#
#  MATH 3330 B, October 2001
#
#  Week 5a: Where Regression Got Its Name
#          Galton & Pearson ca 1900
#

# Fathers' heights and son's heights

# generate your own data by removing comments in next two lines:
# fs.dat <- data.frame( father = 68 + 3*rnorm(2000))
# fs.dat$son <- 68 + 3*((fs.dat$father - 68)*0.6/3 + 0.8*rnorm(2000))  


summary( fs.dat )
attach( fs.dat )
par( pty = "s" )
lab.vals <- seq( 59, 77, by = 3 )
labs <- list( labels = lab.vals, at = lab.vals )
plot( father, son , xlim = c(58,78), ylim = c(58,78) ,axes = F )
	box()
	axis( 1, at = lab.vals )
	axis( 2, at = lab.vals )
	
cor( dd$son, dd$father )
sqrt( var(father) )
sqrt( var(son) )

plot( father, son , xlim = c(58,78), ylim = c(58,78), type = 'n',axes=F)
	box()
	axis( 1, at = lab.vals )
	axis( 2, at = lab.vals )
	data.ell( father, son )
	data.ell( father, son, radius = 2 )
	data.ell( father, son, radius = 3 )


plot( father, son , xlim = c(58,78), ylim = c(58,78), type = 'n',axes=F)
	box()
	axis( 1, at = lab.vals )
	axis( 2, at = lab.vals )
	abline( coef(lm(son ~ father )))


plot( father, son , xlim = c(58,78), ylim = c(58,78), type = 'n',axes=F)
	box()
	axis( 1, at = lab.vals )
	axis( 2, at = lab.vals )
	abline( coef(lm(son ~ father )))
	abline( a = 0 , b = 1 )
	inv.reg <- coef( lm ( father ~ son ) )
	abline( a = - inv.reg[1]/inv.reg[2], b = 1/inv.reg[2] )