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stat512review1

# stat512review1 - Statistics 512 Review Problems for First...

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Statistics 512: Review Problems for First Midterm Exam Keep for First Exam Review (October 6) 1. In a simple linear regression problem with n = 28, the following estimates were obtained: b 0 = 4 . 30, b 1 = 0 . 56, s { b 0 } = 0 . 012, s { b 1 } = 0 . 034, s = 0 . 1385, ¯ X = - 0 . 0773, SS X = 14 . 598. Values of X were in the range - 1 . 43 to 0.683. (a) Write the simple linear regression model. Include the distributional assumption. (b) Write the estimated regression line and the estimated error variance. (c) If appropriate, estimate the mean value of Y for the given X . If not appropriate, say why. i. X = 0. ii. X = 2. (d) Give a 95% confidence interval for the slope of the regression line. (e) Give a 99% prediction interval for the next value of Y when X = 0 . 5. 2. Short answer questions. Unless stated otherwise, each part is unrelated. (a) If the design matrix has dimensions 20 × 4, what is the dimension of the error vector? (b) If the power for detecting a difference of means is 0.03, what can you say about the test’s α level?

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