national multiple family submetering and allocation billing program ...

properties built before 1995 were coded as “1” while those built in 1995 or later were coded as
“0.” When year is included in the model, the B coefficient can be interpreted as the difference in
average water use between properties built before 1995 compared to those built in 1995 or later.
The factor “property is a rental” was defined so that rental properties were coded as “1” while all
non-rental properties were coded as “0.” Again, the B coefficient represents the difference in
average water use between rental properties and non-rental properties.
There are a couple ordinal (continuous) variables included in one of more of the models
presented below. These include: average number of bedrooms per unit, average rent, and
average price charged for water by the local utility. For these variables, the B coefficient
represents the average difference in the amount of water used per unit for every unit increase
(e.g., bedroom size, dollar of rent, or dollar charged per kgal) in these predictor variables.
The three models selected for presentation in this report represent the range developed for
this study from fairly simple models involving five independent variables to the complex stepwise
regression model that includes numerous independent variables. Because of the inherent
range of water use and human behavior associated with the use of water across different
properties, cities, and regions, none of the models did a particularly good job of explaining the
variability of water use observed in multi-family properties. These models do consistently show
a statistically significant reduction in water use attributable to submetering programs at the 95
percent confidence level. The models do not show any statistically significant water savings
from RUBS.
The coefficient of determination (R 2 value), a measure of the goodness of fit of the
model, for these multivariate models were only on the order of 0.15 – 0.3, indicating that these
models explain between 15 and 30 percent of the variability of the data. While not a particularly
strong result in scientific and engineering research, these values are typical to what is found in
studies of human behavior and attitudes in the social sciences. While these models are weakly
predictive, they are useful in identifying the most important factors that influence water use in
these multi-family properties. Submetering was the only billing methodology consistently found
to effect a statistically significant reduction in water use. RUBS achieved statistical significance
in only a few of the models developed and in some of those cases the sign of the coefficient
indicated an increase in water use associated with the billing practice. Significant efforts were
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