Question

A department of transportation's study on driving speed and miles per gallon for midsize automobiles resulted in the following data: Speed (Miles per Hour) 30 50 40 55 30 24 60 24 51 56 Miles per Gallon 28 24 24 22 30 33 21 Compute the sample correlation coefficient (to 2 decimals and enter negative value as negative number). 35 26 24 What can you conclude, based on your computation of the sample correlation coefficient? - Select your answer - Select the correct interpretation for the sample correlation coefficient. (i) For driving speeds between 24 and 60 miles per hour, higher speeds are associated with higher miles per gallon. (ii) For driving speeds between 24 and 60 miles per hour, higher speeds are associated with lower miles per gallon. (iii) For driving speeds between 24 and 60 miles per hour, lower speeds are associated with lower miles per gallon. (iv) There is no relationship between driving speed and miles per gallon. - Select your answer - -

Answer 1

30 28 784 So 24 576 40 576 55 484 24 22 30 33 21 35 30 900 2500 1600 3025 900 576 3600 576 2601 3136 19414 840 1200 960 1210 900 792 1260 60 900 1089 441 1225 676 24 51 26 840 1326 1344 10672 576 56 420 24 267 7327

= 420 = 267 = 19414 = 7327 = 10672 n = 10 = 1774 n 10 Sax = x?.002 = Sux – Ly2 Cm2 = Sax=Exy. (99€) 19414 - (420)? 7327 - (267) 10672– 420-267 = 198.1 = -542 10

Sxy Correlation coefficient r =- Exy - x)(Ey) (2x2 – 572 )(cy2 – (p2) VSxxSyy -542 V1774*198.1 =-0.9143 -0.91 There is a negative correlation hence the variables are in inverse proportion Hence (ii) is correct