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Re: Extrapolation in mathematica

  • To: mathgroup at
  • Subject: [mg51545] Re: Extrapolation in mathematica
  • From: Bill Rowe <readnewsciv at>
  • Date: Thu, 21 Oct 2004 22:21:25 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

On 10/20/04 at 1:21 AM, brindaban at (nilaakash) wrote:

>Anybody could you tell me how to extrapolate data in
>mathematica. I can interpolate my data, but extrapolation is not

There is no specific function to extrapolate data in Mathematica because there is no general procedure for extrapolation. The best you can do is fit some specified function to your data then compute the value of that function at the value of interest.

For example consider

{#1, 4*#1 + 10 + Random[]}&/@ Range[10]
Fit[%, {1, x}, x]
% /. x -> 100

Here the first line generates some random points about the line 4x+10,the second finds the best fit line to the data generated and finally a result is computed for x = 100. But note the validity of this method hinges on knowing the underlying function. If the underlying function isn't known and there is no basis for choosing a specific function to fit to the data, there is no basis for any extrapolation.

There are non-parametric regression methods as well which by definition do not require knowledge of a specific function. Instead, these methods make assumptions about smoothness of the function. But these are not generally good candidates for extrapolation.
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