Main effect Suggest: I need these variables: \(N^{\frac{3}{2}}or\ N^{ }\), \(x_m^2\text{ or}\ x_m\), \(\tau_{abs}^2or\ e^{\tau_{abs}}\), \(m_0,\ and\ \tau_s\)
Interaction plots suggest: only four interaction terms are required, all other possible interactions are insignifcant.
Let's see what a careful analysis of stepwise regression gives:
\(C_0 = 170.7 - 8570 N^{(-0.5)} - 502.7xm - 69\tau_a - 16.03m0 + 90697N
- 119.2xm^2 + 641\tau_a^2 + 31610N^{(-0.5)}*x_m - 12084N^{(-0.5)}*\tau_a
+ 2028 xm\tau_a + 434.8\tau_a m_0 - 351903 N xm
\)
Which is surprisingly perfect. There is no red flag at all. All the terms are perfectly reasonable. Maybe my equations need not be re-evaluated at all.
- Do not use N^-0.5 if it does not significantly improve against N. Try to stay linear as much as possible. This is especially important for N because the whole idea that the parameterization might work comes from the assumption that extrapolating to larger N is easier as long as one stays within the scope of the model for the other variables.