Short term load forecasting (STLF) is an important issue for an electricity power system, to enhance its management efficiency and reduce its operational costs. However, STLF is affected by lots of exogenous factors, it demonstrates complicate characteristics, particularly, the multi-dimensional nonlinearity. Therefore, it is desired to extract some valuable features embedded in the time series, to demonstrate the relationships of the non linearity, eventually, to improve the forecasting accuracy. Due to the superiorities of phase space reconstruction (PSR) algorithm in reconstructing the phase space of time series, and of bi-square kernel (BSK) regression model in simultaneously considering original spectral signature and spatial information, this paper proposes a novel electricity load forecasting model by hybridizing PSR algorithm with BSK regression model, namely PSR-BSK model. The electricity load data can be sufficiently reconstructed by PSR algorithm to extract the evolutionary trends of the electricity power system and the embedded valuable features information to improve the reliability of the forecasting performances. The BSK model reasonably illustrates the spatial structures among regression points and their neighbor points to receive the rules of rotation rules and disturbance in each dimension. Eventually, the proposed PSR-BSK model including multi-dimensional regression is successfully established. The short term load data from the New South Wales (NSW, Australia) market and the New York Independent System Operator (NYISO, USA) are employed to illustrate the forecasting performances with different alternative forecasting models. The results demonstrate that, in these two employed numerical examples, the proposed PSR-BSK models all significantly receive the smallest forecasting errors in terms of MAPE (less than 2.20%), RMSE (less than 30.0), and MAE (less than 2.30), and the shortest running time (less than 400 s) than other forecasting models.