Quiz 4 (10 minutes, 3 points):

In some of the work we will do in Chapter 11, we will have to assume that
the residuals from a regression model are normally distributed. For the
sake of concreteness, take the model lm.a from the lab.

a) Write code to compute a qq-plot for testing whether or not the 
residuals from lm.a are consistent with a Normal distribution.

b) You will find out that the qq-plot suggests the answer 
"The residuals do not seem to come from a Normal." This conclusion
does follow from the qq-plot; but EXPLAIN why it is so? In other words,
based on only the data, provide some argument as to why the residuals 
turn out to be non-Normal. Also provide code to support your argument.


# a) The following qq-plot suggests that the distribution of the residuals
# is not too consistent with a Normal distribution.

 qqnorm(lm.a$residuals)

# b) The residuals are the difference between predicted and observed size.
# and the predicted value is based on performing linear regression on
# size and rotate. So, it's reasonable to see if the data itself is
Normal - in this case size and rotate.

  qqnorm(size)
  qqnorm(rotate)
 
  # Neither one is really Normal!  That's one explanation.