Question

In: Statistics and Probability

Do heavier cars really use more gasoline? suppose a car is chosen at random. Let x...

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

Solutions

Expert Solution

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


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