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Stat 430/830 Solutions 2
2.
a) Experimental unit: one run of the MLE algorithm with a specific set of random starting values
for the parameters
Treatment: algorithm’s convergence tolerance with three levels log (
*
) = 1, 2, 3
Response variable: running time of algorithm
Plot of data is on sol4302.doc
We see a linear decrease in running time as log tolerance increases. One point at log
*
= 2 stands
out a bit.
However a plot of Cook’s statistic
(see sol4302.doc, but plot is NOT needed on the
assignment) indicates that it is not that influential  the observation does not stand out that far
from the rest and is not beyond the rule of thumb, the 50 percentile of F(3,9), 0.85.
th
b)
The model is :
with
and
ij
Y = response variable = running time for the jth observation of the ith convergence tolerance
:
= overall mean
ii
i
J
= mean deviation of treatment i from the overall mean so that
:
=
:
+
J
is the mean effect of
treatment I
ij
,
= normally distributed random error variable
OR
The model is :
with
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Y = response variable = running time for the j observation of the i convergence tolerance
th
th
i
:
= population mean for i convergence tolerance
th
ij
,
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 Winter '09
 OHaraHines

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