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I have some mineralogical data of the Earth and I would like to carry out some statistical analysis on the data to observe correlations between variables locally as finding global relations is near impossible due to human processes and natural processes. I have already looked at bivariate analysis and found some reasonably good indicators of correlations using the Pearson Correlation coefficient locally, but as I know that not all bivariate correlations could be trusted as some could be a simple coincidence. I would appreciate any recommendations to tackle this problem on how to assess correlations on local scales (specific regions) and go ahead and factor in other variables in the analysis (multivariate analysis).

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