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mont4e_sm_ch11_mind - Mind-Expanding Exercises 11-91 The...

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11-59 Mind-Expanding Exercises 11-91 The correlation coefficient for the n pairs of data ( x i , z i ) will not be near unity. It will be near zero. The data for the pairs ( x i , z i ) where 2 i i y z = will not fall along the line i i x y = which has a slope near unity and gives a correlation coefficient near unity. These data will fall on a line i i x y = that has a slope near zero and gives a much smaller correlation coefficient. 11-92 a) xx xY S S = 1 ˆ β , x Y 1 0 ˆ ˆ β β = xx xx i xx i i i xx xY S V Cov nS x x nS x x Y Y Cov S S Y Cov Y Cov Cov x Y Cov Cov 2 1 1 1 2 1 1 1 1 1 0 ) ˆ ( ) ˆ , ˆ ( 0 ) ( )) ( , ( ) , ( ) ˆ , ( ) ˆ , ˆ ( ) ˆ , ( ) ˆ , ˆ ( σ β β β σ β β β β β β = = = = = = = . Therefore, xx S x Cov 2 1 0 ) ˆ , ˆ ( σ β β = b) The requested result is shown in part a). 11-93 a) 2 2 ) ˆ ˆ ( 2 2 1 0 = = n e n x Y MS i i i E β β 0 ) ˆ ( ) ˆ ( ) ( ) ( 1 0 = = i i i x E E Y E e E β β )] ( 1 [ ) ( 2 ) ( 1 2 xx i S x x n i e V + = σ Therefore, 2 2 ) ( 1 2 2 2 ] 1 1 [ 2 )] ( 1 [ 2 ) ( 2 ) ( ) ( 2 σ σ σ = = + = = = n n n n e V n e E MS E
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