syntax error: unterminated quoted string
The line with
DROPBOX="/root/Dropbox/Backups
does not have a " at the end.
The MYSQL, MYSQLDUMP and GZIP variables refer to the programs used to execute various commands. So they should contain the path of those programs:
MYSQL="/usr/bin/mysql"
MYSQLDUMP="/usr/bin/mysqldump"
GZIP="/bin/gzip"
You can use the output of which <program name> to see what to put there:
$ which mysql
/usr/bin/msql
$ which gzip
/bin/gzip