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 air-pollution 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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