Please help! Question about tv ratings and cancellations..?

It's a combination of factors. First, many networks produce TV shows as well. For example, House airs on Fox but is produced by NBC Universal, which sells it to Fox. Networks are more likely to keep shows with low ratings if they produce them themselves, because it keeps jobs and is less expensive. In the case of Terminator vs Dollhouse, Dollhouse was a Fox property, Terminator wasn't. Another issue is the cost of the show - special effects cost money, and some actors have huge salaries. By the time Friends ended, the actors were getting over $100,000.00 per episode (each). While the show had cheap sets, paying the actors cost too much - an action series with lots of SFX would be cheaper. So the salaries negotiated by various cast members can be an issue. Another key factor is demographics. Advertisers pay based upon the demographics of the audience. The audience they want is males aged 18-24. They pay top dollar for this group. So if a show has low ratings but good demographics and is watched primarily by males 18-24, it has a good chance of surviving. A show that has much better ratings but is popular among women or people over 30 generates less advertising revenue, despite the larger audience, and therefore is more likely to get canceled in favor of a show that appeals to a different demo.