# [R] Matrix multiplications

george brida george.brida at gmail.com
Sat May 21 21:26:06 CEST 2016

```Roy,

Yes, t(y-X %*% b) is the transpose of y-X %*% b. In principle the product
of  t(y-X %*% b) *(y-X %*% b) is a scalar, I don't know why I have an error
message after the following line:

(t(y-X %*% b)%*%(y-X %*% b)/(length(y)-ncol(X)))*solve(t(X)%*% X)

Thanks

On Sat, May 21, 2016 at 9:10 PM, Roy Mendelssohn - NOAA Federal <
roy.mendelssohn at noaa.gov> wrote:

> >  str(t(y-X %*% b))
>  num [1, 1:10] 0.595 -1.7538 -0.0498 -1.651 -0.6328 ...
> > str((y-X %*% b))
>  num [1:10, 1] 0.595 -1.7538 -0.0498 -1.651 -0.6328 …
>
> -Roy
>
>
> > On May 21, 2016, at 12:00 PM, 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
> >
> >
> >
> > Thank you
> >
> > George
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
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> > and provide commented, minimal, self-contained, reproducible code.
>
> **********************
> "The contents of this message do not reflect any position of the U.S.
> Government or NOAA."
> **********************
> Roy Mendelssohn
> Supervisory Operations Research Analyst
> NOAA/NMFS
> Environmental Research Division
> Southwest Fisheries Science Center
> ***Note new address and phone***
> Santa Cruz, CA 95060
> Phone: (831)-420-3666
> Fax: (831) 420-3980
> e-mail: Roy.Mendelssohn at noaa.gov www: http://www.pfeg.noaa.gov/
>
> "Old age and treachery will overcome youth and skill."
> "From those who have been given much, much will be expected"
> "the arc of the moral universe is long, but it bends toward justice" -MLK
> Jr.
>
>

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