DMtutorial4 - Tutorial 5 1. comparing the estimators of on...

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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 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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