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My point shapefile has four fields, three of which are numerical: longitude, latitude, and homicides. However, the homicides field does not appear for me to select it as an interpolation attribute (the field name has no spaces).

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First check in the layer properties and check the fields tab. Make sure that the field that you want to interpolate is not an integer64 one. The interpolation field can be a decimal number (real) or an integer with a width less than ten characters. It seems that the interpolation plugin can not understand integer64 fields. If interpolation field is an integer 64, you can use the field calculator and create a new one either decimal or integer with less than 10 as width. For the numeric expression you can multiply times 1 the original value.

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