Finally found the widget and learned how to use it. Can anyone make out what's wrong from this data below? Note: "Test" is the name of a small partition on my HD. I find this very confusing because it looks like it is saying that all previous backups have been deleted except today's, but today's failed because it still says there is not enough space, despite the 750 GB drive.
Starting automatic backup
Backing up to: /Volumes/Time Machine Backups/Backups.backupdb
Forcing deep traversal on source: "Macintosh HD" (mount: '/' fsUUID: 3297952C-EA30-3576-AF5E-26E3A75BB4E8 eventDBUUID: 1973A079-0704-441C-9F9F-FE9C655D929D)
Deep event scan at path:/ reason:must scan subdirs|require scan|
Finished scan
Using file event preflight for Test
Will copy (Zero KB) from Test
Found 1594724 files (341.86 GB) needing backup
412.62 GB required (including padding), 366.92 GB available
Deleted backup /Volumes/Time Machine Backups/Backups.backupdb/Hazel’s iMac 27/2015-05-26-182438.inProgress/ADC7ECEC-0EF6-41EE-8A8A-5402E6634A12 containing 4 KB; 366.92 GB now available, 412.62 GB required
Removed 1 expired backups so far, more space is needed - deleting oldest backups to make room
Deleted 1 backups containing 4 KB total; 366.92 GB now available, 412.62 GB required
Backup date range was shortened: oldest backup is now May 27, 2015
Backup failed with error: Not enough available disk space on the target volume.