Selection of appropriate climatic variables for prediction of electricity demand is critical as it affects the accuracy of the prediction. Different climatic variables may have different impacts on the electricity demand due to the varying geographical conditions. This paper uses multicollinearity and backward elimination processes to select the most appropriate variables and develop a multiple regression model for monthly forecasting of electricity demand. The former process is employed to reduce the collinearity between the explanatory variables by excluding the predictor which has highly linear relationship with the other independent variables in the dataset. In the next step, involving backward elimination regression analysis, the variables with coefficients that have a low level of significance are removed. A case study has been reported in this paper by acquiring the data from the state of New South Wales, Australia. The data analyses have revealed that the climatic variables such as temperature, humidity, and rainy days predominantly affect the electricity demand of the state of New South Wales. A regression model for monthly forecasting of the electricity demand is developed using the climatic variables that are dominant. The model has been trained and validated using the time series data. The monthly forecasted demands obtained using the proposed model are found to be closely matched with the actual electricity demands highlighting the fact that the prediction errors are well within the acceptable limits.