Statistics 850 yandell
Homework # 3-Due Mon 20 Feb
Gray cast iron is a common commercial iron-based casting alloy. The
two principal alloying elements are carbon and silicon. This problem
examines the relationship between carbon level (C) and a
particular melting property (resp), specifically called the
``primary austenite liquidus arrest temperature of the cooling
curve''. Three levels of added carbon were used, low (1), medium (2)
and high (3). However, it is not possible to set these levels
exactly, for a variety of practical reasons. Instead, the scientist
can measure the actual carbon afterward (Cactual). The
questions for this homework concern how to relate carbon level to the
response. Is it enough to just consider the 3 discrete levels (coded
as Clevel=1,2,3) or is there further information about the
response in the actual carbon? Use plots, models and tables of means
and/or analyses of variance to present your arguments.
1. Run a one-factor analysis of variance comparing the effect of the
three levels of carbon on response. Include multiple comparison of
means. In particular, consider whether the linear contrast of means
(
) is zero.
2. Regress the discrete carbon levels on response. Why does the
variation explained differ from the contrast considered in the
previous problem?
3. Test lack of linear fit. That is, is there evidence that the
relationship between carbon level and respose could be nonlinear?
4. Regress the actual carbon on response. Why is the fit worse than
in problem 2, even though more ``accurate'' measure of carbon is used?
[You may want to use plots to show this.]
5. Fit a model with both discrete level and actual carbon to examine
the question of error in variables. How strong is the evidence?
The data can be found in file hwk3.dat (in the usual directory,
/p/stat/course/st850-yandell/data), with some SAS and S suggestions for this problem
in hwk3.sas and hwk3.s, respectively, for your
information. [The last SAS proc glm (or S ervar2) checks
for a nonlinear error in variables, finding no significant evidence.
This is for your information.]