When trying to fit an exponential curve, don’t weight all the points equally
We didn’t. We fit a line in log space, but weighted the points by sqrt(y). The reason we did that is because it doesn’t actually appear linear in log space.
This is what it looks like if we don’t weight them. If you want to bite the bullet of this being a better fit, we can bet about it.
Interesting, thanks. This “unweighted” (on a log scale) graph looks a lot more like what I’d expect to be a good fit for a single-exponential model.
Of course, if you don’t like how an exponential curve fits the data, you can always change models—in this case, probably to a curve with 1 more free parameter (indicating a degree of slowdown of the exponential growth) or 2 more free parameters (to have 2 different exponentials stitched together at a specific point in time).
Of course, if you don’t like how an exponential curve fits the data, you can always change models—in this case, probably to a curve with 1 more free parameter (indicating a degree of slowdown of the exponential growth) or 2 more free parameters (to have 2 different exponentials stitched together at a specific point in time).
Oh that’s actually a pretty good idea. Might redo some analysis we built on top of this model using that.
We didn’t. We fit a line in log space, but weighted the points by sqrt(y). The reason we did that is because it doesn’t actually appear linear in log space.
This is what it looks like if we don’t weight them. If you want to bite the bullet of this being a better fit, we can bet about it.
Interesting, thanks. This “unweighted” (on a log scale) graph looks a lot more like what I’d expect to be a good fit for a single-exponential model.
Of course, if you don’t like how an exponential curve fits the data, you can always change models—in this case, probably to a curve with 1 more free parameter (indicating a degree of slowdown of the exponential growth) or 2 more free parameters (to have 2 different exponentials stitched together at a specific point in time).
Oh that’s actually a pretty good idea. Might redo some analysis we built on top of this model using that.