In situations where a single driving factor causes variation in energy consumption, we generally expect to see a straight-line relationship on the scatter diagram of energy against the relevant factor. The intercept of the regression line on the vertical axis represents the fixed background consumption in kWh per week month or day, while its slope represents the sensitivity of consumption to variation in the driving-factor quantity. The numerical value of the slope could be kWh per unit of product output, per degree day, per hour of darkness, etc depending on the circumstances.
It is highly unusual for either the intercept or the slope to be zero. What are the exceptions? For the intercept to be zero there would need to be no consumption unrelated to the job the energy is doing. The most common example would be fuel used for a car or van: if it does zero miles in a particular week, you’d expect it to use no fuel. In a building where fuel is used exclusively for space heating (and not for continuous uses like water heating or catering) you’d expect the regression line to go through the origin of the chart. Note, however, that in the latter case the line will only pass through the origin if the degree-day values are computed to the correct base temperature.
For the slope to be zero, consumption would need to be effectively constant and thus totally unrelated to the chosen driving factor. This could signal that we have chosen the wrong driving factor. However, there is one circumstance when I would deliberately do that. When monitoring general electricity consumption in gas-heated buildings I habitually set up a degree-day related model with zero slope because I know there is a risk of people bringing in electric heaters, the effect of which will be to impose a degree-day-related slope on what should be a horizontal regression line. In a similar vein I once did a pre-survey regression analysis of electricity use on a college campus, revealing that it was unexpectedly weather-related. In fact 41% of the consumption appeared to be for heating and the explanation was electric heaters imported by resident students.
The other side of the coin is where you see zero or near-zero slope in a situation where you are certain that you have picked the correct driving factor. I encountered this situation once in a pulp mill where consumption in the log chipper did not vary with throughput when quite obviously, given the energy intensity of the process, there should have been a strong link. It turned out here that material flow was sparse and sporadic: most of the time the chipper was running idle waiting for the next log and the bulk of energy consumption was attributable to idle losses. The solution was to batch the logs for short intensive chipping campaigns and stand the equipment down between batches.