Statistics 850 yandell
Homework # 4-Due Mon 27 Feb
Consider the catalyst example from the handout entitled
``Catalyst Interaction Plot Using S''. This example comes from
Chapter 5 of Statistical Models in S by Chambers and Hastie
(1992). However, relevant details are included in the handout and
below.
Basically, there are 3 design factors, Temperature, and Concentration and Catalyst type, each at 2 levels, in a
completely randomized design. That is, there are 8 cells, or levels
of treatment combinations, with two replications per cell. The broad
goal is to determine what factors (main effects, or factor
combinations through interaction) affect the response, Yield.
(a) Develop plots to display the key features of these data. You may
want to begin with ideas in the handout. This part may be
incorporated into the following sections of the problem.
(b) Fit a model which ignores Conc. Present results and
interpret.
(c) Examine the lack of fit caused by ignoring Conc. This may
be done using residual plots and/or formal tests.
(d) Develop a full model which includes all possible interactions.
(e) Reduce the full model to a ``parsimonious'' model which only
includes significant terms, plus terms needed to maintain hierarchy
(i.e. main effects if interactions are significant).
(f) Interpret the ``final'' model in words. Use your plots and analyses to
demonstrate the strength of evidence.
The data can be found in file hwk4.dat (in the usual directory,
/p/stat/course/st850-yandell/data), with some SAS and S suggestions for this problem
in hwk4.sas and hwk4.s, respectively, for your
information.