Vapor injected compressors are one of the promising technologies for cold climate heat pumps because it enables compressor operation with a large range of evaporating temperatures at acceptable efficiency. However, the large operating range also makes it difficult to generate empirical maps that are applicable to most of its operating conditions. This paper discusses a method to create an empirical map using the Buckingham-PI theorem and estimates the resulting extrapolation uncertainty. Data from the laboratory testing of a cold climate heat pump were used to generate the map. The uncertainties from model random error and training data were calculated to examine if the model is reliable at extrapolation.