Nonlinear Regression in Excel 2000 with the Maple 6 Add-in

There are numerous methods for performing a generalised regression of data to nonlinear functions. One of the most efficient for a wide range of cases is the Levenburg-Marquardt method, which has been coded and submitted to the Maple Application Center by Dr. David Holmgren of Brandon University in Canada, with help from other Maple users from all over the world.

The project is not only an excellent example of Maple users collaborating to enhance the capabilities of Maple, but also capably demonstrates the use of Maple throughout the solution development process, from initial explorations through to the deployment of the solution using Excel as the user interface.

The code is the result of a collaboration of a number of Maple users through the Maple User Group (MUG) mail-list, initiated by David. "I was just curious as to whether or not I could get Maple to do a nonlinear least-squares fit," he told us, " I wrote a fairly simple code to do a binary star orbit fit, which is a highly nonlinear problem (you have to solve Kepler's equation iteratively as part of finding the function value and its derivatives)".

Following a discussion on MUG, a number of users combined their efforts and the result is the Maple code that allows the user to symbolically define the nonlinear fitting function, in terms of independent variables and coefficients; enter the data, and obtain the resulting coefficients that minimize the residuals.

The code was then turned into a Maple 6 package, which can be used in Excel 2000 by using the Maple 6 add-in, a new utility that allows Excel users to gain access to Maple's capabilities in order to perform more advanced analyses.

Not only does the add-in give you access to the built-in functionality of Maple 6, but you can also access any solutions that you develop with Maple 6 directly from within Excel. This provides a very flexible way of deploying your solutions in an environment that is more familiar to the end-user.