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07exLRs1b

07exLRs1b - (o Part n provides a predicted value for an...

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ISOM111 Business Statistics (Fall 2010) Suggested Solutions for Tutorial Set 7 Exercise (Q1 Part b) 1. (l) A 95% C.I. for the β 1 is: b β 1 ± t 10 2 , 0 . 025 s SSX = 12 . 000 ± 2 . 306 20 . 4052 16 . 276 = ( 23 . 663 , 0 . 337) (m) x p = 10 b y = 464 . 54 12 . 000(10) = 344 . 54 A 95% C.I. for the E ( y | X = x p ) is: b y ± t 10 2 , 0 . 025 s s 1 n + ( x p x ) 2 SSX = 344 . 54 ± 2 . 306 20 . 4052 s 1 10 + (10 9 . 62) 2 16 . 276 = (329 . 014 , 360 . 066) i.e. (329014 , 360066) (n) A 95% P.I. for the predicted value of y | X = x p is: b y ± t 10 2 , 0 . 025 s s 1 + 1 n + ( x p x ) 2 SSX = 344 . 54 ± 2 . 306 20 . 4052 s 1 + 1 10 + (10 9 . 62) 2 16 . 276 = (294 . 990 , 394 . 090) i.e. (294990 , 394090)
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Unformatted text preview: (o) Part ( n ) provides a predicted value for an individual response of Y (predict the sales of homes for a particular year given the mortgage rate) and Part ( m ) provides an estimate for an average value of Y (estimate the mean number of homes sold given the mortgage rate). Therefore, the width of the interval estimate in Part ( n ) is wider than that in Part ( m ). 1...
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