#Chapter 4 Example 1 Apple

Apple <- read.delim("//dfs.science.psu.edu/storage/profiles/mxc18/Desktop/Apple.txt") 
#please change the code here to your local address where you save the file. 
#hint: use "/" if "\" shows in the local address and does not work.
attach(Apple)
plot(X,Y,main="Scatterplot of Y vs X", xlab="X = Apple weight",ylab="Y = Apple juice's weight", pch=19)
#check linear relationship and whether pass through origin
r_est_check<-lm(Y~X)
summary(r_est_check)

#Descriptive summary
summary(Apple)
#Standard Deviation
sd(X)
sd(Y)

#Calculate r
r<-mean(Y)/mean(X)
r

#mean estimation
mu_hat_r<-r*mean(X)
mu_hat_r
#total estimation
tau_x=2000
tau_hat_r=r*tau_x
tau_hat_r

#Variance for mean
n=15
s_sq_r<-(1/(n-1))*sum((Y-r*X)^2)
s_sq_r
#Variance for total
Var_tau_r=tau_x/mean(X)*(tau_x/mean(X)-n)*s_sq_r/n
Var_tau_r

#Standard deviation for total
SD_tau_r= Var_tau_r^0.5
SD_tau_r
#95% confidence interval for the total estimation 
CI95=tau_hat_r+SD_tau_r*qt(c(.025,.975),14)
CI95