# tutorial 10 - Tutorial 10 1 Derive the weighted least...

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Tutorial 10 1. Derive the weighted least square normal equations for Ftting a simple linear regression function when σ 2 i = kX i ,where k> 0isaconstant . 2. ±or linear regression model Y i = β 0 + β 1 X i 1 + ... + β p X ip + ε i ,i =1 , ..., n. with Var ( ε 1 . . . ε n )= σ 2 1 0 ... 0 0 σ 2 2 ... 0 ··· 00 ... σ 2 n (a) If the LSE, b , is used, is the estimator unbiased? what is the variance of the estimated coeﬃcients, ( b ). (b) with w i 2 i , derive the weighted least square estimator b w , and calculate ( b w ) 3. ±or model Y i = β 1 X i 1 + β 2 X i 2 + β 3 X i 3 + ε i , if we estimate the coeﬃcients by minimizing Q ( b 1 ,b 2 3 n X i =1 { Y i - b 1 X i 1 - b 2 X i 2 - b 3 X i 3 } 2 + λ ( b 2 1 + b 2 2 + b 2 3 ) Give the estimator of ( b 1 2 3 )inmatr

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tutorial 10 - Tutorial 10 1 Derive the weighted least...

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