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(b1 <- sum((x-mean(x))*(y-mean(y)))/sum((x-mean(x))^2)) 
(b0 <- mean(y)-b1*mean(x))
yhat <- b0+b1*x
e <- y-yhat
SSE <- sum(e^2)
MSE <- SSE/(length(y)-2)

plot(faithful$waiting,faithful$eruptions,main="Old Faithful",xlab="Wait time (minutes)",
		ylab="Eruption duration (minutes)")

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(b1 <- sum((x-mean(x))*(y-mean(y)))/sum((x-mean(x))^2))
(b0 <- mean(y)-b1*mean(x))
yhat <- b0+b1*x
e <- y-yhat
SSE <- sum(e^2)
MSE <- SSE/(length(y)-2)

plot(faithful$waiting,faithful$eruptions,main="Old Faithful",xlab="Wait time (minutes)",

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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

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unm <- read.csv("enrollment.csv")
plot(unm$unem,unm$enroll,xlab="Unemployment (%)",ylab="Enrollment")
#
# We could use our commands, but there are built in tools
# 
res <- lm(enroll~unem,data=unm)
names(res)
res$coef
res$fitted
res$resid

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install.packages("faraway")
library(faraway) # for data

#
# A regression that meets the assumptions
# 

plot(stat500$midterm,stat500$final)
res <- lm(stat500$final~stat500$midterm)
res <- lm(final~midterm,data=stat500)

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library(car)
library(alr3)
#
# Example 1
#
data(sniffer)
plot(sniffer$TankTemp,sniffer$Y)
res <- lm(Y~TankTemp,data=sniffer)
# Combine plots on 1 page in R
par(mfrow=c(2,2))

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data <- read.csv("cdi.csv")
attach(data)
names(data)
plot(p.bach,per.cap.inc,pch=as.character(region),col=as.numeric(region))
resNC <- lm(per.cap.inc~p.bach,data[region=="NC",])
resNE <- lm(per.cap.inc~p.bach,data[region=="NE",])
resS <- lm(per.cap.inc~p.bach,data[region=="S",])
resW <- lm(per.cap.inc~p.bach,data[region=="W",])
confint(resNC,level=.90)
confint(resNE,level=.90)

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data <- read.csv("sparrow.csv")
attach(data)
plot(ppha,pairs,xlab="Pedestrians per ha per min",ylab="Breeding pairs per ha")
res <- lm(pairs~ppha)
summary(res)
abline(res)
# Add the quadratic term
res2 <- lm(pairs~ppha+ppha^2)
summary(res2)
res2 <- lm(pairs~ppha+I(ppha^2))

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#
# What Polynomial?
#
data <- read.csv("sparrow.csv")
attach(data)
plot(ppha,pairs,xlab="Pedestrians per ha per min",ylab="Breeding pairs per ha")

res3 <- lm(pairs~ppha+I(ppha^2)+I(ppha^3))
summary(res3)
res3b <- lm(pairs~poly(ppha,3))

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library(faraway)
data(savings)
attach(savings)
summary(savings)
help(savings)
pairs(savings)
#
# A better 'pairs' plot
#res <- lm(sr~pop15)
summary(res)