# PS 3 - Econ 104 Problem Set 3 Solutions Lorenzo Braccini...

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Econ 104 - Problem Set 3 Solutions Lorenzo Braccini * October 4, 2011 Problem 1 a) First note that: E [ Y i | X i ] = β 0 + β 1 X i Therefore we have that: E [ Y i | X i = 1] - E [ Y i | X i = 0] = β 1 where Y i is the probability of causing an accident and X i is the color of the car (1 if red). Last equality tells us that β 1 represents the diﬀerence in the ex- pected probability of causing an accident between a red car owner and the rest of the world. The estimate ˆ β 1 = 0 . 15 suggests that a red car owner has, on aver- age, a probability of causing an accident 0 . 15 greater than the owner of a diﬀerently colored car. b) For Susan to judge that her estimate is signiﬁcantly diﬀerent from 0 at a 5% level we need that: ± ± ± ± ± ˆ β 1 SE ( ˆ β 1 ) ± ± ± ± ± > z 0 . 975 = 1 . 96 (1) where ( ˆ β 1 ) is the estimate for the asymptotic standard error of the OLS estimator for β 1 . * [email protected] 1

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This result comes from the fact that, asymptotically: ˆ β 1 - β 1 SE ( ˆ β 1 ) ∼ N (0 , 1) Hence, testing the null hypothesis H 0 : β 1
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PS 3 - Econ 104 Problem Set 3 Solutions Lorenzo Braccini...

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