In order to help folks get started with writeback applications, I'm posting here an Analysis Services database, it's associated data source, and three sample Excel applications demonstrating different forms of writeback.
By downloading these, you assume all risk and agree to work with these in an isolated, test environment only. I want to make sure I'm clear that these are not thoroughly tested, do not employ validation or error handling, and are otherwise in no way ready for a production deployment.
That said, if you do download and use these, you'll need to change the data source connection string in the Analysis Services database to point to wherever you deployed the WritebackDemo database. You'll need to deal with permissions issues between your Analysis Services instance and SQL Server Database Engine instance. You'll also need to modify the connections in the workbooks; these are accessible through the Data tab's Connections item.
Also, I should note that both databases use SQL Server 2012 RTM. You should be able to download a copy of Evaluation Edition to get these to work if you do not otherwise have Developer Edition available to you.
I hope these are helpful in demonstrating the concepts explained in the posts and giving you a starting point for your writeback applications.