# Scott Merrill
# heteroscedasticity vs homoscedasticity

rm(list = ls(all=TRUE))

# Below in the graphics function par, pty = "s" 
#	forces individual graphs into squares
par(mfrow = c(1,1), pty = "s") 


#############
## linear  ##
#############

wheat.height = sample(seq(0,5, by = .01),50,replace=TRUE)
aphids=numeric(length(wheat.height))
aphids = 10*wheat.height + rnorm(mean=0,n=length(wheat.height),sd=10)
plot(wheat.height,aphids, ylim=c(-25,60))

modL = lm(aphids ~ wheat.height)
summary(modL)
abline(modL$coefficients,lwd=3, col ="blue")

plot(wheat.height,modL$residuals)

###########
## non-linear function
############

aphids=numeric(length(wheat.height))
aphids = 3*wheat.height^3 + rnorm(mean=0,n=length(wheat.height),sd=4)
plot(wheat.height,aphids, ylim=c(-150,400))

modA = lm(aphids ~ wheat.height)
summary(modA)
abline(modA$coefficients,lwd=3, col ="blue")

plot(wheat.height,modA$residuals)
# Contrasted with linear
points(wheat.height,modL$residuals, lwd = 3, col=2)



########
## variation increasing with increasing x value
########


aphids=numeric(length(wheat.height))
aphids = 10*wheat.height + 2*wheat.height*rnorm(mean=0,n=length(wheat.height),sd=10)
plot(wheat.height,aphids)

modM = lm(aphids ~ wheat.height)
summary(modM)
abline(modM$coefficients,lwd=3, col ="blue")

plot(wheat.height,modM$residuals)


require(graphics)
locator(n = 512, type = "l", lwd = 4, col = "green")
# Cool locator function site: http://www.inside-r.org/r-doc/graphics/locator

# Contrasted with linear
points(wheat.height,modL$residuals, lwd = 3, col=2)
locator(n = 512, type = "l", lwd = 4, col = "green")

######
# Independence of errors
######

plot(modM$residuals,aphids)

plot(modA$residuals,aphids)



# plot points that are of interest from one plot onto a second plot
plot(locator(n = 512, type = "l", lwd = 4, col = "green"))