If you are having issues installing Office 2013 or Office 365 versions of Microsoft Office here is the best way to resolve the issue as they are both related.
Remove all folders under C:\Program Files\ That relate to Microsoft Office or Microsoft Office 15.
Then run this Microsoft Fixit to resolve the issue http://go.microsoft.com/?linkid=9815935
Reboot your machine and try again, the issue should now be resolved.
This is related to the click to run office application that comes pre-installed on a lot of machines, In my case this had already been uninstalled correctly but was still causing an issue until I ran the above.