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I have a CSV file which has data for different counties income, Population and Proximity of United States of America like this :

I have a CSV file]1

I have already joined the CSV file with the shapefile of United States map and duplicated them to use them as different layers.

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How can I use them to do weighted overlay analysis to find the list of top 10 counties with respect to these 3 attributes and respective weights?

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In this case you can create new attribute with expression using Field calculator in attribute table. The expression would be something like:

("Income"*0.1)+("Population"*0.5)+("Proximity"*0.9)

where values (0.1, 0.5, 0.9) are coresponding weights. Than you can simple use a categorised symbology.

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