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A study was conducted to evaluate the potential for using a linear relationship between the power input to a residential water heater and the output of thermal energy in hot water for rating the energy efficiency of the unit. This approach has the potential for simplifying the currently used test method while providing information that can be used to predict performance under different demands. A gas tankless water heater and an electric storage water heater were tested under a range of output rates, and linear relationships were developed for each system. The equations were then used to predict the input required to provide particular output rates demanded by the user. The accuracy of these models was assessed against five different 24-hour simulated-use tests, consisting of the approach from the current test method and alternative profiles that involved more draws of hot water and varying amounts of daily hot water removed from the water heaters. Discrepancies between predicted water heater efficiencies and measured efficiencies indicate that a linear model relating input rate and output rate may not be appropriate for fully describing residential water heater performance. This paper discusses the challenges in applying a linear model for predicting the daily efficiency of a water heater.