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


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@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 TI84 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 TI84 re= turned exactly the same equation. > > Thanks for any insight. >

