# Scott Merrill
# Colinearity
# Nov 27

rm (list = ls(all=TRUE))
z = runif(1,100, n=100)

x1 = 2*z + rnorm(mean=0,sd=3,n=100)
a2 = 1.001*x1 + rnorm(mean=0,sd=3,n=100)
x3 = .5*z*z +  rnorm(mean=0,sd=3,n=100)



cor(x1, x2)

y = x1 + x2 + x3 + rnorm(mean=1,sd=8,n=100)

mod1 = lm(y~x1 + x2)
summary(mod1)

# imagine data for 50 different sites
#	days above 0 degrees C in march
# 	average temperature in march
# 	amount of coal burned per household

# What if x1 is days number of days above 
# 	0 and x2 is average temperature in march
# What is your interpretation of the effect of average 
# temperature on coal burning

mod2 =lm(y~x1)
summary(mod2)

mod3 =lm(y~x2)
summary(mod3)

AIC(mod1)
AIC(mod2)
AIC(mod3)

modx=lm(mod1$residuals~x2)
summary(modx)