# Quantile plots

# Normal quantile

qqmath( ~ Income, prestige )
qqmath( ~ Education, prestige )
qqmath( ~ Women, prestige )
qqmath( ~ Prestige, prestige )

qqmath( ~ Income, prestige , dist = qunif)
qqmath( ~ Education, prestige , dist = qunif )
qqmath( ~ Women, prestige, dist = qunif )
qqmath( ~ Prestige, prestige , dist = qunif )

plot( prestige, ask = F )

# defining a function in S-Plus

pow <- function( x , power = 1 ) {
	if ( power == 0 ) ret <- log(x)
	else ret <- ( x^power - 1 ) / power
	ret
}

pow

pow( 1:3 )
pow(1:3, 0)
pow(1:3, -2)

x <- (1:10)/5
matplot(x , 
	cbind( pow(x,2) , pow(x,1) , pow(x,1/2) , 
		pow(x,0), pow(x,-1/2), pow(x, -1)) , 
	type = 'l')

qqmath( ~ Income, prestige )
qqmath( ~ log(Income), prestige)
qqmath( ~ sqrt(Income), prestige)
summary( prestige$Income )
qqmath( ~ log( Income + 1000 ), prestige )  # adding a constant 'weakens' 
													# powering down transformations
													
# Transforming to linearity

xyplot( Income ~ Education, prestige)
xyplot( Income ~ Education, prestige,
		panel = function(x,y,...) {
			panel.xyplot( x,y,...)
			panel.loess(x,y,span = 1/3,...)
		})

xyplot( log(Income) ~ Education, prestige,
		panel = function(x,y,...) {
			panel.xyplot( x,y,...)
			panel.loess(x,y,...)
		})



xyplot( log(Income + 1000) ~ Education, prestige,
		panel = function(x,y,...) {
			panel.xyplot( x,y,...)
			panel.loess(x,y,...)
		})



xyplot( sqrt(Income) ~ Education, prestige,
		panel = function(x,y,...) {
			panel.xyplot( x,y,...)
			panel.loess(x,y,...)
		})