Looking at that graph, there is way too much scatter / too little data in order to plot clean exponential fits like that. A linear model would likrly fit the data just as good. At least throw on some bands indicating uncertainty in the fit.
As you say, the pps and bps don't show much curvature, so a linear fit could indeed work for them for the displayed portion of the graph. But it's non-sensical when you look further back in time... predicting negative attack volumes prior to mid-2011. ;)
You would just choose a point of time in the past where you believe the model is inapplicable. Maybe it was a different linear model then, or maybe mostly constant, who cares, we’re modeling today’s range of data, which might be well explained by a linear model, doesn’t really matter what 2011’s data was doing unless we separately believe the same growth law had to apply across all the years, and I see no reason why.
I think the question is really about the growth of volume of connected, compromised devices. Growth curves are often sigmoid shaped, meaning, exponential until they're not. The exponential is often great for modeling growth trends up until the plateau, but it's hard to know when the corner will turn.
Exponentials are also well motivated by differential equations... (Say, if you're modeling growth of IOT devices based on word of mouth.) Polynomials with degree 1+epsilon, less so.
That's the problem, no? You can draw a line/curve over any data and convince a lot of people that it's relevant, but that's more cognitive bias than anything.
Prediction is hard, especially about the future ;)
What is the R^2 for other fits? Say linear or quadratic (the most obvious alternative choices)?
> it's non-sensical when you look further back in time
Of course, because the factors that are at work in producing the data are not constant in time. So there is no reason to expect a single curve fit with a single set of parameters to be applicable for all times.
Looking at each individually I have to disagree. They look like perfectly kosher (and in fact good) exponential fits. Bands would still be nice though.
In this case it's about 2.5 years of missing data that is substantiating a claim of 2x+ increase during the same time. It's reasonable to say it had an exponential function up until two years ago, and we don't know what it was since then.
R squared doesn't capture that inaccuracy because there is no data to compare it against during the scary time period in question. It's just a line in a void.
Or change to thin dashed line when no more data