2025 Orange County Water Demand Projection Model
Model Fitting Procedure
Description
If the model fit is poor or if coefficient estimates are illogical or insignificant, several actions can be taken, including but not limited to: Identifying and removing outlier data points that have significant leverage on coefficient estimates. Remove explanatory variables with insignificant or illogical coefficient estimates from the regression equation. Testing alternate specifications of explanatory variables. Model fits and explanatory variables are compared across sectors to judge estimates relative to prior expectations, for example, testing if the relative effects of price and socioeconomic variables vary by sector in a logical way based on past experience.
Refine the model to improve measures of fit and coefficient estimates
Check models for cross-sector consistency
The models are fit to historical data using a combination of data management and statistical analysis software (R, SAS, or EViews). The model estimation results were checked to ensure strong measures of fit (e.g., R 2 ) and that coefficients were significant and reasonable. Goodness of fit is a holistic exercise requiring judgement based on two classifications of indicators: 1) Overall summary statistics used to evaluate relative model performance: these may include R 2 , Measures of average error (mean absolute error, standardized error metrics such as SAME and RMSE), and measures of bias; and 2) Visual inspection applied to plots of historical data provides an indication of the model’s ability to represent long-term trends, perform as expected during periods of interest (for example, COVID and State water use restrictions), allows the modeler to evaluate the presence of systematic biases and assess the variance in the underlying data. Section 3.3 summarizes the statistical model fits and their performance in comparison to historical observations of water consumption.
3.2.2
Summary of Explanatory Variables
The initial selection of explanatory variables is discussed in detail in Section 2. However, during the model fitting process, derivatives of initially selected variables were also developed and included in model equations. For example, an agency’s monthly water use may also be influenced by the precipitation, or temperature, in the prior month. In some cases, time lags of 1 to 3 months in weather variables improved the estimation of weather impacts on demand. Table 3-2 details the explanatory variables used to develop the demand models and identifies the expected sign and magnitude of the coefficient estimates resulting from the linear regression. The coefficient sign represents whether an explanatory variable will have a negative or positive impact on demand, for example, water use will decrease as price increases and the price coefficient should be negative. The coefficient magnitude illustrates the importance of the explanatory variable relative to all others. For example, a persons per household coefficient of 0.3 indicates that persons per household has a lesser influence on demand than a coefficient of -0.5 assigned to density.
3-5
Appendix G - 42
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