The accurate estimation of electricity supply costs has become increasingly relevant due to growing demand, variable generation sources, and regulatory changes in emerging power systems. This study models the average unit cost of electricity supply (USD/kWh) in Ecuador using multiple linear regression techniques and ARIMAX forecasting, based on monthly data from 2018 to 2024. The regression models incorporate variables such as energy demand, generation mix, transmission costs, and regulatory indices. To enhance model robustness, we apply three variable selection strategies: correlation analysis, PCA, and expert-driven selection. Results show that all models explain over 70% of price variability, with the highest-performing regression model achieving $R^2=0.9887$. ARIMAX models were subsequently implemented using regression-based forecasts as exogenous inputs. The ARIMAX model based on highly correlated variables achieved a MAPE below 5%, showing high predictive accuracy. These findings support the use of hybrid statistical models for informed policy-making, tariff planning, and operational cost forecasting in structurally constrained energy markets.