Problem 1 Consider a linear regression model: and Bo = 75, 81 Yį = Bo + B₁ Xi + €i = = 24.7 and o² = 3.5. Suppose an obs

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Problem 1 Consider A Linear Regression Model And Bo 75 81 Yi Bo B Xi I 24 7 And O 3 5 Suppose An Obs 1 (151.54 KiB) Viewed 15 times

Problem 1 Consider a linear regression model: and Bo = 75, 81 Yį = Bo + B₁ Xi + €i = = 24.7 and o² = 3.5. Suppose an observation is made on Y for X = 5. (a) (3 pts) Can you state the exact probability that Y will fall between 185 and 205? Explain. (b) (4 pts) If €; follows a normal distribution, can you now state the exact probability that Y will fall between 185 and 205? Explain. (c) (5 pts) An analyst conducted an F test of Ho: ₁ = 0 versus H₁ : ₁ 0. The p-value of the test was .033, and the analyst rejected Ho. Was the a level used by the analyst greater than or smaller than .033? If the a level had been .01, what would have been the appropriate conclusion? (d) (4 pts) We established that the Maximum Likelihood Estimate of o² was 1/1(Yi - bo - b₁X₁)², biased for o². Compute its bias and variance.