Question

Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where bo is some hypothesized value for B1, for instance bo could be chosen to be zero c) What is the rejection rule when testing Ho : B1 = bo vs. Ha: B1 bo in terms of the t-statistic Bbo(3 points) se(B1) Now consider testing Ho: A1 = bo vs. Ha: B1 > bo d) Intuitively what should the rejection rule be in this case, in terms of the t-statistic 2ibo? (It is a se(B1) slight modification from the rejection rule in part c).) (3 points)

Answer 1

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