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Re: Re: Re: Mathematica function to calculate correlation coefficient?

• To: mathgroup at smc.vnet.net
• Subject: [mg108186] Re: [mg108131] Re: [mg108094] Re: Mathematica function to calculate correlation coefficient?
• From: Yun Zhao <yun.m.zhao at gmail.com>
• Date: Wed, 10 Mar 2010 01:44:03 -0500 (EST)
• References: <hmvq80$17c$1@smc.vnet.net> <201003081113.GAA03974@smc.vnet.net>

Would Correlation[ ] still work if n(t) and the actual data points were not
linear functions of time?  By that, I mean, n(t) is something like
C1*exp(rate*t)+C2.  I am asking because in one case, where I think I have
some errors in my data, n(t) does not come close to any of the data points,
it is far apart, and Correlations [ ] gives me 0.97.

On Tue, Mar 9, 2010 at 12:27 PM, DrMajorBob <btreat1 at austin.rr.com> wrote:

> If n is a InterpolationFunction returned by NDSolve or a symbolic function
> returned by Solve, n[t] is obviously not a list of 8 values; it's one value
> for each t.
>
> You can create such a list, of course, with, for instance, Array[n,8] or
> n/@{.1,.3,.4,.8,.9,1.2,...} (any list of eight t values).
>
> Once you have a pair of same-length lists, Correlation will calculate what
> the name says.
>
> Bobby
>
>
> On Tue, 09 Mar 2010 05:20:19 -0600, Yun Zhao <yun.m.zhao at gmail.com> wrote:
>
> Thanks for your reply.  But remember, the set of data values is 20 data
>> points, and my computed distribution of n(t) is a function of t, so
>> thousands and thousands of points.  When I tried to use
>>
>> Correlation[data1, n(t)]
>>
>> I get the error "Correlation::vctmat: The arguments to Correlation are not
>> a
>> pair of vectors or a pair of matrices of equal length."  Please tell me
>> what
>> I did wrong.  Thank you.
>>
>> Correlation::vctmat: "
>>
>> StyleBox[\"\"\", \"MT\"] The arguments to Correlation are not a pair of
>> vectors or a pair of matrices of equal length
>>
>>
>> On Mon, Mar 8, 2010 at 5:13 AM, Sjoerd C. de Vries <
>> sjoerd.c.devries at gmail.com> wrote:
>>
>>  Surprisingly, you can use the function Correlation to calculate the
>>> correlation between two lists. In your case you should probably use
>>> the set of predicted values and the sat of actual data values.
>>>
>>> Cheers -- Sjoerd
>>>
>>> On Mar 7, 11:05 am, Yun Zhao <yun.m.z... at gmail.com> wrote:
>>> > Hi everyone,
>>> >
>>> >   I solved a differential equation, and got a solution n(t).  Now I
>>> have
>>> > collected 8 data points at 8 different times.  I plotted the solution
>>> of
>>> > n(t), and the curve intersect the 8 data points quite well on a graph
>>> of
>>> > n(t) vs. t.  How do I use Mathematica 7.0 to calculate the correlation
>>> > coefficient R^2 value of how well the n(t) solution fit the data
>>> points?
>>> > Thank you very much.
>>>
>>>
>>>
>>>
>>
>>
>
> --
> DrMajorBob at yahoo.com
>

• References:
  • Re: Mathematica function to calculate correlation coefficient?
    • From: "Sjoerd C. de Vries" <sjoerd.c.devries@gmail.com>