Re: exponential regression

*To*: mathgroup at smc.vnet.net*Subject*: [mg129668] Re: exponential regression*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sun, 3 Feb 2013 20:19:56 -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*: <20130203074543.780E568A2@smc.vnet.net>

I do not have a TI calculator so I cannot check; however, it appears that the calculator was given (or defaults to) a different model: a*x^b vice a*b^x. Although even with this other model, Mathematica comes up with different results than what you indicate came from the calculator. data = {{1, 4.5}, {3, 14.0}, {5, 28.6}, {7, 54.1}, {8, 78.6}} // Rationalize; f1[x_] = a*b^x /. FindFit[data, a*b^x, {a, b}, x] 4.666254411839531*1.4227203453064998^x f2[x_] = a*x^b /. FindFit[data, a*x^b, {a, b}, x] 1.17537380064539*x^2.0035258937349667 There does not appear to be a locally optimal fit ("In the nonlinear case, [FindFit] finds in general only a locally optimal fit") near the reported results irrespective of the method used. FindFit[data, a*x^b, {{a, 3.947506}, {b, 1.334589}}, x, WorkingPrecision -> 16, Method -> #] & /@ { Automatic, "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "NMinimize", "QuasiNewton"} {{a -> 1.175373799417422, b -> 2.003525894261809}, {a -> 1.175373793803054, b -> 2.003525896660905}, {a -> 1.175373798908934, b -> 2.003525894474658}, {a -> 1.175373799417422, b -> 2.003525894261809}, {a -> 1.175373798541258, b -> 2.003525894637715}, {a -> 1.17538, b -> 2.00352}, {a -> 1.175373798541583, b -> 2.003525894637293}} Plot[ Evaluate[{ Tooltip[f1[x], f1], Tooltip[f2[x], f2]}], {x, 0, 9}, Epilog -> {Red, AbsolutePointSize -> 3, Point[data]}] Bob Hanlon On Sun, Feb 3, 2013 at 2:45 AM, <r.aufmann at gmail.com> wrote: > 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. Th= e input returned {a->4.66625, b->1.42272} > > Fine. However, a student of mine entered the same data in a TI-84 calcul= ator and it returned 3.947506 (x^1.334589). These two equations are obviou= sly not the same. Does anyone know why there is a discrepancy? By the way= , I tested a data set that is exactly exponential. FindFit and the TI-84 re= turned exactly the same equation. > > Thanks for any insight. >

**References**:**exponential regression***From:*r.aufmann@gmail.com