Numerical Integration and Statistical Modeling for Real-World Applications

This paper presents a unified computational and statistical framework bridging numerical mathematics with real-world data-driven decision making. Two research contributions are presented. First, a Riemann Sum-based numerical integration model for estimating energy consumption in smart buildings, achieving 98% accuracy against ground-truth metered data collected at 15-minute intervals. Second, a multiple regression and Pearson correlation analysis across 30 schools in Faisalabad, Pakistan, quantifying the relationship between teacher qualifications, teaching experience, and student academic performance, yielding a strong correlation coefficient of r = 0.76 (p < 0.001) and adjusted R² = 0.71. Together, these studies demonstrate the power of applied mathematics and computational modeling in solving educational and engineering challenges.