Which relationships would most likely be causal? check all that apply.

a negative correlation between the temperature and the amount of snow still on the ground

a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

a positive correlation between the length of the side of a pool and its depth

a positive correlation between the height of a woman and the height of her brother

a negative correlation between the volume of water in a pot and the amount of time that the water takes to boil

Let’s begin by define correlation and causation and establish the difference between the two.

Correlation is a statistical measure that describes the relationship between two or more variables; in simple terms, correlation tell us how much two or more variables are related. Causation, on the other hand, indicates that one event occurs because of other event; in other words, the first event cause the second. Correlation does not imply causation. Two events (variables) can be related, but that is not enough to tell that one event cause the other.

Now, positive correlation indicates that the variables move in the same direction, as one variable increases so does the other. Negative correlation indicates that the variables move in opposite directions, as one variables increases, the other decreases.

Now, we can analyze each of one of our examples:

1. A negative correlation between the temperature and the amount of snow still on the ground. Since the correlation is negative, it suggest that as the temperature increases the amount of snow in the ground decrease, which is very logical. Think about it, as the temperature rises, the snow melts, so there is less snow in the ground. You can even infer that the cause of the snow melting is the rise in the temperature, so this is likely a causal relationship.

2. A negative correlation between the number of digital photos uploaded to a website and the amount of storage space left. Another negative correlation; as the number of photos increases, the amount of storage space decreases, which makes sense. Photos take a space; the more photos are uploaded to the site, the mores space they are going to occupy reducing the storage space left in the site. Since the increase in the number of photos is the cause of the decrease in the storage amount left, this is likely a causal relationship.

3. A positive correlation between the length of the side of a pool and its depth. This is a positive correlation: the longer the pool the deeper, which is not always the case. After all, you can have a long shallow pool. Even though the variables are related, one not necessarily cause the other, so this is not a causal relationship.

4. A positive correlation between the height of a woman and the height of her brother. This positive correlation implies that the taller the woman, the taller his brother, which again is not always the case. This is not a causal relationship. After all, taller women can have shorter brothers.

5. A negative correlation between the volume of water in a pot and the amount of time that the water takes to boil. This negative correlation implies that the grater the volume of water, the less time it takes to boil, which not even logical. This is not a casual relationship.

We can conclude that the relationships 1 and 2 are likely causal relationships.