Ch2_2_10_hints - ^ & = & + & u ± & x &...

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Hints for 2.10 (p. 64) Question 2.10 consists of questions that require materials covered in the stat courses. The following hints should help to go through these questions. (i) ^ 1 = P n i =1 ( x i x )( y i y ) P n j =1 ( x j x ) 2 Use the following facts: y i = & 0 + 1 x i + u i y = & 0 + 1 x u P n i =1 ( x i ± x ) = P n i =1 x i ± n P n i =1 x i n = 0 (ii) Need to show E ^ 1 ± 1 ± ² u i = 0 Rewrite ^ 1 ± 1 ± by using the result of (i) Use the following facts E ( u i u j ) = ² ± 2 if i = j 0 if i 6 = j P n i =1 w i = 0 (iii) ^ & 0 y ± x ^ 1 Use the following facts: y = & 0 + 1 x u (iv) Start with the resut of (iii):
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Unformatted text preview: ^ & = & + & u ± & x & ^ & 1 ± & 1 ± & Use the following facts: & V ar ( ax + by ) = a 2 V ar ( x ) + b 2 V ar ( y ) if Cov ( x; y ) = 0 & The variance of constant is zero & Need to derive the variance of ^ & 1 &rst by using the result of (i) 1 (v) & Start with the outcome of (iv) & Use the fact that P n j =1 ( x j ± & x ) 2 n = 1 n n X i =1 x 2 i ± (& x ) 2 2...
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This note was uploaded on 10/05/2009 for the course DEPARTMENT Eco375 taught by Professor Suzuki during the Spring '09 term at University of Toronto- Toronto.

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Ch2_2_10_hints - ^ & = & + & u ± & x &...

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