# read in data (table format), you need to change the address where the file is located
usair <- read.table("/Users/yasu/Desktop/ma/Data/usair.txt", header=TRUE)

# one way to obtain mean
sum(usair$SO2)/length(usair$SO2)
sum(usair$Pop)/length(usair$Pop)

# easier way to calculate mean
mean(usair)

# one way to obtain standard deviation
sqrt(sum((usair$SO2 - (sum(usair$SO2)/length(usair$SO2)))^2)/(length(usair$SO2)-1))

# better to break things down
xbar <- sum(usair$SO2)/length(usair$SO2) # xbar is the sample mean
df <- length(usair$SO2)-1 # df is the degrees of freedom
sse <- sum((usair$SO2 - xbar)^2) # sse is the sum squared error (deviation)
var <- sse/df # var is variance, the mean squared error (deviation)
s <- sqrt(var) # s is the standard deviation

# easier way to get standard deviation
sd(usair)

# correlation in a hard way
sum(((usair$SO2-mean(usair$SO2))/sd(usair$SO2))*((usair$Pop-mean(usair$Pop))/sd(usair$Pop)))/(length(usair$Pop) - 1)

# breaking down the correlation
df <- length(usair$Pop) - 1 # degrees of freedom
dx <- (usair$SO2-mean(usair$SO2))/sd(usair$SO2) # deviation scores for x (variable 1)
dy <- (usair$Pop-mean(usair$Pop))/sd(usair$Pop) # deviation scores for y (variable 2)
r <- sum(dx*dy)/df

# or just use the built in function
cor(usair$SO2, usair$Pop)

# attach the dataframe so we can access the columns without calling the dataframe 
attach(usair)

cor(SO2, Neg.Temp)
cor(SO2, Manuf)
cor(SO2, Pop)
cor(SO2, Wind)
cor(SO2, Precip)
cor(SO2, Days)

# plotting scatterplot is easy
plot(SO2, Manuf)
plot(SO2, Manuf, type='b')