# class 11 examples for correlation
# loader function for Albany, NY Central Park
# station data
source("scripts/loaddata.R")



# Albany station data: USW00014735
# only January, July anomalies
buffer<-loaddata()











# time series Albany  and NY Central Park January
plot(c(1950,2012),c(-6,6),typ='n',xlab='year',ylab='Tavg [C]',main="Monthly Anomalies")
lines(buffer$time,buffer$Albany,
     typ='b',pch=1,col=4)
lines(buffer$time,buffer$Central_Park,
      typ='b',pch=3,col=2)



res<-readline("Next plot: a scatter plot")
# scatter plot Albany July with NY Central Park July
y<-buffer$Central_Park
x<-buffer$Albany
plot(c(-6,6),c(-6,6),typ='n',
     xlab='Alb. Tavg [C]',ylab='NYC Tavg [C]',main="Monthly Anomalies")
points(x,y,pch=3)


res<-readline("Is the distribution of y depending on the value of x?")
ineg<-( x< 0)
ipos<- (x > 0)
xneg<-x[ineg]
xpos<-x[ipos]
yxneg<-y[ineg]
yxpos<-y[ipos]



points(xneg,yxneg,pch=1,cex=0.8,col=4)
points(xpos,yxpos,pch=1,cex=0.8,col=2)
lines(c(-8,8),c(0,0),col="gray")
lines(c(0,0),c(-6,6),col="gray")

print(summary(yxneg))
print(summary(yxpos))

res<-readline("Is the distribution of y depending on the value of x?")
ineg<-( x< 0)
ipos<- (x > 0)
xneg<-x[ineg]
xpos<-x[ipos]
yxneg<-y[ineg]
yxpos<-y[ipos]

# plotting the center of the two sub-samples
# pch=2 creates an 3
# cex=2 makes it large 
points(mean(xneg),mean(yxneg),pch=3,lwd=5,cex=5,col=5)
points(mean(xpos),mean(yxpos),pch=3,lwd=5,cex=5,col=6)



res<-readline("Fit a linear regression line into the scatter plot")
# regression line
y<-buffer$Central_Park
x<-buffer$Albany
res<-lm(y ~ x )
print(summary(res))
lines(x,res$fitted,col=3)