linear R Documentation

## Multivariate linear ridge regression estimator

### Description

Computes the parameter estimates in a linear least squares ridge regression.

### Usage

```linear(x, y, eleg=TRUE, lambda=0)
```

### Arguments

 `x` n*d data matrix; the matrix of the values of the explanatory variables `y` n vector; the values of the response variable `eleg` TRUE or FALSE; an internal parameter related to the method of calculation `lambda` nonnegative real number; the degree of penalization in ridge regression; if lambda=0, then the usual linear least squares estimates are calculated

### Value

list of beta0 and beta1; beta0 is a real number and beta1 is a d vector; beta0 is the estimate of the intercept and beta1 is the vector containing the estimates of the coefficients

### Author(s)

Jussi Klemela

`linear.quan`,

### Examples

```set.seed(1)
n<-100
d<-2
x<-8*matrix(runif(n*d),n,d)-3
C<-(2*pi)^(-d/2)
phi<-function(x){ return( C*exp(-sum(x^2)/2) ) }
D<-3; c1<-c(0,0); c2<-D*c(1,0); c3<-D*c(1/2,sqrt(3)/2)
func<-function(x){phi(x-c1)+phi(x-c2)+phi(x-c3)}
y<-matrix(0,n,1)
for (i in 1:n) y[i]<-func(x[i,])+0.01*rnorm(1)

linear(x,y)
```