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I know Mathematica has the FindFit function to determine the parameters of a known function that fits a sequence of points, but what if you do not know the relationship (linear, log, quadratic, etc)?

For example, if I have two lists of values:

x={1, 3, 5, 11}
y={1, 9, 25, 121}

Is there a way Mathematica can automatically figure out that y=x^2 ?

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  • $\begingroup$ x = Table[2 i + 1, {i, 10}]; y = x^2; FindSequenceFunction[Transpose[{x, y}], n] // Simplify $\endgroup$
    – Dr. belisarius
    Oct 1, 2015 at 20:02
  • $\begingroup$ But FindSequenceFunction[ ] doesn't guess very well ... $\endgroup$
    – Dr. belisarius
    Oct 1, 2015 at 20:03

2 Answers 2

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FindFormuala is EXPERIMENTAL and new in v10.2

Clear[x, y];

xData = {1, 3, 5, 11};
yData = {1, 9, 25, 121};

y[x_] = FindFormula[Transpose[{xData, yData}], x]

(*  x^2  *)
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Try the following:

data = Transpose[{x, y}];
FindFormula[data, z]
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