What size wire and heatre do I need for a room size 15*11

Here in the northeast, we use 11 watts per square foot for 2x4 insulated exterior walls, and 9 watts/sq ft for 2x6 insulated exterior walls.

This method is only a rough rule of thumb estimate that works with normal conditions, and is not very scientific that calculates the true heat loss. Such as large windows, no or little insulation, and other factors that increase heat loss.

The W/SqFt works OK for one or two rooms, and a bit more heat is added in to insure the space will be heated in a reasonable time, but is not a good substitute for proper heat loss calculations that should be done for larger areas, which will include the amount and type of windows, type of insulation, geographic location, etc.

So my rough calcs show between a 1500 and 2000 watt heater. Perhaps someone will follow up with the actual heat loss calculations to help further.

Or check over in the HVAC forum for heat loss and heat sizing questions.