Re: exponential regression
- To: mathgroup at smc.vnet.net
- Subject: [mg129675] Re: exponential regression
- From: svkeeley at aol.com
- Date: Sun, 3 Feb 2013 20:22:16 -0500 (EST)
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> I entered Clear[a, b, x]; FindFit[{{1, 4.5}, {3, 14.0}, {5, 28.6}, {7, 54.1}, >{8, 78.6}}, a*b^x, {a, b}, x] as a text of exponential regression. The input >returned {a->4.66625, b->1.42272}
>
> Fine. However, a student of mine entered the same data in a TI-84 calculator >and it returned 3.947506 (x^1.334589).
One problem is that you and your student fitted different curves. You fitted the data to a*b^x and your student fitted the data to a*x^b.
This fits the data to the same curve as your student:
Clear[a, b, x]; FindFit[{{1, 4.5}, {3, 14.0}, {5, 28.6}, {7,
54.1}, {8, 78.6}}, a x^b, {a, b}, x]
The result will be different:
{a->1.17537,b->2.00353}
Your student's calculator probably did a modified linear regression; Mathematica did a more sophisticated fit. If you plot your student's 3.9475*x^1.3346 and Mathematica's 1.17537*x^2.00353 along with the origional data, you'll see that the Mathematica version gives a much better fit. The Mathematica answer for your first try, 4.66625*1.42272^x, also gives a better fit.