One item on my PerformancePoint wish list is the ability to change a datasource for an Analytic Chart/Grid.  There is no way to do this.  Instead you must create a new datasource and build the Analytic Charts/Grids from scratch using the new datasource.  Why would someone want to change the datasource of an Analytic Chart/Grid?  Well, here is what happened to me recently: A bunch of Analytic Charts were using the same datasource, and I had a request to limit the “drill down to” for a certain half of the Analytic Charts to just a couple of dimensions, as opposed to the couple dozen dimensions being shown.  So, I created a perspective in the cube that limited the visible dimensions to those couple of dimensions.  But then the problem crept up: if I changed the datasource to use this new perspective, then all Analytic Charts that use this datassource would be changed to have just the couple of dimensions visible.  But I only wanted half the Analytic Charts to change.  So then I decided to create a new datasource that used the new perspective, then went to change half the Analytic Charts to use this new datasource.  But no luck – there is not a way to do that.

Note: Scorecards have the option to change the data source, but that ability was never given to Analytic Charts/Grids.

Bottom line: Use different data sources for groups of Analytic Charts/Grids if you think down the road you will want to use different perspectives for each group.

UPDATE: I have not tried it, but this appears to solve the problem via API calls: PerformancePoin​t Services 2010: Change Analytic Report Data Source Sample