Edit: on second thought, you're probably right. I think I was too off the cuff in responding. Left original response below. If by best fit you mean minimizing

Edit: on second thought, you're probably right. I think I was too off the cuff in responding. Left original response below. If by best fit you mean minimizing sum squared error, that's fair. But to be sure, if someone said t-test, and they only had one group, I would first guess they were doing a one-sample t-test. Even with two dependent variables and one group, I would think over whether they did a dependent t-test. I figured it was a simple linear model (in this case a correlation) because they mentioned that they tested the relationship, and it makes sense, but it seems important to sanity check the use of the term t-test, which can be highly ambiguous (and I have seen used in very surprising ways).