# ==================================================
# Homework R: 1
# ==================================================

# A
x <- c(8,10,14,3,9,12,12,16,16,6,11,15,28,22,16,7,9,14,5,10,11,13,17,15,5,12,14,17,21,18)
y <- c(5,7,8,5,7,10,9,17,15,9,11,15,18,25,10,5,7,8,5,8,10,9,18,14,9,10,16,18,25,10)

mean(x)
median(x)
var(x)
sd(x)

mean(y)
median(y)
var(y)
sd(y)

sum(x^2)-(sum(x))^2/length(x)
sum(y^2)-(sum(y))^2/length(y)
sum(x*y)-(sum(x)*sum(y))/length(x)

boxplot(x)
boxplot(y)

cor(x,y)
lm(y~x)

plot(x,y)
abline(lm(y~x))

# B

mydata <- read.csv("c:/Documents and Settings/username/Desktop/soc510hw1.csv")
attach(mydata)
names(mydata)

mean(age)
mean(wage)
mean(educ)

sd(age)
sd(wage)
sd(educ)

bins=seq(0, 60, by=2)
hist(wage, breaks=bins, col="gray", freq=FALSE)
x <- rnorm(1000,mean(wage),sd(wage))
curve(dnorm(x, mean=mean(wage), sd=sd(wage)), col="darkgreen", add=TRUE)
abline(v=mean(wage), col="blue", lty=2)
abline(v=median(wage), col="red", lty=2)

boxplot(age)
boxplot(wage)
boxplot(educ)

cor(wage, age)
cor(wage, educ)

lm(wage~age)
lm(wage~educ)

plot(educ, wage)
abline(lm(wage~educ))



# C

pnorm(1.21532) - pnorm(-.83235)
1-pnorm(2.5321)
pnorm(-1.6523583)
1-pnorm(3.65, mean=3.21, sd=.28)
1-pnorm(3.65, mean=3.21, sd=.28/sqrt(50))







# --------------------------------------------------------------
# additional examples: histogram with a normal distribution line
# --------------------------------------------------------------
hist(wage, freq=FALSE)
x <- rnorm(1000,mean(wage),sd(wage))
curve(dnorm(x, mean=mean(wage), sd=sd(wage)), col="red", add=TRUE)

hist(wage, nclass=30, freq=FALSE, col="grey")
x <- rnorm(1000,mean(wage),sd(wage))
curve(dnorm(x, mean=mean(wage), sd=sd(wage)), col="red", add=TRUE)

abline(v=mean(wage), col="blue", )
abline(v=median(wage), col="darkgreen", lty=2)

# --------------------------------------------------------------
# editing your data with an data window
# --------------------------------------------------------------

mydata <- edit(as.data.frame(NULL))
attach(mydata)
names(mydata)

# if you find an error, you can edit your data by doing

edit(mydata)


# --------------------------------------------------------------
# graph of the standard normal distribution
# --------------------------------------------------------------
x <- rnorm(1000,0,1)
curve(dnorm(x, mean=0, sd=1), from=-4, to=4)



# --------------------------------------------------------------
# to calculate area of a normal distribution
# --------------------------------------------------------------

install.packages('PASWR')
library(PASWR)
normarea(-1.96, 1.96, 0, 1)