8.16 - 8.16(a Travel Speed Stopping Distance mph ft Xi Yi...

Info icon This preview shows pages 1–3. Sign up to view the full content.

8.16 (a) Car # Travel Speed Stopping Distance mph ft Xi Yi Xi 2 Yi 2 XiYi Yi'=a+bXi (Yi-Yi') 2 Total: 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 . 29 10 11525 ( 9 1 2 2 = × = x S , 01 . 1232 ) 3 . 51 10 37405 ( 9 1 2 2 = × = y S From Eq. 8.9, the correlation coefficient is, 99 . 0 01 . 1232 61 . 313 3 . 51 5 . 29 10 20665 9 1 1 1 ˆ 1 = × × = = = y x n i i i s s y x n y x n ρ
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

We can say that there is a reasonable linear relationship between the stopping distance and the speed of travel. (b) Travel s (c) E(Y X) = a + bx + cx 2 ; let x’ = x 2 So E(Y X) = a + bx + cx’ 492 , 11525 ' , 295 = Σ = Σ = Σ i i i y x x 4 2 2 10 06 . 1186 ) ' ' ( , 5 . 2822 ) ( × = Σ = Σ x x x x i i i , 5 . 177387 ) ' ' )( ( = Σ x x x x i i i 5641 ) )( ( = Σ y y x x i i i 5 . 35829 ) )( ' ' ( = Σ y y x x i i
Image of page 2