I am trying to find the best predictor for Leaf Area Index (LAI, a plant growth indicator) among several spectral indices (these are calculated from reflectances measured in different spectral wave lengths). I am using exponential model like this: $y=a \exp(b x)$. Two of the spectral indices gave me relatively good results but I do not know which is better.
The problem is that the first spectral index has smaller residual standard error but the $a$ coefficient is insignificant; the second spectral index has significant $a$ but the residual standard error is higher. For both models $b$ is significant. Graphs of the two model fits are shown below. As I have some very low LAI measurements I think that it is not unusual to have “a” that is not significantly different of zero.
So my question is should I reject (in this situation) the model with the lower residual standard error just because the $a$ coefficient is not significant.