I have "data" points as given below (e.g., for x-value = 1, the corresponding value of y is -23.110606616537147. (I apologize, it is rather large data array.) I need to find out the exact function that generated these values. I tried to guess by assuming some functional forms like below in Nonlinearfit, but no matter what I do, I do not get a perfect match between the actual data points and the fitted model. For some similar looking data, earlier I successfully guessed a simple functional form like c0*x^c1, and it was indeed a correct one. But this one gives me a headache. Any hints would be appreciated.
data = {{1, -23.110606616537147`}, {2, -22.634559807032698`}, {3, \
-22.169391395259122`}, {4, -21.714928417099323`}, {5, \
-21.27099702070698`}, {6, -20.837422557417913`}, {7, \
-20.414029677397547`}, {8, -20.00064242987733`}, {9, \
-19.59708436779354`}, {10, -19.20317865660647`}, {11, \
-18.818748187036604`}, {12, -18.44361569142125`}, {13, \
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-2.0269401485288645`}, {264, -2.0193053338702636`}, {265, \
-2.0117275563473562`}, {266, -2.004206182315287`}, {267, \
-1.9967405874795818`}, {268, -1.9893301568484185`}, {269, \
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-1.9530845707790225`}, {274, -1.9459927058478763`}, {275, \
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-1.832825441675692`}, {292, -1.8265755709541789`}, {293, \
-1.820368029301432`}, {294, -1.814202389691782`}, {295, \
-1.8080782314221209`}, {296, -1.8019951386958164`}, {297, \
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NonlinearModelFit[data,
c0 + c1*x^c2 + c3*x^c4, {c0, c1, c2, c3, c4}, x]
ff = FindFormula[data, x]; Show[ListPlot[data], Plot[ff, {x, 0, 300}, PlotStyle -> Red], ImageSize -> Large]
will reproduce the data pretty well but I find it hard to believe that you'll be successful to find the "exact" formula used to generate the data. $\endgroup$ – JimB Jan 6 at 22:09FindFormula
in a comment. Plus, @MikeY's formula uses far fewer parameters and results in a much better fit. $\endgroup$ – JimB Jan 7 at 2:17