**Unformatted text preview: **ˆ β ? Problem 3: For the simple regression model y i = β + β 1 x i + ± i ,, i = 1 ,...,n , suppose x i are ﬁxed, and ± i ∼ N (0 ,σ 2 ) independently. (1) What is the distribution of the least squares estimate ˆ β 1 ? (2) Suppose we want to test H : β 1 = 0 versus H 1 : β 1 6 = 0. If we set the type I error to be α , then what is the decision rule? (3) Give a non-technical discussion on the issue of overﬁtting. 1...

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