Is a nonlinear regression model valid even if it not Homoscedastic? I have a couple of experimental data sets where I am trying to determine if there is, for each data set, a particular linear/nonlinear regression model that correlates both variables. To this end, I have fitted multiple different models to the data (using Graphpad Prism), determined the respective AICc and selected the lowest valued AICc model as the best model (out of the ones tested).
For the sake of simplicity, I will refer to a single of these data sets, but I am hoping to get a general idea.

For this particular data set, the model with lowest AICc was a log line (defined as:Y = Slope*log(X) + Yintercept). Following are the results from the statistic analysis (made in GraphPad Prism):

So, according to these results, the residuals are normal, but there is no homoscedasticity. Does this mean that I should exclude the log line model as being a valid model for this data set? How should I interpret this?
Let me know if you need any more info on my end. I should make a disclaimer that I am not a mathematician, so go easy on me :D
 A: The "significant" p-value doesn't tell you whether departure from homoscedasticity assumptions is hugely violated or only slightly. 
In the case on only slight departure, your model could still be useful because the estimates of parameters might not be so much biased after all. 
However in the event of huge heteroscedasticity, simple linear model might not be enough.
There are many methods to deal with heteroscedasticity :
- on the first hand, your model might not incorporate an important predictor. Finding which predictor in lacking is then probably very important.
- on the other hand, assuming you have specified the right model, you could try 1) refine the predictors (sometime the scale of a predictor is just too large and that seems to be a common reason for heteroscedasticity. This modifier might perhaps be successfully replaced by another similar but me focused predictor ; 2) use weighted linear modeling with correct weights, that weights more those data points that are within a list variance zone, and give less importance to the high variance zone... ; 3) transform dependent variable so as to try to eliminate artificially the problem of heteroscedasticity (I prefer 1 and 2 because 3 might be difficult to interpret)
All that being said, one good and well designed plot of residuals vs fitted values is as valid (if not more IMO) as any test from a scientific perspective, to identify heteroscedasticity of the residuals.
