Hello,
This month we are talking about the third and final curve fitting capability in DeltaGraph, “Creating a Custom Curve Fit”. This option in DeltaGraph allows the end user to create just about any custom curve fit their data requires. This information is also available
in a
flash presentation from our web site.I look forward to your comments.
Andrea Maize
Product Manager
Red Rock Software, Inc.
amaize@redrocksw.com
A Custom Curve Fit
In this third example, we'll consider temperature data for a sample of material at an initial temperature of 110º F in a surrounding environment of 32º F. The cooling of the sample in this situation is governed by
Newton's Law of Cooling, given by...
The Sample data are shown in figure 8.
Figure 8, Newton's Law Of Cooling Sample Data.
While DeltaGraph does not have a model for Newton's Law of Cooling built in, we can easily define it using the custom formula dialog.
As in the first example generate a scatter chart from the data, select the chart and choose "Curve Fitting...". Now, in the Curve Fitting Type area, select the "User Defined" button, then click the "Define" button. This will bring up the "User Defined Curve Fit" dialog, shown below.
Figure 9, User Defined Curve Fit Dialog.
The first box labeled
Data is where the name of the independent variable is entered. Here we've called it
t, but it could be any letter. The next box is
Model. This is where our model formula is entered. Here we've entered the form of the Newton's Law of Cooling equation with letters "a" substituted for
T0 and "b" for
Ts. Be sure to put a semicolon at the end of your formula definition. Next, we set some initial values for our free parameters. a = 20, b = 100, and k = 1, all separated by semicolons. The next important step in this example is to set
Max Iterations. In this case we've set it to 10. This controls the number of iterative steps the Least Squares algorithm takes to find converging values for our parameters. This value must be set on a case by case basis and can range from 1 to 32767. See the references or check the DeltaGraph help for more information on this topic.
To finish generating your custom curve fit click OK in the dialog then click OK in the Curve Fitting Dialog to finish the process. For this data set you should get a graph that looks like figure 10.
Figure 10, Custom Curve Fit.
As we've seen, curve fitting in DeltaGraph is easy and accurate. Curve fitting can be a very useful tool for understanding data and for making more useful and visually compelling charts. Like any tool, however, one must master a few basic concepts to use it effectively. In this article we have covered many of the basic concepts of curve fitting and have learned the essentials of the curve fitting tools in DeltaGraph. To learn more the reader is encouraged to consult the references following this article and as always, the DeltaGraph user manual and online help is an excellent place to start.
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