Regression analysis in ArcGIS uses spatial analyses and autocorrelation, with the intention of predicting different facets and characteristics of spatial variables. It is a fairly standard variety of empirical study- wherein one collects data, defines dependent and independent variables, performs all manner of arcane statistical procedures involving both numbers and Greek letters, all with the intent of attempting demonstration that one variable has a measurable positive or negative effect on another.
Issues can arise, however, when one needs some kind of certainty that the regression model employed is accurate and/or non-biased, among other things. Fortunately ArcMap produces a lovely table with all of the calculated numbers required to determine various likelihood of errors, like the "Jarque-Bera" statistic, which gives a measure of model bias. The R-squared and intercept coefficients are included as well, which are also used to determine the validity/reliability of the model.
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