Questions about spatial dependence and Moran's I in Regression Analysis

[HannesZiegler1]

I'd like to attempt a regression analysis that can help me understand the relationship between septic tanks, landuse patterns, and population (independent variables) and nitrogen concentration (dependent variable) in an estuarine waterbody. I've read in numerous places that spatial dependence between variables is a fundamental problem when applying statistics to spatial data. From what I understand, in order to apply ordinary least squares regression, the data cannot exhibit spatial dependence (or is it the residuals of the regression model that cannot exhibit spatial dependence, correct me if I'm wrong)? I expect to see higher concentrations of nitrogen in the estuary clustered around nitrogen sources such as septic tanks, high population density, and certain landuses.

Does a Moran's I test identify spatial dependence between dependent and independent variables?

Is spatial autocorrelation simply a measure of spatial dependence/independence?

And if Moran's I were to show significant clustering between dependent and independent variables, would I not be able to continue with a regression analysis (or, again, is this only for the residuals of a regression model)?

Thank you so much for anyone who can help me better make sense of this.

[DanPatterson_Retired]

Sorry to ask more questions but, have you narrowed in on your selection using...

An overview of the Spatial Statistics toolbox—Help | ArcGIS for Desktop

and have you seen

Spatial Statistics Resources | ArcGIS Blog  

and why regression ?

and which Moran's

Search Result | ArcGIS for Desktop

[HannesZiegler1]

No, I haven't yet began exploring any data (I haven't even collected the data yet) because I first wanted to make sure that what I'm planning to do is sound. I'd like to do a regression to show that as more septic tanks, population density, and certain landuse patterns are present in a watershed, nitrogen concentrations in the estuary tend to also be higher. This is Indian River Lagoon in Florida, btw, a very large area.

I am planning on using the spatial autocorrelation (moran's I) tool from esri.

[DanPatterson_Retired]

Moran's is fine...regression should be reserved for those cases where you would like to 'predict', 'obtain a value for' two or more variables.  I am sure that you don't want to know the value of Y if there are X septic tanks are there.  These types of question I view as tests of association or correlation or even tests of difference...but regression...IMHO, no. Keep us posted

[HannesZiegler1]

Thank you for your reply. You are correct, I am not trying to predict at this time. There are no tools for simply correlating data, I assume I would grab data from tables and simply correlate using another software such as Excel. Do problems with spatial dependence of values also exist when doing simply a correlation?

Also, I am interested in a space-time relationship between the variables, so not only how they relate in space, but also how they relate in time. So, temporal autocorrelation, and spatial autocorrelation. I will be researching more into this, but if anyone knows off the top of their head a method that combines both spatial and temporal autocorrelation, I would really appreciate it. It might save me some time.

Thanks