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Unformatted text preview: Assignment 4 Professor Rakhlin STAT 101 HW Solutions total points = 40 points Question. Chapter 19, # 26 (2 point) 1 point for result: Only if r 2 = 1 . 1 point for explanation(The following is one explanatation, others that make sense could also get credit.): The regression of y on x is ˆ y ¯ y s y = r x ¯ x s x , and the regression of x on y is ˆ x ¯ x s x = r y ¯ y s y . Compare two lines, we knew if and only if r 2 = 1 two fitted lines are coincide if they are drawn on the same plot. Question. Chapter 19, # 28 (3 points) This histogram summarizes residuals from a fit that regresses the number of items produced by 50 employees during a shift on the number of years with the company. Estimate s e from this plot. 1 For this question, students can estimate it precisely like method one, and also can esti mate it less precisely like method two. Method 1: Notice that there are exactly 4 bars in the interval [0 , 75], so the length of each bar is 75 / 4 = 18 . 75. For example, there are 11 counts of residuals that lie in [0 , 18 . 75] (we will take all them as (0+18.75)/2=9.375 in later calculation) and 5 in [18 . 75 , 37 . 5] (we will take mean value 28.125 for calculation). We can make a list like this: Counts Interval Mean 1 [93.75, 75]84.375 [75, 56.25]65.625 4 [56.25, 37.5]46.875 9 [37.5, 18.75]28.125 11 [18.75, 0]9.375 11 [0, 18.75] 9.375 5 [18.75, 37.5] 28.125 5 [37.5, 56.25] 46.875 1 [56.25, 75] 65.625 1 [75, 93.75] 84.375 ( n 2) s 2 e = 48 X i =1 r 2 i =1 × ( 84 . 375) 2 + 0 × ( 65 . 625) 2 + 4 × ( 46 . 875) 2 + 9 × ( 28 . 125) 2 + 11 × ( 9 . 375) 2 + 11 × (9 . 375) 2 + 5 × (28 . 125) 2 + 5 × (46 . 875) 2 + 1 × (65 . 625) 2 + 1 × (84 . 375) 2 = 51328 . 12 s e = r 51328 . 12 48 2 = 33 . 404 ( items ) Method 2: s e ≈ 25 items. As the data are bellshaped, the interval ± 2 s e should hold about 95% of the residuals. Question. Chapter 19, # 32 (2 points) If the correlation between x and y is 0.8 and the slope in the regression of y on x is 1.5, then which of x or y has larger variation? 2 According to the description, we have: r = 0 . 8 , b 1 = r s y s x = 1 . 5....
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This note was uploaded on 04/04/2012 for the course STAT 101 taught by Professor Heller during the Fall '08 term at UPenn.
 Fall '08
 Heller
 Statistics

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