Supervised dimension reduction methods have been extensively applied in different scientific fields like biology and medicine in recent years. However, they have hardly ever been used in micro economics, and in particular cost function modeling. Nonetheless, these methods can also be useful in regulation of natural monopolies such as gas, water, and electricity networks, where firms’ cost and performance can be affected by a large number of environmental factors. In order to deal with this ‘dimensionality’ problem we propose using a supervised dimension reduction approach that aims to reduce the dimension of data without loss of information. Economic theory suggests that in the presence of other relevant production (cost) drivers, the traditional all-inclusive assumption is not satisfied and, hence, production or cost predictions (and efficiency estimates) might be biased. This paper shows that purging the data using a partial regression approach allows us to address this issue when analyzing the effect of weather and geography on cost efficiency in the context of the Norwegian electricity distribution networks.