unm <- read.csv("enrollment.csv")
plot(unm$unem,unm$enroll,xlab="Unemployment (%)",ylab="Enrollment")
#
# We could use our commands, but there is built in tools
#
res <- lm(enroll~unem,data=unm)
names(res)
res$coef
res$fitted
res$resid
summary(res)
#
# We will discuss some of this output more in detail on Monday
#
plot(unm$unem,unm$enroll,xlab="Unemployment (%)",ylab="Enrollment")
abline(res)
confint(res)
confint(res,level=.90)
#
# Predicted values based on model
#
xh <- data.frame(unem=7)
predict(res,newdata=xh)
xh <- data.frame(unem=c(6,7,8,9,10))
predict(res,newdata=xh)
predict(res,newdata=xh,se.fit=T)
predict(res,newdata=xh,interval="confidence",level=.95)
predict(res,newdata=xh,interval="prediction",level=.95)
#
# Can we graph this in a useful fashion?
#
attach(unm)  # Break apart the file so we have easy access to data
plot(unem,enroll,xlab="Unemployment (%)",ylab="Enrollment",pch=20)
abline(res,lwd=2)
newData <- data.frame(unem=seq(min(unem),max(unem),by=(max(unem)-min(unem))/45))
conf.lim <- predict(res,newData,interval="confidence")
pred.lim <- predict(res,newData,interval="prediction")
matlines(newData$unem,conf.lim[,-1],col="red",lty=2)
matlines(newData$unem,pred.lim[,-1],col="green",lty=3)
legend(8.5,7000,legend=c("Fitted Line","Confidence Bands","Prediction Bands"),
	lty=c(1,2,3),col=c("black","red","green"))