Question

for a strong correlation, people often assume that change in one quantity causes change in the second quantity. this is not always true. for the following situation, predict the type of correlation you might find. do you think that change in the first quantity causes change in the second quantity?
a cars fuel consumption and its weight

what correlation, if any, is there between the quantities?
a. there is a negative correlation.
b. there is a positive correlation.
c. there is no correlation.
do you think that change in the first quantity causes change in the second quantity?
a. notice that it is likely that change in the second quantity causes change in the first quantity. this is also true in the reverse. therefore, change in the first quantity causes change in the second quantity.
b. while change in the second quantity might affect change in the first quantity, it is unlikely that this is true in the reverse. therefore, change in the first quantity does not cause change in the second quantity.
c. notice that it is unlikely that change in the second quantity causes change in the first quantity. this is not true in the reverse. therefore, change in the first quantity causes change in the second quantity
d. there is no correlation between the quantities, so change in the first quantity cannot possibly cause change in the second quantity

Explanation:

For the correlation between a car’s fuel consumption and its weight: Heavier cars typically require more fuel to move, so as weight (first quantity) increases, fuel consumption (second quantity) tends to increase, indicating a positive correlation. For causation, a heavier car (change in first quantity) needs more energy, so it causes higher fuel consumption (change in second quantity), and the reverse (fuel consumption causing weight change) is unlikely. So option B for the first part (positive correlation) and option B for the causation part (while the reverse is unlikely, change in first causes change in second) is correct? Wait, re - evaluating the causation options: Option B says "While change in the second quantity might affect change in the first quantity, it is unlikely that this is true in the reverse. Therefore, change in the first quantity causes change in the second quantity." A car's weight is a physical property, and fuel consumption is about energy use. A heavier car needs more fuel (so first causes second), and fuel consumption doesn't make the car heavier (so reverse is unlikely). So for the correlation question, the correct option is B. There is a positive correlation. For the causation question, option B is correct. But the user's question seems to be about the correlation first. Let's focus on the correlation. Heavier cars generally use more fuel, so as one increases, the other increases - positive correlation. So the answer for the correlation is B. There is a positive correlation.

Answer:

B. There is a positive correlation.