Tutorial 8
1. In regression analysis of onthejob head injuries of warehouse laborers caused by
falling objects.
Y
is a measure of severity of the injury,
X
1
is an index reﬂecting both
the weight of the object and the distance it fell, and
D
1
and
D
2
are indicator variables
for nature of head protection worn at the time of the accident, coded as follows
type of protection
D
1
D
2
Hard hat
1
0
Bump cap
0
1
None
0
0
the response function to be used in the study is
E
(
Y
) =
β
0
+
β
1
X
1
+
β
2
D
1
+
β
3
D
2
(a) Develop the response function for each type of the protection category
(b) For each of the following questions, specify
H
0
and
H
a
for each appropriate
test (1) with
X
1
fixed, does wearing a bump cap reduce the expected severity
of injury as compared with wearing no protection?
(2) with
X
1
fixed, is the
expected severity of injury the same when wearing a hard hat as when wearing
a bump cap?
2. Refer to the toll wear example (in the lecture notes, part 5 of Chapter 2), consider
model
Y
=
β
0
+
β
1
X
1 +
β
2
D
1 +
β
3
D
2 +
β
4
D
3 +
β
5
X
1
D
1 +
β
6
X
1
D
2 +
β
7
X
1
D
3 +
ε
.
Indicating the meaning of (1)
β
3
, (2)
β
4

β
3
, (3)
β
1
, (4)
β
7
= 0, (5)
β
5

β
6
3.
Steroid level.
(Data)
An endocrinologist was interested in exploring the relation
ship between the level of a steroid (
Y
) and age (
X
) in healthy female subjects whose
ages ranged from 8 to 25 years. She collected a sample of 27 healthy females in this
age range.
a. Fit regression model
Y
=
β
0
+
β
1
X
+
β
2
X
2
+
ε
. Plot the fitted regression function
and the data.
Does the quadratic regression function appear to be a good fit
here? Find
R
2
.
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 Fall '09
 XIAYingcun
 Linear Regression, Regression Analysis, Per capita income, bump cap

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