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I am trying to determine the best process to analyse some predicted water levels against observed values at specific points. I can do this simply as 1 to 1 relationship to get a r square. I would however like to analyse this relationship with a third variable such as the distance from the closest surface water (ie lake). Is there a ARCGIS 10.1 statistics tool or process that anyone can recommend? Thank you for any suggestions.

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    What is the basis for the prediction? Does it use the distance to lakes? And what "water levels" are you observing if your points are not actually surface bodies of water? Are you talking about stream gauge levels, groundwater levels, or what? – whuber Oct 29 '13 at 15:12
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    The basis of the prediction is generalized water table configurations between known surface water bodies and the distance to the known surface water bodies is not used for the prediction. The observed points are groundwater levels measured in wells. – user6784 Oct 29 '13 at 19:32
  • Neural networks maybe. – multigoodverse Oct 29 '13 at 19:55
  • This seems like a simple multiple regression problem. You can try the OLS tool. – Jeffrey Evans Oct 29 '13 at 22:08
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I would recommend you not to use Arcgis but to use a statistical program like R, which has a good support for spatial operations and a much better support for other statistical operations.

A good intro is the book by Tomislav Hengl: A Practical Guide to Geostatistical Mapping

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