17. A Statistical Approach to the Prediction of Fluoride in River Water Using the Best Subset Method

Water quality parameters were predicted by many methods in the past, but the application of the best subset method is yet to be explored much. This method is unique in its application as it adopts the statistical regression modeling procedure to fit a separate model for every combination of any number of predictors while selecting the best subset for making the optimal decision. The present chapter demonstrates the application of the best subset model for the prediction of fluoride in river water by developing the regression equations for various combinations of other physicochemical parameters of the water quality of the Godavari River, the second largest river in India. The desired fluoride concentrations were evaluated using the concentrations of 16 other water quality parameters data collected for a period of 13 years (1993–2005) from 13 monitoring sites during the Monsoon (June-October) and Post-Monsoon (November-February) periods in the study region. Several best subsets of independent variables are chosen based on the percentage variation in the dependent variable, with a gradual increase in the number of predictors using various combinations of water quality parameters, and the best models are selected in agreement with the highest R² value and the lowest RSS value. The final best subset regression model is selected among the various best models using F-value statistics criteria. The best subset regression model is successful in explaining 90% variation in fluoride concentrations for both seasons in the study area. It would be interesting to try this method for the study of both surface water and groundwater quality parameters.