Solution to Tutorial 6 - Solution to Tutorial 6 1. For each...

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Solution to Tutorial 6 1. For each of the following regression models, indicate whether it is a general linear regression model. If not, state whether it can be expressed in the form of a linear regression model after some suitable transformation a. Y i = β 0 + β 1 X i 1 + β 2 log X i 2 + β 3 X 2 i 1 + ε i b. Y i = ε i exp( β 0 + β 1 X i 1 + β 2 X 2 i 2 ) ,w i t h ε i > 0 c. Y i = β 0 log( β 1 X i 1 )+ ε i d. Y i =log( β 1 X i 1 β 2 log X i 2 + ε i e. Y i =[1+exp( β 0 + β 1 X i 1 + ε i ] - 1 No of these are linear models, but a, b, d e can be transformed to linear regression models 2. Consider the multiple linear regression models Y i = β 1 X i 1 + β 2 X i 2 + ε i ,i =1 , ..., n where ε i are uncorrelated with i =0and 2 i = σ 2 state the least square criterion and derive the least squares estimators for β 1 and β 2 . Let Q ( b 1 ,b 2 )= n X i =1 { Y i - b 1 X i 1 - b 2 X i 2 } 2 by calculus, we have dQ ( b 1 2 ) db 1 = - 2 n X i =1 { Y i - b 1 X i 1 - b 2 X i 2 } X i 1 dQ ( b 1 2 ) db 2 = - 2 n X i =1 { Y i - b 1 X i 1 - b 2 X i 2 } X i 2 The normal equations are n X i =1 X 2 i 1 b 1 + n X i
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This note was uploaded on 10/04/2010 for the course STAT ST3131 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.

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Solution to Tutorial 6 - Solution to Tutorial 6 1. For each...

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