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Re: Re: Fit function vs Hand Calculation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104586] Re: [mg104528] Re: Fit function vs Hand Calculation
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Wed, 4 Nov 2009 01:37:44 -0500 (EST)
  • References: <4AEDB3D2.4010604@accardi.com> <4AEE0305.8070404@gmail.com>
  • Reply-to: drmajorbob at yahoo.com

The jpeg is a time-waster; you could have put a notebook at the link,  
instead.

BUT: all we need is code, and you don't need a notebook, a link, OR a  
picture for that.

Here's a look at the problem:

data = {{7, 1}, {5, 0}, {4, -1}};
g[x_] = InterpolatingPolynomial[data, x];

FindFit[data, a + b Log@x, {a, b}, x]
f[x_] = a + b Log@x /. %

{a -> -5.80756, b -> 3.52568}

-5.80756 + 3.52568 Log[x]

Show[Plot[{f@x, g@x}, {x, 0, 10}],
  Graphics[{PointSize[.02], Point@data}]]

Show[Plot[f@x, {x, 3.9, 7.1}, PlotStyle -> Red],
  Graphics[{Blue, PointSize[.02], Point /@ data}],
  Plot[g@x, {x, 3.9, 7.1}, PlotStyle -> Blue]]

InterpolatingPolynomial gives an exact fit, but the Fit function only  
tries to get close.

In this case, I assume there's no function of the form a + b Log[x] that  
precisely fits your three points.

Bobby

On Tue, 03 Nov 2009 01:53:58 -0600, John Accardi <accardi at accardi.com>  
wrote:

> Hello,
>
> Reading this forum I know my question is quite elementary.  I am
> new to Mathematica and have been pulling my hair out here (and I'm
> bald to being with!).
>
> Any insights on this one?
>
> I assume a *.nb file can be attached here to this posting.  It
> contains the question.  If not, it can be viewed here:
>
>          http://www.accardi.com/zane.jpg
> Thanks in advance for helping out.
>
>


-- 
DrMajorBob at yahoo.com


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