Preliminary, the measure of regression co-efficient R2 (for instance, R2 > 0.5) and cross-validated co-efficient Q2 (for instance, Q2 > 0.5) may be used as indicators of the model predictivity. There are also other validational parameters (linked attached).

https://www.sciencedirect.com/science/article/pii/S1093326301001231

http://onlinelibrary.wiley.com/doi/10.1002/qsar.200710043/abstract

https://www.sciencedirect.com/science/article/pii/S0223523417304026?via%3Dihub

https://www.sciencedirect.com/science/article/pii/S0960894X16310964?via%3Dihub

The conditions for a valid (interpretation of the) analysis are:

• the functional model makes sense (i.e. it is is specified "correctly")
• the assumption of normal distributed residuals makes sense
• the residual variance does neither depend on any predictor nor on the (expected) response.

Everything else follows from these conditions. For instance, a prerequisite for normal distributed residuals is that the response variable is continuous; the correct specification of the model means to include all relevant covariables and interaction, that the predictors are not collinear, that there is no auto-correlation, and that the realtionships between the predictors and the response are linear (means: that it makes sense to assume a linear relationship). [Note: response and/or predictors in the model may be transformed versions of the observed variables to model non-linear relationships].

One may use other different error-models for the regression, in which case the assumption about the conditional distribution should make sense (e.g. Poisson for count data when the "event rate" can be assumed constant between observations); there may then also be a particular dependency between the residual variance and the expected response (e.g. in a Poisson-model, variance and expectation are identical).

Thanks dr Amin and Dr Jochen for interesting input