## A simple Analysis of Variance example

> chickwts

> plot(chickwts)
> Y <- chickwts[,1]
> X <- chickwts[,2]
> n <- length(Y)

> plot(X,Y)

> Mod <- lm(Y~X-1)
> beta.hat <- Mod$coef
> beta.hat

> X == "casein"
> mean(Y[X=="casein"])
> mean(Y[X=="horsebean"])

> Mod0 <- lm(Y~1)
> beta.dhat <- Mod0$coef
> beta.dhat
> mean(Y)

> Design <- model.matrix(Mod)
> Design0 <- model.matrix(Mod0)

> RSS <- sum((Y - Design%*%beta.hat)^2)
> RSS0 <- sum((Y - Design0%*%beta.dhat)^2)

> p <- ncol(Design)
> p0 <- ncol(Design0)

> F <- ((RSS0 - RSS)/(p-p0))/(RSS/(n-p))
> F

> qf(0.95,p-p0,n-p)
> 1 - pf(F,p-p0,n-p)

> anova(Mod0,Mod)