Are GWR results are valid when OLS is biased?

[NastaranPourebrahim]

I am doing OLS and GWR at census tract level. I have included whatever variables that are in the literature (based on availability) and actually I do not have any other data to add at this level. But my OLS shows very low adjusted R2 (0.11) and significant jarque-Bera Statistic. Even running GWR, there is no improvement in adjusted R square and maximum local R2 is 0.20. The low to high coefficient surfaces show a west-east pattern and in almost all of variables the coefficient sign (negative/positive) does not change in the low to high coefficient. 

with the OLS showing biased and these GWR results, can I still use GWR and report it in my paper as a valid analysis?

Thanks.

[DanPatterson_Retired]

If the requirements for the use of a particular statistical test are not met, (for instance, normalcy) and transformations of the data to accommodate for this (for instance, a numeric transform) do not improve the situation, then the use of parametric statistics should be abandoned in favor of statistical measures/tests that make no underlying assumptions about the input data ( ie non-parametric statistics).   Regression is one example... if linear regression shows an exceptionally poor correlation and variable transformation does not reveal linearity, then one might move on to rank correlation (or other approaches).  There may be a time to accept that no correlation exists, no matter how hard one tries to squeeze one out.  The academic literature is full of such bad examples ... don't contribute to it... instead, maybe you can provide some context as to what you are looking at, and what you think is going on.  An approach, a suggested statistical technique or method of analysis might be suggested that you hadn't thought of.