I'm working on a continuous set of data that tries to identify upward spikes in trends. The way I'm identifying these "spikes" are comparing the goodness of fit of the data on a linear, exponential, and logistic regression.
How would I compare these goodness' of fit? Or like: does the dataset resemble more of a linear, exponential, or sigmoid function?
(I'm no statistician, so please correct me of any improper vocabulary). Based on some Google searches, using $r^2$ for everything isn't the best so I tried to divvy up some tests with variances of residuals, but it seems like $r^2$ shouldn't even be used for logistic regression.
Edit: I tried to conceal the model of the data, but I suppose it won't really help if I keep it secret.
The data is modeled over something like a social media site that has tags/hashtags and the number of posts that use those tags/hashtags per hour. The continuity of data sources from the posts that users continuously generate, but the reason for identifying is for identifying which tags are trending. It's like primitive machine learning, in which getting an exponential goodness of fit being the best fit is what I'd consider as trending, at least for my code base. (There are some other logic that I've implemented, but that's the gist of it.)