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8.16 (a) Car #Travel SpeedStopping DistancemphftXiYiXi2Yi2XiYiYi'=a+bXi(Yi-Yi')2Total:On the basis of calculations in the above table we obtain the respective sample means of X and Y as, X=295/10 = 29.5, Y= 513/10 = 51.3 and corresponding sample variances, 61.313)5.291011525(9122=×−=xS, 01.1232)3.511037405(9122=×−=ySFrom Eq. 8.9, the correlation coefficient is, 99.001.123261.3133.515.2910206659111ˆ1=⋅××−=−−=∑=yxniiissyxnyxnρ
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We can say that there is a reasonable linear relationship between the stopping distance and the speed of travel. (b) Travel s(c) E(YX) = a + bx + cx2; let x’ = x2So E(YX) = a + bx + cx’ 492,11525',295=Σ=Σ=Σiiiyxx4221006.1186)''(,5.2822)(×=−Σ=−Σxxxxiii,5.177387)'')((=−−Σxxxxiii5641))((=−−Σyyxxiii5.35829))(''(=−−Σyyxxii