
Re: exponential regression
Posted:
Feb 3, 2013 8:19 PM


> 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 TI84 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.

