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MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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MIT 6.780J 2008: Problem set 8 solutions Problem 1: e xa m p le s ol uti o n c o u r t e sy o f M. I m ani N e jad a) fi r st w e ca l cu l at e th e av er ag e s and th e n us e th e f orm u l a in May and S p an o s t o find b and b 0 : x = 1 n x i = ±²³´µ ¶· y = 1 n y i = ¸³²¹±¸º¶· n i = 1 n i = 1 (x x)(y y) 2397.779 b = = = 0.96601 (x x) 2 2482.148 b 0 = y b x »·¸³²¹±¸º¶¼³²¶±±³ ½ ±²³´µ ¶· »·µ¸²µ¹º´¾· ¿À·ÁÂ·ÃÄÅÂÆ· y = 35.387 + 0.966x 35 30 25 20 15 10 5 0 90 80 70 60 50 40 30 20 10 0 x y S 9 80695 R-Sq 45.4% R-Sq(adj) 43.5% Regression 99% CI 99% PI F i tt ed L ine P l o t y = 35.39 + 0.9660 x 20 0 -20 -40 99 90 50 10 1 Resid u a l Per c en t 60 50 40 20 0 -20 -40 F i tt ed V a lu e Resid u a l 30 20 10 0 -10 -20 -30 20 15 10 5 0 Resid u a l F req cy 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 20 0 -20 -40 Ob ser v a t ion O rder N or m a l Pro b a b i l i ty P l o t V ers u s F i t s H is t ogra m V ers u s O rder Resid u a l P l o t s f or y
In th e a bo v e g r a p h th e int er va l is ca l cu l at e d b as e d o n th e f ollo wing f orm u l a: y 0 ± t α /2 V(y) wh ere α = 99% and V(y) = n 1 + (x (x x) x) 2 2 *s 2 F or e ach po int. The regression equation is y= 35.39 + 0.9660 x S = 9.80695 R-Sq = 45.4% R-Sq(adj) = 43.5% Analysis of Variance Source DF SS MS F P Regression 1 2316.28 2316.28 24.08

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sol8 - MIT OpenCourseWare http/ocw.mit.edu 2.830J 6.780J...

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