'NonlinearFit` confusion

• To: mathgroup at smc.vnet.net
• Subject: [mg49844] 'NonlinearFit` confusion
• From: klingot at yahoo.com (Klingot)
• Date: Wed, 4 Aug 2004 10:46:20 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I'm trying to fit a sinusoidal function to my data using
'NonlinearFit' but it's exhibiting rather odd behaviour. Please see my
examples below:

EXAMPLE (1).

**** As a test, I created a list of data from a function of the form y
= 6 + 2Sin[3 + x] with:

datay = Table [6 + 2Sin[3 + x], {x, -10Pi, 10Pi, 0.05}];
datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
data = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];

**** Then tested to see whether NonlinearFit would correctly deduce
the equations parameters with:

NonlinearFit[data, c + a Sin[d + e x], x, {a, c, d,e}]

**** As expected, it gave me '6.+ 2. Sin[3. + 1. x]' ... exactly as
one would expect :)

EXAMPLE (2).

**** Second test, I modified the equation by multiplying x by 5, ie.
y = 6 + 2Sin[3 + 5x]:

datay = Table [6 + 2Sin[3 + 5 x], {x, -10Pi, 10Pi, 0.05}];
datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
data = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];

***** and applied the NonlinearFit as before:

NonlinearFit[data, c + a Sin[d + e x], x, {a, c, d,e}]

***** but this time I get a wildly innacurate result:    6.000165 +
0.025086 Sin[0.0080308 - 0.247967 x]

Specifically, the parameters 'a', 'd' and 'e' are all completely in
error by orders of magnitude.

I tried extending the range of the data to include more cycles of the
sinusoid, thereby making it more continuous/monotonic but that made no
difference.

Am I missing something fundamental here?

Any assistance would be greatly appreciated.

PS: I'm using Mathematica 5.0 on a MAC.

```

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