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Fit.rSquared

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Fit.rSquared

Danju Men
7 posts
Hi all,

 

Does anyone know what exactly does "Fit.rSquared" return? Is it:

1 - SSE (divided by) SSD;

Or:

1 - SSE (or) SSD?

Why "1 minus"?

 

Thanks,

Danju


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Re: Fit.rSquared

Michael Schmid
2136 posts
Hi Danju,

it is a division, R^2 = 1 - SSE (divided by) SSD,
where:  SSE = sum of the squared errors (residuals) and
        SSD = sum of the squared deviations about the mean (related to the variance of data)

> Why "1 minus"?

If the errors are zero, SSE is zero, and R^2 becomes 1, this is what one calls perfect correlation.

See also
  http://en.wikipedia.org/wiki/Coefficient_of_determination
(we use the last equation in the paragraph 'Definitions')

Michael
________________________________________________________________
On Nov 2, 2012, at 01:10, Danju Men wrote:

> Hi all,
>
>
>
> Does anyone know what exactly does "Fit.rSquared" return? Is it:
>
> 1 - SSE (divided by) SSD;
>
> Or:
>
> 1 - SSE (or) SSD?
>
> Why "1 minus"?
>
>
>
> Thanks,
>
> Danju
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html

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Re: Fit.rSquared

Danju Men
7 posts
But in my case I have only 20 data points, what's the difference between
population mean and sample mean?  Shouldn't they be the same?
Why take the ratio of SSE (divided by) SSD? Why "1 minus" this ratio? What's
the statistical meaning behind this expression?

Thanks,
Danju

-----Original Message-----
From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of
Michael Schmid
Sent: Friday, November 02, 2012 2:40 AM
To: [hidden email]
Subject: Re: Fit.rSquared

Hi Danju,

it is a division, R^2 = 1 - SSE (divided by) SSD,
where:  SSE = sum of the squared errors (residuals) and
        SSD = sum of the squared deviations about the mean (related to the
variance of data)

> Why "1 minus"?

If the errors are zero, SSE is zero, and R^2 becomes 1, this is what one
calls perfect correlation.

See also
  http://en.wikipedia.org/wiki/Coefficient_of_determination
(we use the last equation in the paragraph 'Definitions')

Michael
________________________________________________________________
On Nov 2, 2012, at 01:10, Danju Men wrote:

> Hi all,
>
>
>
> Does anyone know what exactly does "Fit.rSquared" return? Is it:
>
> 1 - SSE (divided by) SSD;
>
> Or:
>
> 1 - SSE (or) SSD?
>
> Why "1 minus"?
>
>
>
> Thanks,
>
> Danju
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

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ImageJ mailing list: http://imagej.nih.gov/ij/list.html