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Assignment1_2011

# Assignment1_2011 - Assignment 1 Due Monday Feb 14th at...

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Assignment # 1 Due Monday Feb 14 th at 2:30pm Instructions: While cooperating on the assignment is encouraged, plagiarism is not. I will only accept hand written assignment submitted in person. Do NOT submit your assignment electronically. No late assignment will be accepted; late assignments (during or after the correction in class) will receive a mark of zero. Question 1 (20 pts) Let Y 1 , …, Y 4 be a random sample such that the four random variables Y j for j=1, …, 4 are independent and identically distributed from a population with mean and variance σ 2 . Define the sample mean estimator Y = 1/4 Σ Y j , the average of these four random variables and define the following estimator: Ϋ = 1/4 (1/2Y 1 + 3/2Y 2 + 1/2Y 3 + 3/2Y 4 ), a weighted average of the four random variables such that the observations are alternately weighted by 1/2 and 3/2. (a) Calculate the mean of Y and Ϋ . (b) Calculate the variance of Y and Ϋ . (c) Based on your answers in part (a) and (b), which estimator do you prefer between the two? Question 2 (10) pts) (a) Assume the regression model Y i = 10 + βX i + ε i What is the ordinary least square estimator of β in this case? Calculate E( β ) showing that it is unbiased. (b) Assume the regression model Y i = βX i + ε i What is the ordinary least square estimator of β in this case? Calculate E( β ) showing that it is unbiased. Question 3 (20 pts) Suppose you are interested in testing the rationality of assessments of used cars. A simple model is: Price = β 0 + β 1 assessment + u The assessment is rational if β 0 =0 and β 1 =1. The estimated equation is: Price = -12.23 + 0.981 assess (15.13) (0.048)

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Where the standard errors of the coefficient are given in parenthesis.
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Assignment1_2011 - Assignment 1 Due Monday Feb 14th at...

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