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Predictive chart - how to limit lines based on filters?

I have only just started to use the predictive analysis functionality in a VizLib Line Chart and have never used the Visibility field.  My data includes region and country fields (among many others) and I'd like to have a line for each region, unless the user restricts the results to one or more specific regions (in which case, I'd only want to see those).  So my questions are:

1.  Is there a formula I can use that would automatically produce a separate line for each region or do I have to use a separate measure for each?  Right now I'm using separate ones.

2.  If I have to use a separate measure for each, how can I use the Visibility functionality based on whether or not the results are restricted to specific regions, if one or more are selected in the filter?

3.  Is there a way to make those lines visible only if data exists for a region based on other selected filters?  For example, if the user limits the results to just China, which means only the JAPAC region contains data, can the chart only show the JAPAC line without the user also having to select JAPAC?

See attachment for filters and chart.

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