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Unformatted text preview: SIEO 3600 (IEOR Majors) Solution of Assignment #12 Introduction to Probability and Statistics April 27, 2010 Solution of Assignment #12 ( Regression: linear (simple and multiple) and polynomial ) 1. The following data represent the relationship between the number of alignment errors and the number of missing rivets for 10 different aircrafts. Number of Number of Missing Rivets = x Alignment Errors = y 13 7 15 7 10 5 22 12 30 15 7 2 25 13 16 9 20 11 15 8 (a) Plot a scatter diagram. (b) Estimate the regression coefficients. (c) Compute the coefficient of determination R 2 . Is a linear model a good fit? Solution: We compute from the given data: X ( n ) = 17 . 3 , Y ( n ) = 8 . 9 , n summationdisplay i =1 X i Y i = 1783 , n summationdisplay i =1 X 2 i = 3433 . Then we have = n i =1 X i Y i n X ( n ) Y ( n ) n i =1 X 2 i n X ( n ) 2 = 1783 10 17 . 3 8 . 9 3433 10 17 . 3 2 = 0 . 5528 , = Y ( n ) X ( n ) = 8 . 9 . 5528 17 . 3 = . 6639 , R 2 = 1 S RR S Y Y = 1 n i =1 ( Y i  X i ) 2 n i =1 ( Y i Y ( n )) 2 = 0 . 9863 . Since we have such a big R 2 , we can say the linear model is a good fit. 2. The following data indicate the gain in reading speed versus the number of weeks in the program of 10 students in a speedreading problem. 2 SIEO 3600, Solution of Assignment #12 Number of weeks Speed Gain (wds/min) 2 21 3 42 8 102 11 130 4 52 5 57 9 105 7 85 5 62 7 90 (a) Plot a scatter diagram to see if a linear relationship is indicated. (b) Find the least squares estimates of the regression coefficients. (c) Compute the coefficient of determination R 2 . Is a linear model a good fit? Solution: We compute from the given data: X ( n ) = 6 . 1 , Y ( n ) = 74 . 6 , n summationdisplay i =1 X i Y i = 5387 , n summationdisplay i =1 X 2 i = 443 . Then we have = n i =1 X i Y i n X ( n ) Y ( n ) n i =1 X 2 i n X ( n ) 2 = 5387 10 6 . 1 74 . 6 443 10 6 . 1 2 = 11 . 797 , = Y ( n ) X ( n ) = 74 . 6 11 . 797 6 . 1 = 2 . 639 , R 2 = 1 S RR S Y Y = 1 n i =1 ( Y i  X i ) 2 n i =1 ( Y i Y ( n )) 2 = 0 . 9863 ....
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This note was uploaded on 10/03/2011 for the course SIEO W3600 taught by Professor Yunanliu during the Spring '10 term at Columbia.
 Spring '10
 YUNANLIU

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