Built-in models_Linear regression

!Model
The multiple linear regression model with dependent variable \(y\) and independent variables \(\mathbf{x}=(x_{1},\ldots,x_{p})\),
{{%%
\[
y_{i}=\beta_{0}+\beta_{1}x_{1}+,\ldots,+\beta_{p}x_{p}+e_{i}
\]
%%}}
where \(e_{i}\) is usually assumed to be iid \(N(0,\phi)\). As an example, we let \(p=2\) in the code.

!Code

{{
model{
for (i in 1:N){
mu[i]<-beta0+beta1*(x1[i]-mean(x1[]))+beta2*(x2[i]-mean(x2[]))
y[i] ~ dnorm(mu[i],pre.phi)
}
beta0~dnorm(0,1.0E-6)
beta1~dnorm(0,1.0E-6)
beta2~dnorm(0,1.0E-6)

pre.phi~dgamma(.001,.001)

phi<-1/pre.phi
}

}}