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Unformatted text preview: answer? Problem 12 If e is normally distributed and σ 2 is known, what is the distribution for ˆ β ? Problem 13 Show that ˆ Y and ˆ e are orthogonal, and explain its implication. Problem 14 Explain the variance decomposition of the estimated regression equation and derive R 2 . Problem 15 Distinguish R 2 and ¯ R 2 . What drawbacks are there to the use of each of them as the primary determinant of the overall quality of a regression? Problem 16 Explain how to construct a random variable W ∼ χ 2 ( n ) given mutually independent standard normally distributed random variables Z 1 ,Z n ,..,Z n . Problem 17 Explain how to construct a random variable V ∼ t ( n ) given mutually independent W ∼ χ 2 ( n ) and Z ∼ N (0 , 1) . Problem 18 Explain how to construct a random variable K ∼ F ( n 1 ,n 2 ) given mutually independent W 1 ∼ χ 2 ( n 1 ) and W 2 ∼ χ 2 ( n 2 ) . 2...
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 Spring '09
 gtewewa
 Linear Regression, Standard Deviation, Variance, Probability theory, OLS

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