8.3 - 8.3 (a) Plot of peak hour traffic vs daily traffic...

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8.3 (a) Plot of peak hour traffic vs daily traffic 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 01234567 Daily traffic (1000 vehicles) Peak hour traffic (1000 vehicles) (b) Let X be the daily traffic volume and Y the peak hour traffic volume, both in thousand vehicles. By Eq. 8.9, the correlation coefficient between X and Y is estimated by y x n i i i s s y x n y x n = = 1 1 1 ˆ ρ With n = 5, = 25.54, = n i i i y x 1 x = 1.02, y = 4.72, and the sample standard deviations s x = 0.303315018 while s y = 1.251798706, ˆ = (1/4)(1.468 / 0.379689347) 0.967 (c) x i y i x i y i x i 2 i i x y β α ˆ ˆ ' + = (y i – y i ’) 2 5 1.2 6 25 1.085577537 0.0130925 4.5 1 4.5 20.25 0.968474793 0.00099384 6.5 1.4 9.1 42.25 1.436885769 0.00136056 4.6 0.9 4.14 21.16 0.991895341 0.00844475
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3 0.6 1.8 9 0.61716656 0.00029469 Sum 23.6 5.1 25.54 117.66 0.02418634 Mean 4.72 1.02 Since we know the total (daily) traffic count (X), and want a probability estimate about the peak hour traffic (Y), we need the regression of Y on X, i.e. the best estimates of
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8.3 - 8.3 (a) Plot of peak hour traffic vs daily traffic...

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