Question

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:

• For a positive correlation between depth under water and pressure: As depth under water increases, pressure increases due to the weight of the water above. There is a causal relationship. The formula for pressure in a fluid is \(P = P_0+

ho gh\) (where \(P_0\) is the atmospheric pressure, \(
ho\) is the density of the fluid, \(g\) is the acceleration due to gravity, and \(h\) is the depth).

• For a negative correlation between total distance run and the runner’s height: There is no logical causal connection. A runner's height does not cause the distance they run. Taller runners can run long - distance and shorter runners can too.
• For a positive correlation between a puppy’s age and weight: As a puppy gets older (in a normal growth scenario), it gains weight. There is a causal relationship (related to growth and development).
• For a negative correlation between temperature and snowboards sold: As temperature decreases (colder weather), more snowboards are sold (because there is more snow for snowboarding). There is a causal relationship.
• For a positive correlation between the price of milk and the price of socks: There is no inherent causal link. These are two different consumer goods with their own supply - demand and cost structures.

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.