Logarithmic Regression of 3x3 PB Averages

[goodatthis]

So I was thinking, if I calculate the equation for the logarithmic regression of my 3x3 PB averages, what do I get? So I used this website to plug in my data points, with the x value corresponding to AoX and the y value being the time. Since obviously everyone solves at different speeds, meaning b in aln(x)+b would be different for everyone, I was wondering what your coefficient is. So for me, "my equation" was y=0.991254ln(x)+11.01467, meaning my coefficient was a little less than 1. So in other words, my averages follow a near perfect natural logarithmic regression, which I think is fairly interesting.

FYI, I used my PB averages of 5, 12, 50, and 100 for consistency's sake, since often times people's ao12 and 5 are much faster than 50 and 100. Using ao1000 is pretty useless as there is definitely a big plateauing effect after ao100, as my ao1000 is only about .8 slower than my ao100 yet this equation would predict it to be in the high 18s.

So go calculate it, and tell me what you got!

 

[AlphaSheep]

Mine is also a little less than 1, but I don't think it's anything more than coincidence. Just to check, I used all of my solves stored on the PC I was currently on (around 14000 solves over 2 years) and did the analysis for on every single PB change in that time. Here's my results.

Just to be clear, I fitted each curve to 4 points. So if my current PB averages of 5, 12, 50 and 100 are 16.48, 17.81, 18.84 and 19.25, I did a logarithmic regression on the four points (5, 16.48); (12, 17.81); (50, 18.84) and (100, 19.25).

Personally, I feel fitting a curve to 4 points is not going to be that accurate (that's why the above graph is so jagged), so I wouldn't read that much into it. Also, if I include my average of 1000, 5000 and 10000, then it becomes obvious that averages don't actually follow much of a power law.