       Re: exponential regression

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• Subject: [mg129675] Re: exponential regression
• From: svkeeley at aol.com
• Date: Sun, 3 Feb 2013 20:22:16 -0500 (EST)
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• References: <kel4u3\$38p\$1@smc.vnet.net>

```> 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.

```

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