Question

correlation and causation
which relationships would most likely be causal? check all that apply.
□ a positive correlation between depth under water and pressure
□ a negative correlation between total distance run and the runners height
□ a positive correlation between a puppys age and weight
□ a negative correlation between temperature and snowboards sold
□ a positive correlation between the price of milk and the price of socks

Explanation:

Step1: Analyze each option

• Option 1:

The formula for pressure \(P=
ho gh\) (where \(
ho\) is the density of water, \(g\) is the acceleration due to gravity, and \(h\) is the depth under water). As depth \(h\) increases, pressure \(P\) increases. So, there is a causal relationship.

• Option 2:

There is no logical reason why the total distance run would be causally related to the runner's height. A runner's height does not cause the distance they run.

• Option 3:

As a puppy ages, its weight generally increases (a positive correlation). But a puppy's age causes its weight to change (as it grows, matures, and its body mass changes over time).

• Option 4:

As the temperature decreases, more snowboards are sold. The temperature change causes a change in the number of snowboards sold (people are more likely to buy snowboards when it is cold and there is snow).

• Option 5:

There is no causal relationship between the price of milk and the price of socks. These are two unrelated consumer goods, and a change in the price of one does not cause a change in the price of the other.

Answer:

a positive correlation between depth under water and pressure, a positive correlation between a puppy’s age and weight, a negative correlation between temperature and snowboards sold.