### Fitting constrained least square regression in R

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Yes. There is something in R for such tasks. This requires a special package called mgcv, which should be installed in standard R configuration. See http://sekhon.berkeley.edu/library/mgcv/html/pcls.html. Especially, check out the option Ain and bin.

Here is an example I wrote:

(copy-paste these lines into R console)

## load the special package first.

library(mgcv)

options(digits=3)

## generate some fake data

x.1<-rnorm(100, 0, 1)

x.2<-rnorm(100, 0, 1)

x.3<-rnorm(100, 0, 1)

x.4<-rnorm(100, 0, 1)

y<-1+0.5*x.1-0.2*x.2+0.3*x.3+0.1*x.4+rnorm(100, 0, 0.01)

## make your own design matrix with one column corresponding to the intercept

x.mat<-cbind(rep(1, length(y)), x.1, x.2, x.3, x.4)

## this is the regular least-square regression

ls.print(lsfit(x.mat, y, intercept=FALSE))

## since you already have an X column for intercept, so no need for lsfit to assume another intercept term.

## the penalized constrained least square regression

M<-list(y=y,

w=rep(1, length(y)),

X=x.mat,

C=matrix(0,0,0),

p=rep(1, ncol(x.mat)),

off=array(0,0),

S=list(),

sp=array(0,0),

Ain=diag(ncol(x.mat)),

bin=rep(0, ncol(x.mat)) )

pcls(M)