## Example

A regression is performed for a library building with electric resistance heating. The results of the analysis indicate an R2 of 0.457. In other words, only 46% of the variation in monthly electricity usage is explained by the regression. The figure below is a plot of the monthly electric consumption versus Degree Days calculated for a 65°F reference.

Heating Degree Days - 65 Degree Base Figure 9.28.

The plot following shows the result of the regression run using monthly Degree Day referenced to 55°F. Notice in the figure that there are less data points showing. This is explained by the observation that all the days with average temperatures greater than 55°F are not included in the data set. The resulting R2 has increased to 0.656.

The next figure shows the result of the regression run using monthly Degree Day referenced to 45°F. The resulting R2 has increased to 0.884. Notice how few data points are left. Normally in statistical analysis great emphasis is placed on the importance of having an adequate data sample for the results to be meaningful. While we would like to have as many points as possible in our analysis, the concern is not so great with this type of analysis. Statistical analysis usually concerns itself with whether there is a relationship to be found. The type of analysis we are advocating here assumes that the relationship does exist, and we are merely attempting to discover the most accurate form of the relationship. Another way of saying this is that we are using a trial-and-error technique to discover the building balance point.

The final figure shows the result of the regression run with monthly degree days referenced to 40°F. The resulting R2 has decreased to 0.535.

We have learned from the above that the balance point of the building analyzed is somewhere between 40° and 50°F, with 45°F probably being pretty close. Additional iterations can be made if more precision is desired, and if the referenced Degree Day data are available.

If the published Degree Day data desired are not available, it is a relatively simple matter to construct it

from the average daily temperatures published for the local climate. If this is done with a spreadsheet, a table can be constructed in such a way that the degree days, BLC, monthly base and R2 values are all linked to an assumed balance temperature. This balance temperature is modified iteratively until R2 is maximized. Of course any energy saving calculations should consistently use both the derived BLC and degree days that accompany the correlation with the highest R2.

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