Introduction to Multiple Linear Regression and its application to simulate daily pan evaporation

Evaporation is one of the main parameters for the optimum operation of reservoirs, design of irrigation systems and scientific management of water resources. Accurate estimation of the water evaporation level is crucial in any region especially in arid and semiarid regions. In this study, the feasibility of simulation of pan evaporation in Maraghe station using the multiple regression models were investigated. Meteorological data, including the maximum and minimum air temperatures, dew point temperature, the maximum and minimum relative humidities, the number of sunshine hours, the wind speed records during the 1992 to 2012 (using the daily time scale) of Maraghe synoptic station were used. Various models of multiple linear regression (MLR) were derived for simulating the evaporation in the mentioned station. The selected MLR model was tested for multi-collinearity of input repressors using the Ridge Regression. For this purpose, the Variance Inflation Factor (VIF), responsible for the multi-collinearity in regression analysis, was calculated for each of the input variables. The results showed that all of the obtained VIFs values were less than 10 and the multi-collinearity is not created. Furthermore, the ratio of eigenvalues of the correlation matrix, λmax\λmin, for the selected model was calculated as 6.2. The selected model consisted of the maximum relative humidity (RHmax), number of sunshine hours (n), and minimum air temperature (Tmin) as independent inputs, and the Pan evaporation as the dependent variable, f (RHmax, Tmin, n). Therefore, it can be concluded that there was no multi-collinearity in the selected MLR model. The RMSE and R2 values of the selected model (MLR) was calculated as 2.37 and 0.676 mm/day, respectively.