Does anyone know of software that will return (3^(x+1)-1)/2 as the best-fit equation for the following data: (0,1),(1,4),(2,13),(3,40),(4,121),(5,364)?

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- December 7th 2010, 04:42 PMManxRegression software
Does anyone know of software that will return (3^(x+1)-1)/2 as the best-fit equation for the following data: (0,1),(1,4),(2,13),(3,40),(4,121),(5,364)?

- December 8th 2010, 06:31 AMCaptainBlack
There are lots of ways of ways of fitting data to a member of a family of functions and lots of packages that will do the job. But that is not what you are asking. What you want is a method of identifying the pormula that produces the sequence: 1,4,13,40,121,364

Now such a formula will not be unique, but you can use the Online Encyclopedia of Integer sequences

CB - December 8th 2010, 06:54 AMManx
Thank you very much CaptainBlack. That is a very interesting link. I will surely investigate it. The problem I posed was just an example of a type of problem that I do not believe is addressed by popular software, at least not directly. Although the data I listed implies a sequence, I could have included (0.5,2.0981) and/or (1.7,9.2095). Instead of only giving pure power functions or exponential functions, does any software give variations such as y=3(2^(x+h)-k?

- December 8th 2010, 09:02 AMCaptainBlack
No you have to know what general form you want to fit to your data, then you will use a general purpose fitting tool like the solver that ships with Excel

If any piece of software pretends to do general fitting without being steered in the direction you want you should look vary carefully at what it purports to do.

CB - December 8th 2010, 04:22 PMManx
Thanks again CB. I will check out the solver with Excel. I was unaware that it existed.

As for other software, I would expect to give the basic information such as wanting to fit an exponential function, but the variation I mentioned does not satisfy the definition of "exponential function". Unfortunately, the function that fits the data best (perfectly) is not technically an exponential function. I am looking for software that allows for such variation, and hence gives the best fit equation, even if the equation is not a true exponential function. The software could require some interaction with the user; I wouldn't necessarily expect it to do all of the work automatically.