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Tutorial 5
1. comparing the estimators of
β
on the top of page 2 (chapter 2 part 1 ) and (2.3) on
page 3 of part 2. Explain why there is no weight function in the estimator of page 2.
2. Based on the notation in Lecture note (Chapter 2, part 2), eqns between (2.2) and
(2.3), prove (2.3)
3. Consider the airpollution and health
data
in Hong Kong. Suppose we consider the
eﬀect of pollutants (NO
2
, SO
2
, O
3
, Particulate matters (PM)) on the number of
hospital admission suﬀering respiratory diseases
Y
. We ﬁt each pollutant a linear
regression model to ﬁnd the dependence. For example
Y
=
a
+
b
*
NO
2
+
ε.
(1)
If we want to see how the weather conditions (temperature or humidity) change the
dependence between
Y
and the pollutants. We may further consider a varying coeﬃ
cient regression model. For example
Y
=
a
(
Temperature
) +
b
(
Temperature
)
*
NO
2
+
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 Fall '09
 XIAYingcun

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