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Re: Difference Fit vs. Correlation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96806] Re: Difference Fit vs. Correlation
  • From: Ray Koopman <koopman at sfu.ca>
  • Date: Wed, 25 Feb 2009 04:05:02 -0500 (EST)
  • References: <go0j8u$n53$1@smc.vnet.net>

The slope of the regression line will equal the correlation
only when the two standard deviations equal one another.

Dimensions[XY = Transpose@{X,Y}]
{1078,2}

f = Fit[XY,{1,x},x]
a = f[[1]]
b = f[[2,1]]

33.8866 + 0.514093 x
33.8866
0.514093

{mx,my} = Mean@XY
{sx,sy} = StandardDeviation@XY
   r    = Correlation[X,Y]

{67.6871,68.6841}
{2.74487,2.8147}
0.501338

b == r*sy/sx
True

a == my - b*mx
True

On Feb 24, 2:47 am, Claus <clausena... at gmail.com> wrote:
> Hi,
> in the code below, using Correlation I get 0.501338, using Fit I get
> 0.514093.
> How come?
>
> Thanks for your help,
> Claus
>
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>
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>
> In[60]:= lm = LinearModelFit[GaltonDat, {1, x}, x]
>
> Out[60]= FittedModel[\!\(\*
> PanelBox[
> TagBox[
> RowBox[{"33.88660435407788`", " ", "+",
> RowBox[{"0.5140930386233082`", " ", "x"}]}],
> Short],
> FrameMargins->5]\)]
>
> In[62]:= lm["BestFit"]
>
> Out[62]= 33.8866 + 0.514093 x
>
> In[63]:= r2 = Correlation[GaltonX, GaltonY]
>
> Out[63]= 0.501338


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