# R code for Lecture 1

# Example 1 in chapter 0

X <- c(1.84, 1.67, 1.68, 1.42, 1.54, 1.59, 1.60, 1.74, 1.83, 1.65, 1.51, 1.80, 
1.64, 1.80, 1.62, 1.67, 1.67, 1.69, 1.74, 1.73)

# calculate sample mean, sample variance and standard deviation.

sm <- mean(X)
sv <- var(X)
sd <- sd(X)

sm; sv; sd

# generate the histogram 

hist(X)


# Example 2

alp <- 0.01
n <- length(X)

# calculate T-statistic
T <- (sm - 1.65)/(sd/sqrt(n))

# calculate (1 - alpha/2)-quantile of t-distribution with df (n-1)
qt <- qt(1-alp/2, n-1)

T; qt


# Example 3

# calculate (1 - alpha/2)-quantile of t-distribution with df (n-1)

alp <- c(0.1, 0.05, 0.01)
qnorm(1-alp/2)

v<- c(2, 10)
qt(0.975, v)

v <- c(10, 5)
qchisq(0.95, v)

alp <-c(0.95, 0.99); v1 <-c(4, 2); v2 <-c(10, 20)
qf(alp, v1, v2)



# Example 4

X <- rbind(c(1.84,91.31), c(1.67, 88.63), c(1.68, 83.94), c(1.42, 75.55), 
c(1.54, 79.57), c(1.59, 82.68), c(1.60, 80.41), c(1.74, 82.42), c(1.83, 92.21), 
c(1.65, 79.63), c(1.51, 71.15), c(1.80, 95.24), c(1.64, 77.38), c(1.80, 91.67), 
c(1.62, 79.57), c(1.67, 80.64), c(1.67, 87.26), c(1.69, 89.52), c(1.74, 93.50), c(1.73, 88.57))

# calcuate the sample varaicne and covariance
Sh <- sd(X[,1]); Sw <- sd(X[,2])
Shw <- cov(X[,1], X[,2])

Sh; Sw; Shw

# calculate the correlation coefficient
rho <- Shw/(Sh*Sw); rho
cor(X[,1], X[,2])

# generate scatterplot
plot(X[,1], X[,2], main="Scatterplot Example") 


# R code for Chapter 1 (Part 1)

# Example 1

X <- c(1.0, 1.5, 2.1, 2.9, 3.2, 3.9)
Y <- c(0.60, 2.00, 1.06, 3.44, 1.17, 3.54)

mX <- mean(X); mY <-mean(Y)
sXY <- sum((X - mX)*(Y -mY))
sX <- sum((X - mX)^2)
b1 <- sXY/sX; b0 <- mY - b1*mX

b0; b1

Y_hat <- b0 + b1*X
res <- Y - Y_hat

Z <- cbind(X, Y, Y_hat, res)
Z