This paper presents a statistical regression bottom up model for the spatial characterisation of the final energy for space heating and domestic water production. For each building of the Swiss national building and dwelling register, the model estimates the heated surface and the floor specific final energy demand for space heating and domestic hot water production, by way of average statistical indicators being derived from two large calibration sets. For each pixel of territory a bootstrap algorithm allows to estimate the confidence interval around the average value given by the model. For a portion of territory with known demand, we checked that the confidence interval is in accordance with the selected confidence level, comforting that the bootstrap algorithm is adequate. Furthermore, the error decreases inversely proportional to the square root of the number of buildings, as predicted by the central limit theorem. At national level, the total aggregated final energy demand (93.7 TWh/year) is in concordance with existing statistics. Finally, we estimate that if the entire Swiss building stock would undergo deep energy retrofit, the realistic saving potential for space heating would amount to 18.4 TWh/year, i.e. almost half of the gross saving potential.