SCCM 2012 R2 - Install - reinstall of SCCM database fails - Configuration Manager requires a dedicated SQL Server instance

Problem: 

You run the Prerequisite check for the SCCM 2012 R2 installer and are met with the following Failure message;

Dedicated SQL Server instance: Configuration Manager requires a dedicated SQL Server instance to host the site database. You selected the SQL Server instance that site hosts the Configuration Manager database for another site. Select a different SQL Server instance for this new site to use, or resolve the conflict by uninstalling The Other excellant site or moving to a different database SQL Server instance.

Chances are you previously had the database for another sccm installed on this server but then uninstalled it. Although the uninstall process went as expected, apparently all is not well since the SCCM Pre-requisite checker still thinks something is occupying the sql instance.

Cause:

Some of the old registry settings were not removed when the previous sccm site was uninstalled. The new install wizard is detecting these reg keys and interpreting them as a current install of sccm on the target instance.

Fix:

Remove the problem registry keys. If you navigate to the below mentioned locations, you should find the following three registry keys are still present even though the uninstall of your old site may have completed without issue. Delete these and only these keys, 

[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\SMS\Components\SMS_SITE_SQL_BACKUP_<SITESERVERNAME>]

[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\SMS\Operations Management\Components\SMS_SITE_SQL_BACKUP_<SITESERVERNAME>]

[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\SMS\Tracing\SMS_SITE_SQL_BACKUP_<SITESERVERNAME>]

After these keys have been removed, re-run the Prerequisite check and you should be good to go