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 our30 50 40 55 30 24 60 25 51 55 Miles per Gallon 28 24 24 23 30 32 21 35 26 25 Compute the sample correlation coefficient (to 2 decimals and enter negative value as negative number) 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 an swer- What can you conclude, based on your computation of the sampl - Select your answer - effic Select your answer her There is a strong positive linear relationship There is a moderate positive linear relationship gher There is neither a positive nor a negative linear relationship There is a strong negative linear relationship There is a moderate negative linear relationship pei

Answer 1

784 30 28 840 900 50 1200 2500 576 40 960 1600 576 23 3025 529 1265 30 30 900 900 900 768 32 1024 576 441 60 21 1260 3600 875 625 1225 25 35 51 1326 2601 26 676 1375 625 3025 25 268 19352 7356 Sum- 10769 420 The correlation coefficient r is computed using the following expression SSxy

where SSYY = In this case, based on the data provided, we get that SSxy 10769- To420 x 268)487 SSxx 19352(420 1712 10 SSYY 7356- (268) 173.6 10 Therefore, based on this information, the sample correlation coefficient is computed as follows SSxY -487 -0.893 VSSxxSSyy V1712 x 173.6

Since, the correlation coefficient is negative , therefore, there is a negative linear relationship and also since the magnitude is close to -1 , relationship is strong.

Correct option : There is a strong negative linear relationship

Interpretation :

Correct option : (ii) For driving speeds between 24 and 60 miles per hour, higher speeds are associated with lower miles per gallon.