#Partial regression.
#Access the data:
a <- read.table("http://www.stat.ucla.edu/~nchristo/statistics_c173_c273/jura.txt", header=TRUE)

#Rename the variables:
y <- a$Pb

x1 <- a$Cd
x2 <- a$Co
x3 <- a$Cr
x4 <- a$Cu
x5 <- a$Ni
x6 <- a$Zn


#Regression of y on x1,x2,x3,x4,x5,x6 (long regression):
#What are the estimates of beta5 and beta6?

#=========================================================
#=========================================================
#Regression of y on x1,x2,x3,x4:

#Residuals from the regression of y on x1,x2,x3,x4:
#Name these residuals e1.

#=========================================================
#Regression of x5 on x1,x2,x3,x4:

#Residuals from the regression of x5 on x1,x2,x3,x4:
#Name these residuals e5.

#=========================================================
#Regression of x6 on x1,x2,x3,x4:

#Residuals from the regression of x5 on x1,x2,x3,x4:
#Name these residuals e6.

#=========================================================
#Run the regression of e1 on e5 and e6.
#What are the estimates of the two slopes?  Compare them to the estimates of beta5 and beta6 from the long regression of y on x1,x2,x3,x4,x5,x6.