We use the preposition “with” with the verb “to correlate. The meaning of correlate is “for two things to have a connection”.
Your opinion does not correlate with mine.
We found no correlation between the studies.
We use the preposition “with” with a verb or adjective when we mean “in relation to”. This is the situation with the verb ”to correlate” as that is the context that we use the verb.
The amount of time each person needed to complete the task correlated with our previous group.
We often use “correlate” in scientific reports to show that two graphs have similar values.
The preposition “to” is usually used to mean “in the direction of” when used with a verb or an adjective. People nowadays also use “To correlate to”. The idea between using “to” and “correlate” is that the numbers are moving in the same direction(or rather, one number is moving in a similar direction relative to another).
“To correlate with” is usually the correct phrasing as we want to compare one thing with another thing.
We can use both “between” and “with” with the noun form of “correlate” which is “correlation”.
There is a correlation between a bad diet and not thinking straight.
As you can see, we tend to use “correlation” when the study is over and we have decided that there is a connection between two things. When we use “correlates”, we often don’t have this finality so we use “with” to show the connection and “to” to show that you are considering the situation.
This study correlates with our earlier findings.
In this case we can see the connection between the study and the earlier study.
The numbers are correlated to ones we found earlier.
In this example, the speaker has this idea of movement that is associated with “to”. They are almost matching up the numbers in their head.
We use the preposition “with” with “correlate” but you will hear people saying “correlate to”. When people use “correlate to”, they also include the idea of “matching up”.