experimental Data A model equation to follow to get predicted

values Initial guesses for variables values.

In the Excel Spreadsheet…

Column 1: Independent variables from experimental data

Column 2: Values measured for the dependent variables

Column 3: Predicted values using the model equation

2 initial guesses for variables

Reaction Rate Example from Text

Given: Rate constant (k) at various temperatures (T)

Need to determine Activation Energy (E) and frequency factor (A)

Fit to Arrhenius equation k(T) = Ae −E / RT

Initial Excel SetupVarying Values:

A (s-1): 2000.0E (J) 25000.0

Constants:R (J/mol*K): 8.314

Prediction Model: k = A*exp(-E/(R*T))

Temperature (K) Experimental Rate constant (s-1) Predicted k value Residuals Squared301 0.403 0.091716623 0.096897341322 0.709 0.175953962 0.284138078339 0.996 0.281046883 0.511157959357 1.464 0.439551663 1.049494395383 2.234 0.778637023 2.118081395406 3.222 1.214772938 4.028960479421 4.013 1.581606675 5.911673502438 5.13 2.086858925 9.260707605

Sum of Residuals Squared: 23.26111075

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Renu and Kaveh