ecm06-midterm - ECN 140-winter 2006 Econometrics MIDTERM...

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ECN 140-winter 2006 1 Econometrics MIDTERM NAME: Time: 1 hour and 20 minutes 100 POINTS TOTAL Date: Tuesday, Feb 21, 2006 INSTRUCTIONS : (1) Please write your answer in the blue book. (2) ABSOLUTELY NO COPYING. Transgressors will be reported to the relevant authorities. 1. [ Total = 25 ] a) [10] Mr. Guy Owens usually sits at the top left corner of the class facing the blackboard. Despite his seemingly shabby hair, Guy ’s girlfriend tells him that he is so good-looking that she would rate him as 99 on a 100-point scale, where the mean is 66 and the variance of all ratings of looks is 400. What is she saying about where Guy is in the percentage distribution of looks (in her mind)? [ Hint : use the standard normal distribution]. b) The expected value of the estimate of the slope parameter 1 β in a simple regression 0 1 y x u β β = + + is: l 1 β 1 1 2 1 ( ) ( ) n i i i n i i x x u x x β = = = + , where l 1 β is the estimated slope, x is the mean of x , i denotes one of the n observations, and 2 1 ( ) n i i x x = is the variance of x . (i) [10] Prove that E( l 1 β ) = 1 β under the assumptions we made to justify estimating this equation.
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