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#### By Jimin Ding, 01/21/2017

## Sir Francis Galton (1822-1911) studied a data set of 1078 heights of fathers and sons. 
## Let's load, summarize, and visualize the data

######################## Step 1. Load Data  ################################

father.son=read.table("http://www.math.wustl.edu/~jmding/math3200/pearson.dat")
names(father.son)=c("fheight","sheight")
head(father.son) 

?read.table

## Otherways to find the data
install.packages("UsingR")
library(UsingR)
data(father.son)

################ Step 2. Summarize the heights of Father and Son ######################
mean(father.son$fheight)
mean(father.son$sheight)
median(father.son$fheight)
median(father.son$sheight)

min(father.son$fheight)
max(father.son$fheight)
range(father.son$fheight)

quantile(father.son$fheight)
quantile(father.son$fheight,prob=seq(from=0,to=1,by=0.1))


var(father.son$fheight)
sd(father.son$fheight)

hist(father.son$fheight)
hist(father.son$sheight,xlab="Son's Height")

boxplot(father.son)
?boxplot

qqnorm(father.son$fheight)
qqline(father.son$fheight)

################ Step 3. Relationship Between the heights ######################

plot(father.son,xlab="Father's Height (inches)", ylab="Son's Height (inches)", main="Heights of Fathers and Their Full Grown Sons")

regfit=lm(sheight ~ fheight, data=father.son)

plot(sheight ~ fheight, data=father.son,bty="l",pch=20,
     xlab="Father's Height (inches)", ylab="Son's Height (inches)", main="Heights of Fathers and Their Full Grown Sons")
abline(a=0,b=1,lty=2,lwd=2)
abline(regfit,lty=1,lwd=2,col='red')

cov(father.son)
cor(father.son)

acfvalues=acf(regfit$residuals)
plot(regfit$residuals)