[R] Matrix multiplications

[peter dalgaard]

> 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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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
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Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com