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Linear regression proof question Consider the case that the value of of is unknown; that is, it needs to be estimated. 1) Construct a statistical

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Linear regression proof question

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Consider the case that the value of of is unknown; that is, it needs to be estimated. 1) Construct a statistical test for testing Ho: B1 = 2 = 0 and the a-level rejection region of the test. [5 points] 2) Construct a statistical test for testing each individual regressor; that is, for the i-th regressor (i = 1, 2), Hoi: Bi = 0 and the a-level rejection region of the test. [5 points] 3) In b2) above, derive the probability of falsely rejecting at least one Hoi , i = 1, 2. In b1) above, derive the probability of falsely rejecting at least one Hoi , i = 1, 2. [7 points]

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