#
# MATH 3330 Section B   F01
# Intro to Regression
# Week 2

# Chapter 2: What is regression analysis

# Capturing the pattern in the 
#    conditional expectation of Y given X
#    E ( Y | X )

#
# An artificial data set:
# plot( c(0,10), c(0,10), type = "n" )  # sets up axes
# z <- locator( n=100, type = "p" )	# generate data for a swan function
# swan <- data.frame(Y = z$y, X = z$x )
# 
# Pretend X is temperature and Y is amount of chemical Z produced
# in a reaction
#

xyplot( Y ~ X , swan )
xyplot( Y ~ X , swan , col = 1 )

# adding lines to the plot with a 'panel' function

xyplot( Y ~ X , swan, col = 1,
		panel = function( x, y ,...) {
			panel.xyplot( x, y, ...)			# plotting points
		} 
	)
	

xyplot( Y ~ X , swan, col = 1,
		panel = function( x, y ,...) {
			panel.xyplot( x, y, ...)
			panel.lmline( x, y, ...)			# add a least-squares line
		} 
	)
	

xyplot( Y ~ X , swan, col = 1,
		panel = function( x, y ,...) {
			panel.xyplot( x, y, ...)
			panel.lmline( x, y, ...)
			panel.loess( x, y, span = 2/3, family = "gaussian")
					# add a very smooth non-resistant loess line
		} 
	)

xyplot( Y ~ X , swan, col = 1,
		panel = function( x, y ,...) {
			panel.xyplot( x, y, ...)
			panel.lmline( x, y, ...)
			panel.loess( x, y, span = 2/3, family = "gaussian")
			panel.loess( x, y, span = 1/3, 
				family = "gaussian", lty = 3, col=8)
					# add a less smooth non-resistant loess line
		} 
	)


xyplot( Y ~ X , swan, col = 1,
		panel = function( x, y ,...) {
			panel.xyplot( x, y, ...)
			panel.lmline( x, y, ...)
			panel.loess( x, y, span = 2/3, family = "gaussian")
			panel.loess( x, y, span = 1/3, 
				family = "gaussian", lty = 3, col=2)
			panel.loess( x, y, span = 1/8, 
				family = "gaussian", lty = 5, col=8)
					# add a much less smooth non-resistant loess line
		} 
	)


xyplot( Y ~ X , swan, col = 1,
		panel = function( x, y ,...) {
			panel.xyplot( x, y, ...)
			panel.lmline( x, y, ...)
			panel.loess( x, y, span = 2/3, family = "gaussian")
			panel.loess( x, y, span = 1/3, 
				family = "gaussian", lty = 3, col=2)
			panel.loess( x, y, span = 1/8, 
				family = "gaussian", lty = 5, col=5)
			panel.loess( x, y, span = 1/8, 
				family = "symmetric", lty = 5, col=8)
					# same smoothness but resistant
		} 
	)
	
#
#  problem: maybe we need a wider window on the left than 
#  on the right
#  
#  S-Plus function supsmu (super smoother) uses a variable
#  window determined by cross-validation [see SGS p. 160 ff]
#
#  There is no special panel function for supsmu so we write
#  it a bit differently:

xyplot( Y ~ X , swan, col = 1,
		panel = function( x, y ,...) {
			panel.xyplot( x, y, ...)
			panel.loess( x, y, span = 1/8, 
				family = "symmetric", lty = 5, col=5)
					# last loess from before
			fit <- supsmu( x, y, span = "cv" )
			panel.xyplot( fit$x, fit$y, type = "l", col = 8)
		} 
	)

#
# supsmu looks better on the left but worse on the right
# it works better with more data (n > 100 or more)
#