At the expense of some speed and precision a multiplication and a pair of parens can be shaved off
Cr=: +/@:*&(% +/&.:*:)&(- +/ % #) 1 3 2 4 Cr 2 4 3 3.5 0.831522 0j20":Cr/900000000(+,:-)1+i.1000000 _0.99999999999203892000 --- Oleg Kobchenko <[EMAIL PROTECTED]> wrote: > Following that logic, (is there a shorter corr?) > > CR=: (+/@:* % *&(+/)&.:*:)&(- +/ % #) > > 1 3 2 4 CR 2 4 3 3.5 > 0.831522 > > But this is already an exercise in arithmetic and > not statistics. > > > > [mailto:[EMAIL PROTECTED] On Behalf Of Raul Miller > > On 6/27/07, Oleg Kobchenko <[EMAIL PROTECTED]> wrote: > > > What does SD stand for? > > > > %:@E@:*:@:- E > > > > where E is arithmetic mean > > > > If you want to think of it as standard deviation, or > > substandard deviation, feel free. > > --- Oleg Kobchenko <[EMAIL PROTECTED]> wrote: > > > Although in correlation the n-1 cancel out, statistical stddev > > and cov should use sample variance, as the estimated mean is > > used in E(X-E(X))^2 is one less degree of freedom. > > > > --- Raul Miller <[EMAIL PROTECTED]> wrote: > > > > > Here's another (straightforward) variant: > > > > > > E=: +/ % # > > > SD=: %:@E@:*:@:- E > > > COR=: E@:*&(- E) % *&SD > > > --- Oleg Kobchenko <[EMAIL PROTECTED]> wrote: > > > My question is why they are defined at all, > > as they separate the sum and the 1/n part. > > > > E.g. ssdev is sum of squared deviations, > > whereas mean E(X) is Sum Xi*Pi, where Pi is 1/n. > > So the semantical relationship is broken into > > the details of arithmetic. > > > > Here's an approach which, using very simple > > opertations, shows relation between > > covariance (numerator) and variance (denominator). > > > > dv=: - +/ % # NB. deviation > > m1=: +/ % <:@# NB. adjusted mean > > cr=: m1@:*&dv % *&(m1&.:*:@dv) NB. correlation > > > > 1 3 2 4 cr 2 4 3 3.5 > > 0.831522 > > > > > > --- "Sherlock, Ric" <[EMAIL PROTECTED]> wrote: > > > > > Is there any practical reason both spdev & ssdev are defined? > > > They both seem to do the same thing (ssdev is a little bit faster). > > > spdev=:+/@(*~ dev) > > > ssdev=:+/@:*:@dev > > > > > > > > > > -----Original Message----- > > > > From: [EMAIL PROTECTED] > > > > [mailto:[EMAIL PROTECTED] On Behalf Of Devon > > > > McCormick > > > > Sent: Wednesday, 27 June 2007 03:54 > > > > To: Programming forum > > > > Subject: Re: [Jprogramming] Correlation Coefficient > > > > > > > > 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 > > --- Henry Rich <[EMAIL PROTECTED]> wrote: > > > 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? > > > > > ____________________________________________________________________________________ > Be a PS3 game guru. > Get your game face on with the latest PS3 news and previews at Yahoo! Games. > http://videogames.yahoo.com/platform?platform=120121 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ____________________________________________________________________________________ Pinpoint customers who are looking for what you sell. http://searchmarketing.yahoo.com/ ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
