Unformatted text preview: Show that for appropriate values of ν 1 and ν 2 , SS R /ν 1 SS E /ν 2 has an Fdistribution. Identify ν 1 and ν 2 . 2. Suppose { ( x i , y i ) , i = 1 , 2 , . . . , n } are independent observations taken from data governed by the model y = β 1 x + ε where ε is exponentially distributed with parameter 1. Suppose that the x values are all positive. (a) Find the maximum likelihood estimator for β 1 . (b) Estimate β 1 given the following data: x 1 2 3 4 5 y 21 41 60 80 100 (c) Does ε satisfy all of the usual assumptions for linear regression? (d) Bonus: Show that the maximum likelihood estimator for β 1 is biased, and provide an alternative estimator which is unbiased. Also, calculate the variance of the maximum likelihood estimator....
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 Fall '10
 Braun
 Regression Analysis, maximum likelihood estimator, XT B−T B−1

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