I always like the version that comes in the standard J stats library:
corr
cov % *&stddev
cov
spdev % <:@[EMAIL PROTECTED]
spdev
+/@(*~ dev)
dev
-"_1 _ mean
mean
+/ % #
stddev
%:@var
var
ssdev % <:@#
ssdev
+/@:*:@dev
On 6/26/07, Pablo Landherr <[EMAIL PROTECTED]> wrote:
Going for educational value rather than terseness, here is an alternative:
corr=: [EMAIL PROTECTED] NB. correlation is the crossproduct of
standardised values
cprod=: (+/ .*)~ |: NB. crossproduct
standard=: [EMAIL PROTECTED] NB. standardised numbers are
'adjusted'
and 'centered'
adjust=: ] %"1 [: sqroot sqsum NB. adjusted numbers have a variance
of
1
center=: -"1 avg NB. centered numbers have a mean of 0
avg=: +/ % # NB. artitmetic mean
sqroot=: %: NB. square root
sqsum=: +/@:*: NB. sum of squared
corr 1 3 2 4,"(0) 2 4 3 3.5
1 0.831522
0.831522 1
On 6/26/07, June Kim <[EMAIL PROTECTED]> wrote:
>
> Thank you, Henry.
>
> While I try to translate a mathematical expression into a J
> expression, I often discover hidden patterns in the expression with
> great joy. It sometimes leads me to a path to new insights.
>
> It's the reason I am looking for the shortest form this time.
>
> 2007/6/26, Henry Rich <[EMAIL PROTECTED]>:
> > Not really, but gee, shouldn't we be using our wonderful
> > language to provide the most expressive form of c rather
> > than just the shortest?
> >
> > a =. (# * +/)@:* - *&(+/)
> > c =. a % [EMAIL PROTECTED] %:@* [EMAIL PROTECTED]
> > 1 3 2 4 c 2 4 3 3.5
> > 0.831522
> >
> > a =. ((# * +/)@:* - *&(+/)) "1
> > c =. %: @ (%~/ . *) @: (a/~) @: ,:
> > 1 3 2 4 c 2 4 3 3.5
> > 0.831522
> >
> > I don't think either of these forms is useful for real work,
> > since they involve subtracting big near-equal numbers, but
> > I learned something about the computation by writing them.
> >
> > Henry Rich
> >
> > > -----Original Message-----
> > > From: [EMAIL PROTECTED]
> > > [mailto:[EMAIL PROTECTED] On Behalf Of June Kim
> > > Sent: Tuesday, June 26, 2007 10:08 AM
> > > To: Programming forum
> > > Subject: [Jprogramming] Correlation Coefficient
> > >
> > > I've been playing with the expression at
> > > http://en.wikipedia.org/wiki/Correlation
> > >
> > >
> > > c=.(*&[EMAIL PROTECTED]@:*)%*&(s(-~(#*s=.+/))&.:*:])
> > > 1 3 2 4 c 2 4 3 3.5
> > > 0.831522
> > >
> > > c is as short as I can get. Could you come up with a verb for
> > > correlation, shorter than c?
> > >
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> > > For information about J forums see
> > > http://www.jsoftware.com/forums.htm
> >
> > ----------------------------------------------------------------------
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> >
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--
Devon McCormick, CFA
^me^ at acm.
org is my
preferred e-mail
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