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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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.