PDE gogogo.pdf x https://web.whatsapp.com X Assignment 2 econometrics.pdf X + X C Dann | C:/Users/ToMupuc/Desktop/polyU/year%204/Assignment%202%20econometrics.pdf . . 2 N13 3 Q + v v Assign 2 Question 3 A study of the relationship between happiness and monetary wealth among people aged between 12 and 15 is performed. Happiness is quantified by an index with continuous scale from 1 to 4. The higher the happiness index of a person has, the happier the person is. The monetary wealth is measured by the total personal saving in thousand Hong Kong Dollar (i.e. for a person with 1,500 Hong Kong Dollar as the total personal saving, the value is recorded as 1.5). 20 people aged between 12 and 15 in Hong Kong are + chosen by simple random sampling, and the indexes of happiness and the total personal savings of the people are collected. Assume that the following simple linear regression model is appropriate: yi = Bot Pix, + E, i= 1,...,20 where y; is the index of happiness of the ith person x; is the total personal saving of the ith person E1. .... E20 are identically and independently distributed random variables with F(z;) = 0, var(e,) = 0', and follow Normal distribution. A sociologist suggests the following estimator for By: 29 _Syi- yi-2 bi = n - 2 4 x 1 - Xi - 2 a) Show that bj is an unbiased estimator of B1 . b) Show that bj is a linear estimator. In other words, express bj as a linear combination of y;. Hence, determine whether bj follows Normal distribution. c) Determine the log-likelihood function of the linear regression model. Hence, derive byLE, the maximum likelihood estimator of B1. d) Which estimator has larger variance, bj or biff? Explain. BBeANTe 3Aecb TEKCT And noncKa O B. 125 Y O 23 .C ~ D E ( ) ENG 2:15 PM 11/24/2022