#A.  Wheat and rain data:
#Read data:
a <- read.table("http://www.stat.ucla.edu/~nchristo/statistics13/rain_wheat.txt", header=TRUE)

#Run the regression of wheat on rain:
q <- lm(a$wheat ~ a$rain)

#Summary of the regression:
summary(q)

#Scatterplot:
plot(a$rain, a$wheat)

#Check the assumptions:
plot(q$fitted, q$res)
plot(a$rain, q$res)

#Obtain leverage values:
influence(q)$hat

#Obtain standardized residuals:
rstandard(q)

#Remove the two influential points (cases 25 and 26):
a1 <- a[-c(25,26), ]

#Run the regression again without case 25 and 26:
q1 <- lm(a1$wheat ~ a1$rain)

#Summary of the new regression:
summary(q1)

#New scatterplot:
plot(a1$rain, a1$wheat)



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#B.  District data:
#Access data:
b <- read.table("http://www.stat.ucla.edu/~nchristo/statistics13/district.txt", header=TRUE)

#Run the regression of change on white:
q <- lm(b$change ~ b$white)

#Summary of the regression:
summary(q)

#Scatterplot:
plot(b$white, b$change)

#Check the assumptions:
plot(q$fitted, q$res)
plot(b$white, q$res)

#Obtain leverage values:
influence(q)$hat

#Obtain standardized residuals:
rstandard(q)

#Remove the two influential points (cases 14 and 40):
b1 <- b[-c(14,40), ]

#Run the regression again without case 25 and 26:
q1 <- lm(b1$change ~ b1$white)

#Summary of the new regression:
summary(q1)

#New scatterplot:
plot(b1$white, b1$change)