Fitting Curves to the XKCD Data Set

[#1]

Randal Munroe publishes one of my all time favorite comics, xkcd.  Last week's  comic  was on curve fitting, and was, arguably kind of hilarious. @Randal Munroe, dude you're hilarious. Anyone who was a discovery and heard about his Thing Explainer concept would surely agree. 

So anyway, I read the comic and then dove into the data. There is an amazing tool that @brady_brady originally published for generating Homerian distributions that can be found buried in this tremendous add-in (which is a collection of other useful scripts and add-ins, a must-have). With the "Get Data Points By Clicking On Image" tool I extracted the exact data from the comic (data attached below) and then started fitting all kinds of conventional and less conventional models and some possibly dishonest models with no regard for how badly overfit the models were (even though I could/should have, with JMP Pro.)

             Quick Note on Axis Scale.  This one seemed good to me, although it was

             missing on the original figure.  I could have done that too, but they there

             would have been a lot of clicking and I just didn't have it in me today. 

Here is a ranked table of fits

Measures of Fit for Y sorted by RSquare

Predictor	Creator		RSquare	RASE	AAE	notes
regression 10 lags	Fit Least Squares		0.9808	2.9103	2.3275	not legal, fit X along with a series of 10 sequential lags to the data. Works great when there is any hint of a trend in the data, might over fit, but only just a little, plus there are 11 parameter and I didn't bother to report adjusted r-square here.
partition BF	Bootstrap Forest		0.8469	7.4494	5.4207	500 trees, and some of them fell in the right direction
partition BT	Boosted Tree		0.6737	10.876	8.1600	50 layers, used defaults, un-tuned
partition over fit	Partition		0.6607	11.091	8.3713	made the minimum split size small and split to the end
regression ^10	Fit Least Squares		0.5687	12.505	9.3912	10th order polynomial, kind of wiggly
regression ^8	Fit Least Squares		0.5479	12.803	9.6483	8th order polynomial, not quite as wiggly as 10th order
regression 2 pieces	Fit Least Squares		0.4459	14.173	9.8317	used partition to split the data in two and fit two regression models
fit curve 4pR	Fit Curve Logistic 4P Rodbard		0.4277	14.404	10.496	4 parameter logistic regression, Robard model
partition 2s	Partition		0.4249	14.439	10.745	partition with only one split, results in two levels, not likely over fitted.
fit curve 5p	Fit Curve Logistic 5P		0.4104	14.620	10.826	5 parameter logistic regression
regression ^4	Fit Least Squares		0.3932	14.832	10.402	4th order polynomial
regression ^2	Fit Least Squares		0.3682	15.134	10.541	regular old 2nd order polynomial
fit curve 3p growth	Fit Curve Mechanistic Growth		0.3393	15.477	11.080	fancy non-linear model
regression	Fit Least Squares		0.2779	16.180	12.209	straight line
regression log	Fit Least Squares		0.2472	16.520	12.695	X is log transformed
regression exp	Fit Least Squares		0.0691	18.371	15.429	X is exponentiated (exp transform)

You might expect to find some rationale behind why I tried each of the different models but at the end of the day this is a blog not an academic paper, so don't burn too much time looking for that.   I got this table from the Model comparison tool in JMP Pro, all I had to do was find all the methods and then save the prediction formula, the fancy platform did all the math.

Just in case you wanted to play with the data (and seriously, I do mean play), it should be attached below this article.

XKCD Curve fitting.jmp