# R IS FOR REGRESSION

To repeat the message from several previous articles in this A to Z series on monitoring and targeting, it is common to model the relationship between energy consumption and a single driving factor (D) as a straight-line relationship which separates consumption into fixed and variable parts. Expected consumption E in a given interval can then be expressed as a formula

E = c + m.D

where c and m are constants: c being the intercept on the vertical axis (fixed or base-load consumption per interval) and m being the gradient of the line (kWh per degree day, or per tonne of output, or whatever). This straight line is sometimes called the regression line, and ‘regression analysis’ is a statistical tool which estimates the values of c and m that best fit the evidence in terms of past consumption and driving-factor values (Excel users may care to check out the INTERCEPT() and SLOPE() functions if they want to explore this idea further).

It is worth mentioning that the so-called ‘regression’ line need not actually be derived by regression analysis. An example may be helpful. Consider the case of gas used in a building’s heating system. Just three figures – the total annual consumption, the corresponding annual degree-day total, and the monthly consumption in summer – are enough to derive the regression line. The summer-month consumption gives you ‘c’ for a monthly expected-consumption model (and can be scaled to a weekly figure). Twelve times the summer-month consumption gives you the annual fixed quantity so what is left, the weather-dependent part, can be divided by the annual degree-day total to give you the gradient, m, in kWh per degree day.

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