The following table shows the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving. Use the data provided in the table to complete parts a) through d).

Weight (hundreds of pounds)

28

33

35

32

30

29

Fuel efficiency (mpg)

20

22

19

22

23

21

a) Determine the correlation coefficient between the weight of a car and the fuel efficiency.

The correlation coefficient between the weight of a car and the fuel efficiency is

r=

(Type an integer or decimal rounded to three decimal places as needed.)

Step-by-step explanation:

Given is a table showing the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving.

Weight Fuel eff. x^2 xy y^2

X Y

28 20 784 560 400

3 22 9 66 484

35 19 1225 665 361

32 22 1024 704 484

30 23 900 690 529

29 21 841 609 441

Mean 26.16666667 21.16666667 797.1666667 549 449.8333333

Variance 112.4722222 1.805555556

Covariance - 553.8611111

r - 0.341120235

Correlaton coefficient = cov (xy) / S_x S_y

Covariance (x, y) = E (xy) - E (x) E (y)

The correlation coefficient between the weight of a car and the fuel efficiency is - 0.341