This analysis doesn't demonstrate anything, unfortunately, except that ratings declined over time and that writers changed over time.
Any factor could have caused the show's decline (like less time given for script writing, less collaboration or rewrites, management directives to change aspects of the show, etc.) -- and it would show the same result.
Any factor could have caused the show's decline (like less time given for script writing, less collaboration or rewrites, management directives to change aspects of the show, etc.) -- and it would show the same result.