Matrix multiplications
On 21 May 2016, at 21:00 , george brida <george.brida at gmail.com> wrote: Dear R users: I have written the following lines :
x=c(10,11,12,13,14,17,15,16,10,11,41,25,26,14,12,14,15,20,14,22) x=matrix(x,ncol=2) a=matrix(1,nrow(x),1) X=cbind(a,x) y=c(12.00, 11.00, 13.00, 12.50, 14.00, 18.50, 15.00, 12.50, 13.75, 15.00)
b=solve(t(X)%*% X)%*% t(X)%*% y
when I wrote the following line
(t(y-X %*% b)%*%(y-X %*% b)/(length(y)-ncol(X)))*solve(t(X)%*% X)
I have obtained an error message, I don't know why namely (t(y-X %*% b)%*%(y-X %*% b)/(length(y)-ncol(X))) is a scalar:
(t(y-X %*% b)%*%(y-X %*% b)/(length(y)-ncol(X)))
[,1] [1,] 3.620354 Can you please help me.
Mistake is that (t(y-X %*% b)%*%(y-X %*% b)/(length(y)-ncol(X))) is NOT a scalar, but a 1 x 1 matrix. This works: as.vector((t(y-X %*% b)%*%(y-X %*% b))/(length(y)-ncol(X)))*solve(t(X)%*% X) as does recognizing the first term as a sum of squares: sum((y-X %*% b)^2)/(length(y)-ncol(X))*solve(t(X)%*% X) (And, for the Illuminati, a Kronecker product works too: (t(y-X %*% b)%*%(y-X %*% b)/(length(y)-ncol(X))) %x% solve(t(X)%*% X) This could be useful for multivariate y.)
Thank you George [[alternative HTML version deleted]]
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