In addition, something has gone wrong, Vincy, with your data x,y between evaluating cov(x,y) and evaluating your explicit formula.
If I repeat your commands: x = c(44,46,46,47,45,43,45,44) y = c(44,43,41,41,46,48,44,43) cov(x, y) # [1] -2.428571 sum((x-mean(x))*(y-mean(y)))/8 # [1] -2.125 which has the right sign and, when changed to incorporate the correct denomonator (n-1 = 7) as suggested by Dimitris: sum((x-mean(x))*(y-mean(y)))/7 # [1] -2.428571 gives exact agreement. With regard to your second formula, this should correspondingly be: sum(x*y)/7 - (mean(x)*mean(y))*8/7 # [1] -2.428571 again agreeing exactly. Your result: >> covariance = sum((x-mean(x))*(y-mean(y)))/8 # no of of paired >> obs. = 8 >> >> or >> >> covariance = sum(x*y)/8-(mean(x)*mean(y)) >> >> gives >> >> covariance = 2.125 agrees in numerical magnitude with the "1/8" form, but has the wrong sign. Or maybe you simply mis-typed "-2.125" as "2.125". Hoping this helps, Ted. On 23-Aug-11 11:25:15, Dimitris Rizopoulos wrote: > well, you don't have the correct denominator, i.e., n-1, > with n denoting the sample size. Have a look at the *Details* > section of the online help file for cov(), and try also > > sum((x-mean(x))*(y-mean(y)))/7 > cov(x, y) > > > I hope it helps. > > Best, > Dimitris > > > On 8/23/2011 1:18 PM, Vincy Pyne wrote: >> Dear R list, I have one very elementary question regrading correlation >> between two variables. >> >> x = c(44,46,46,47,45,43,45,44) >> y = c(44,43,41,41,46,48,44,43) >> >>> cov(x, y) >> [1] -2.428571 >> >> However, if I try to calculate the covariance using the formula as >> >> >> covariance = sum((x-mean(x))*(y-mean(y)))/8 # no of of paired >> obs. = 8 >> >> or >> >> covariance = sum(x*y)/8-(mean(x)*mean(y)) >> >> gives >> >> covariance = 2.125 >> >> I am not able to figure out where I am going wrong w.r.t. the >> covariance formula. Kindly guide. >> >> Regards >> >> Vincy >> >> >> >> >> >> >> >> >> >> >> >> >> [[alternative HTML version deleted]] >> >> >> >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > -- > Dimitris Rizopoulos > Assistant Professor > Department of Biostatistics > Erasmus University Medical Center > > Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands > Tel: +31/(0)10/7043478 > Fax: +31/(0)10/7043014 > Web: http://www.erasmusmc.nl/biostatistiek/ > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@wlandres.net> Fax-to-email: +44 (0)870 094 0861 Date: 23-Aug-11 Time: 12:38:36 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
