What is considered fair for backing out of a rent agreement?

After backing out of a rent agreement for sharing a room, I offered to pay my friend. However, they asked for 1.5xs money that I initially offered. The money is equivalent to half a year's worth of subsidizing her rent for her own room. I am also a student paying rent at another place and am reluctant to pay the full amount that she asked for. But I feel that I am morally obligated to do so and am feeling very guilty as a result. I did not move into the room but did not give much notice. What's a fair amount to pay her? Any input/comments would be great. Thanks!