STAT5044: Regression and ANOVA, Fall 2010
Final Exam on Dec 11
Your Name:
Please make sure to specify all of your notations in each problem
GOOD LUCK!
1
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Problem# 1.
A hospital administrator wished to study the relation between patient satisfaction (
Y
) and
patient’s age (
X
, in year) and severity of illness (
Z
, an index). The administrator randomly
selected 46 patients and collected the data. The larger values of
Y
and
Z
are, respectively,
associated with more satisfaction, increased severity of illness. Based on scatter plot, this
administrator assumed linear relationship between
Y
and
X
and between
Y
and
Z
. The ad
ministrator then fit multiple linear regression of
Y
on
X
and
Z
. Using residuals (
r
) obtained
from this multiple regression, the administrator fit a linear regression of
r
on
X
and
Z
. The
administrator found that there was no special relationships between
Z
and
r
. However, the
administrator found that the scatter plot of
X
and
r
shows that
r
is increasing exponentially
with increasing value of
X
.
•
(a) What is appropriate model and assumption?
•
(b) What are the distribution of the parameters? Justtify your answer
•
(c) Are the estimator of covariate
X
independent of that of variance of error? Justify
your answer
•
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 Fall '11
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 Regression Analysis, administrator, heart attacks, Large sample distribution, Job approval rating

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