In: Statistics and Probability
Do heavier cars really use more gasoline? suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds) and let y be the miles per gallon (mpg). The following information is based on data taken from consumer reports (Vol. 62, No.4). This correlation coefficient r indicates a ____ correlation between the weight of the car and the miles per gallon
X | 27 | 44 | 32 | 47 | 23 | 40 | 34 | 52 |
Y | 30 | 19 | 24 | 13 | 29 | 17 | 21 | 14 |
Choose the correct answer:
A.) Positive strong
B.) Negative week
C.) Negative strong
D.) Negative moderate
The provided data are shown in the table below
X | Y |
27 | 30 |
44 | 19 |
32 | 24 |
47 | 13 |
23 | 29 |
40 | 17 |
34 | 21 |
52 | 14 |
Also, the following calculations are needed to compute the correlation coefficient:
X | Y | X*Y | X2 | Y2 | |
27 | 30 | 810 | 729 | 900 | |
44 | 19 | 836 | 1936 | 361 | |
32 | 24 | 768 | 1024 | 576 | |
47 | 13 | 611 | 2209 | 169 | |
23 | 29 | 667 | 529 | 841 | |
40 | 17 | 680 | 1600 | 289 | |
34 | 21 | 714 | 1156 | 441 | |
52 | 14 | 728 | 2704 | 196 | |
Sum = | 299 | 167 | 5814 | 11887 | 3773 |
The correlation coefficient r is computed using the following expression:
where
In this case, based on the data provided, we get that
Therefore, based on this information, the sample correlation coefficient is computed as follows
which completes the calculation.
C.) Negative strong