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Model Analysis <br />Given the sample data described in the preceding sections, regression <br />analysis was used to examine relationships between water provider per <br />capita water use and provider service area characteristics in an effort to <br />develop a model of per capita water use. In addition, Pearson correlation <br />coefficients were calculated to evaluate statistical correlations among the <br />different variables in the database. <br />Ideally, one would expect to find that water use is a function of <br />demographic, economic and weather conditions as represented by the <br />variables within the sample data. Such a model could be expressed as: <br />GPCD = a+ b1(persons per household) + b2(income) + bs(precipitation) +.... <br />Where: <br />a = intercept <br />bx = parameter coefficient for variable x <br />A mathematical transformation of the data into natural logarithm produces <br />the same model expressed as: <br />GPCD = a • (persons per household)b1 • (income)b2 • (precipitation)b3 • .... <br />When models are expressed in the log form, the coefficient bx is the elasticity <br />of variable x and indicates the percent change in GPCD given a one percent <br />change in the variable. <br />Binary variables (having a value of 0 or 1) were included in the data set with <br />each observation to indicate location in by basin, or location in the Front <br />Range area of the state. <br />Numerous combinations of variables were evaluated to identify the best <br />regression model from the available sample database. The best statistical <br />model is shown in Table 5. This model shows that per capita water use is a <br />function of binary variables representing location within one of three basins <br />and the front-range counties, as well as the ratio of single-family housing to <br />total housing and the ratio of service sector employment to total <br />employment. The model may be interpreted as the value of the intercept with <br />adjustments for location, housing characteristics and employment <br />characteristics. The R-square value of the statistical model indicates the <br />percent of variation in GPCD throughout the data that is explained by the <br />variables in the model. In this instance, the model explains only 18 percent of <br />the variation in GPCD, meaning that much of the variation in per capita <br />water use is not accounted for by variables in the data. <br />15 IIL Data CollectionandAnalysis <br />