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.