I am still learning a lot about nonlinear regression and I have some questions about residual normality and Homoscedasticity:
1) From what I could find here (Consequences of violating assumptions of nonlinear regression when comparing models and/or datasets) One user states that normality of residuals is not a necessary assumption for nonlinear regression, is this correct and, if so, can you explain why and provide some literature on it?
2) I have been using GraphPad prism as my statistics tool and it has multiple possible tests for residual normality (D'Agostino-Pearson, Shapiro-Wilk, Anderson Darling). For some of my datasets, different tests give different results (one tests say residuals are normally distributed while the other says no). Prism recommends D'Agostino-Pearson. Are you on board with this recommendation and could you try and explain to me (a non-mathematician) why the different tests would yield different results?
3) Does the non-normality of residuals mean the model selected for nonlinear regression is incorrect?
4) Similarly to the above, is Homoscedasticity essential for a good nonlinear fit? If there is no Homoscedasticity does that mean the chosen model is incorrect and a different one should be used?
5) At the moment, in my correlations, I have a couple of replicates for some values of X. Does this affect the Homoscedasticity and/or normality of residuals calculation in a way that I need to account for?
I am sure there will be more questions, but for now, I really appreciate the help.