Sorry, but the answer to your question is no. Re-broadcasting signal like that would cause interference to other people trying to use the same signal. You must use some kind of wire like coax or twin-lead to "pipe" the signal to your TV rather than releasing more RF interference into the air.
Does your house have coax (for cable or satellite) already going to each room? If you aren't subscribing to cable or satellite and you can find the distribution point where the signals get split to the different rooms, you can run your antenna there and get the signal to your TV that way.
For homes that are not pre-wired with coax, what most people will do is run the coax along the edges of a room and then go through a small hole to get through walls/ceilings/floors where necessary. Many "professional" satellite and cable installers will even run the cable on the outside of the house and then put a hole into the house where needed (not a method I prefer, but I see it done everywhere).
It is also possible to get wiring into the walls, but it will take more work.
Thanks...I kind of figured this would be the case.
My house is coax cable wired for 8 TVs. Do you think I could hook the attic antenna to the main cable connection outside and get good signal to all the TVs? At the moment all of them are working well with Cox Cable.