Stat 410    HW 6    10-13-2005    D. Scott    Due 10-20 (or 21st)


HOMEWORK PROBLEMS BELOW


OUR TAKE-HOME EXAM IS NOW TENTATIVELY SCHEDULED:
    Handed out:  Thursday November 10
    Due back:    Tuesday  November 15 (beginning of class...not end)
    Materials:   Open book, computer, notes, homeworks.


READ:

Chapter 8

  8.1 Polynomial regression
          Note that the simple device of centering the variables
	  can greatly reduce problems with multicollinearity.
	  Other concepts map directly to these variables.
	  One caveat:  in a cubic model, never perform a test to
	  eliminate the linear term while retaining a higher
	  order term (such as the cubic).  Only consider dropping
	  *all* terms of order p and higher.

  8.2 Interaction regressions
          As we discussed in class, including cross-product terms
	  such as   x1 times x2  in a linear model means that the
	  effect (i.e. slope) on x1 changes as x2 changes.  The
	  contour plots in Figures 8.8 and 8.9 are useful to
	  understand.

  8.3 Qualitative predictors
          Code all binary variables (e.g. yes/no) as 0-1
	  (or sometimes +1 and -1).  If more than 2 levels
	  (but not ordered), then code as in eqn (8.35).

  8.4 Some considerations
          If a variables has more than 2 levels and *are*
	  ordered, then do not code as 1,2,3,...,p as the
	  spacings are very important (and probably should
	  not be assumed to have the same effect going from
	  2 to 3 as from 8 to 9).  Code as in Section 8.3.

  8.5 Modeling quantitative/qualitative variable interactions

  8.6 More complex models

  8.7 Comparison of regression functions
          Write the regression models in such a way that one
	  is a "full" model and the other is a "reduced"
	  model.  Then the comparison is basically whether
	  several of the beta's can be set to zero or not.
	  This is the same F test as we have already used.




Problems from our textbook.

1.  8.8
2.  8.38
3.  8.40
4.  8.41


The datasets needed are in previous
homework directories.