Question

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.)

Answer 1

The correlation coefficient between the weight of a car and the fuel efficiency is: r = -0.224.

In this exercise, we would plot the weight​ (hundreds of​ pounds) on the x-coordinates of a scatter plot while the fuel efficiency​ (mpg) would be plotted on the y-coordinate of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot.

Based on the scatter plot shown below, which models the relationship between the weight​ (hundreds of​ pounds) and the fuel efficiency​ (mpg), a linear equation and correlation coefficient (r) for the line of best fit is as follows:

y = -0.12x + 24.89

R-squared,
`r^2` = 0.05

Correlation coefficient, r =
`√(0.05)`

Correlation coefficient, r = 0.2236 ≈ -0.224.

Answer 2

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