Fit to parabola
\[ OPS(\text{Age}) = \text{MAX} - \gamma (\text{Age} - \text{PEAK_AGE})^2 \] - Instead of fitting this nonlinear model, we transform it into this linear model:
\[
\begin{aligned}
OPS(\text{Age}) &= A + B (\text{Age}-30) + C (\text{Age} - 30))^2\\
\text{PEAK_AGE} &= 30 - \frac{B}{2C}\\
\text{MAX} &= A - \frac{B^2}{4C}
\end{aligned}
\]
- This can be fit with lm
using the formula:
OPS ~ I(Age - 30) + I((Age - 30)^2)