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 25 60 25 50 55 Miles per Gallon 29 26 26 22 29 31 21 35 25 26 Compute the sample correlation coefficient. (Round your answer to two decimal places.) Interpret the sample correlation coefficient. There is a strong negative relationship between the driving speed and miles per gallon. For driving speed between 25 and 60 miles per hour, higher speeds are associated with lower miles per gallon.

Answer 1

R = -0.90 (2 decimal places)

Explanation:

Given the data :

Speed (Miles per Hour) :

30

50

40

55

30

25

60

25

50

55

Miles per Gallon :

29

26

26

22

29

31

21

35

25

26

The correlation Coefficient, R shows the degree or level of relationship between the dependent and independent variable. A positive R value denotes a positive correlation while a negative R value denotes a negative relationship. R values should range between - 1 to +1 with values close to 1 and - 1 depicting strength while value of zero means no relationship exist.

Hence, R value of -0.90 depicts a strong negative relationship. Hence, higher speed are related to lower miles per gallon and vice versa.