We have counts of GitHub users over time. Let's predict how this number changes.
Call new_users/(total_users - new_users) the interest_rate, and skip the first 18 months as this growth rate doesn't fit them. Here's interest rate over time:
lm(formula = interest_rate ~ when_int, data = g[-1:-18, ])
# when_int is the number of months after December 2007.
# interest_rate is really last month's interest rate;
# it's new_users/(total_users - new_users).
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.1467628 0.0080344 18.267 < 2e-16 ***
when_int -0.0015762 0.0002181 -7.226 3.3e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.01248 on 32 degrees of freedom
Multiple R-squared: 0.62,Adjusted R-squared: 0.6081
F-statistic: 52.21 on 1 and 32 DF, p-value: 3.303e-08
Note the that the interest rate decreases by about 0.15% every month. The plots (github-growth[1-4].pdf) make that relationship look very strong and makes the assumptions approximate linearity, homoskedasticity (unvarying variance), &c. seem valid.
I tried converting to a continuous interest formula, (That's what's in my notebook.) but I didn't get very far. So I did monthly compounding; Here's an estimate of the number of GitHub-users over time
A[t+1] = A[t] * ( 1 + r[t] )
where
A[t] = Number of users in the current month (This must come from a month after June 2009.)
A[t+1] = Number of users in the next month
r[t] = 14.67% - 0.15% * (Current number of months since December 2007)
And you can fix that so it chains months together and averages them and whatnot.
So the growth looks exponential with a decreasing exponent; think of it as compounded interest on number of users with a linearly decreasing interest rate.