The Hubbert Parabola

In that post I experiment with 50 different regions of the world. For each one I do two plots:

"In the first one we will place all the data points (Q(t),P(t)) until year 2005 (both measured in
Giga-barrels) and then find the parabola that passes through the origin that better approximates
the data points (by the least squares fitting method). The intersection of this parabola with the
x-axis will give us the estimated URR. In the second plot we want to show how this estimated URR
has changed through time. For this plot, we define the function URR(t) as the estimated URR by the
prior method if we had used the data points up until year t, and discarding later years. In the
second plot we place points at (Q(t),URR(t)). Clearly Q(t)<URR(t) (just note that with a very
strange data set this could be false). So all points in the second plot should be above the URR=Q
line. The dashed line URR=2Q has an interesting property. If point (Q(t),URR(t)) lies above this
line, then according to the logistic model t is before the peak year (as calculated at year t),
i.e. Q(t)<URR(t)/2. If (Q(t),URR(t)) lies below the dashed line then we are after peak year."

Just a couple of plots here: