DEMONSTRATOR: Here, I'm going to describe
how to use nonlinear regression
to analyze kinetic data using the polymath program
and particularly using polymath
because it's relatively easy to use program
to carry out this regression.
So the model that we're looking at is fitting kinetic data
to this rate expression number
determining these kinetic parameters.
And this is explained in more detail in another screencast.
What I wanna do here is show
how we actually get the results tick
through these results for the values of the parameters
and their confidence limits using the polymath program.
So let's look at the actual program and start from scratch
and input the data to see how we can utilize polymath
to very quickly carry out this nonlinear regression.
So I've opened the polymath program and then I'm going
to go to program and select regression
and we're gonna do nonlinear regression
So on the right side here, select nonlinear regression.
And first, I need to put data into the system,
into the program and this is very similar
to a spreadsheet.
So I've actually typed to data into a excel spreadsheet.
And what I'm going to do is just copy the data
to save time.
And now I need to actually label.
So this first column is rate.
So let's just call it R actually corresponds
to the negative of the rate of reaction of A.
So it's a positive number.
The second column is the concentration of A
so if I click on the column heading,
I can change the label.
So that's concentration of A
and then I can click on the next column heading
and the concentration of B.
So these are data that I wanna fit
to a model I've selected to nonlinear regression.
So in the section I'm gonna type in the model
and the model is gonna be
at the rate is rate constant multiplied
by the concentration of A raise to SumPower are calling n
and then multiplied by the concentration
of B also raises some power that I will call m.
So then polymath automatically identifies the parameters
and ask for initial guesses
so I'm gonna enter in initial guesses
of one for each of these values,
and it's important if We're too far off initial guesses
that program's not going to converge
but these turned out to be good values for converging.
The dependent variable it shows
these are the independent variables
or concentrations of a and B.
If I hit the purple arrow
then it's gonna do the calculations
it's gonna carry out the nonlinear regression.
I want the output to be a report
so that's checked a graph.
So I'll check that the residual.
So we get an idea of if the fit is random,
if the arrow, excuse me, is random
and also store model which we'll put into a column,
the calculated value so that if we want
to do more calculations, very much
like a spreadsheet type calculation.
So when I select the purple arrow
it carries out the calculations.
The report shows me the value
of K and the values for n slightly greater
than one for m slightly,
that's the 0.5 also gets confidence.
95% confidence in the vars.
It gives the R squared value to give variance
and then it shows the values calculate
the measured values in the third column
the calculate values, and then the difference,
the residual it also shows a plot
and let's expand this a bit.
This is applied in the residuals
the difference between the experimental value
and the calculated value as a function of the rate.
And then this is a showing a fit
to the data that show
for each point, how close we are compared
to the experimental data, how close the model is.
And you'll notice we have a fourth column now
and it shows it's the calculation.
So can call this our calculate it
so you can see very quickly we can calculate the parameters
to fit data using polymath
and very easy program
to use takes very little time
to actually implement nonlinear regression.