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Unformatted text preview: 1 The University of Western Ontario Department of Statistical and Actuarial Sciences Statistical Sciences 3859a Assignment 1 Due Date: September 28, 2009 1. Suppose ( x 1 , y 1 ) , ( x 2 , y 2 ) , . . . , ( x n , y n ) constitute a sample of independent observations. Consider the model y i = β 1 x i + β 2 i + ε i where the ε i are i.i.d. N(0, σ 2 ) random variables, for i = 1 , 2 , . . . , n . (a) Derive the leastsquares estimators for β 1 and β 2 . Under what condition on the predictor ( x i ) are these estimators not welldefined? (b) For the case where the coefficient estimators are welldefined, write down an unbi ased estimator for σ 2 . 2. Use R to complete the following problem, but do not use builtin functions such as lm() and predict() . A toy car has been released from ramps having nine different angles. Distance travelled (in m) has been measured in each case. angle 1.3 4.0 2.7 2.2 3.6 4.9 0.9 1.1 3.1 distance 0.43 0.84 0.58 0.58 0.70 1.00 0.27 0.29 0.63 (a) Plot the data. What is the predictor and what is the response? Is a linear model reasonable? (On physical grounds?, On statistical grounds?)reasonable?...
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 Fall '10
 Braun
 Normal Distribution, Regression Analysis, Yi, linear regression model, leastsquares estimate

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