\begin{Schunk}
\begin{Sinput}
 plot(gradrate ~ schtype, data = dat, xlab = "Private or Public?", ylab = "Graduation Rate", ylim = range(dat$gradrate, na.rm = TRUE)) 
 points(gradratehat[ , 1] ~ as.numeric(schtype), data = newdf, pch = "x", col = "red", cex = 1)
 arrows(x0 = as.numeric(newdf$schtype), y0 = gradratehat[ , 2],x1=as.numeric(newdf$schtype),  y1 = gradratehat[ , 3], col = "green", angle = 90, code = 3)
 text( c(30,25) ~ c( 1.5, 1.5), pos = 1, adj = 2, label = c("x: Predicted Value", "Green brackets 95% CI"), cex = 0.8, col = c("red", "green"))
\end{Sinput}
\end{Schunk}
