ABSTRACT
This research analyzes the relationship between average temperature and electricity consumption per capita in Indonesia using the Least Squares Polynomial Approximation (LSPA) and the Modified Chebyshev Polynomial method. Temperature and electricity consumption data from 2009-2022 were used to build approximation models of polynomial of orders 1, 2, and 3. Model performance was evaluated based on Root Mean Square Error (RMSE) and numerical stability through the condition number. The results show that the second-order LSPA model provides the lowest RMSE, but its condition number indicates ill-conditioning characteristics. To overcome this limitation, Modified Chebyshev Polynomials were applied. This transformation significantly reduced the condition number, producing well-conditioned systems for all polynomial orders. The second-order Modified Chebyshev model achieved the best performance with the lowest RMSE and stable numerical behavior. Overall, this study demonstrates that while LSPA can approximate the temperature-electricity consumption relationship, applying orthogonal polynomial bases such as Modified Chebyshev improves model stability and accuracy.
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