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

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