plot(grain~rate,data=seedrates,xlim=c(50,180),ylim=c(15.5,22),axes=FALSE)
new.df<-data.frame(rate=(2:8)*25)
seedrates.lm1<-lm(grain~rate,data=seedrates)
seedrates.lm2<-lm(grain~rate+I(rate^2),data=seedrates)
hat1<-predict(seedrates.lm1,newdata=new.df,interval="confidence")
hat2<-predict(seedrates.lm2,newdata=new.df,interval="confidence")
axis(1,at=new.df$rate); axis(2); box()
z1<-spline(new.df$rate, hat1[,"fit"]); z2<-spline(new.df$rate,
hat2[,"fit"])
rate<-new.df$rate; lines(z1$x,z1$y)
lines(spline(rate,hat1[,"lwr"]),lty=1,col=3)
lines(spline(rate,hat1[,"upr"]),lty=1,col=3)
lines(z2$x,z2$y,lty=4)
lines(spline(rate,hat2[,"lwr"]),lty=4,col=3)
lines(spline(rate,hat2[,"upr"]),lty=4,col=3)
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