This study investigates the p-vector norm error between interacting datasets subjected to random noise fluctuations using a numerical simulation approach. A system of nonlinear ordinary differential equations was analyzed to quantify errors between controlled and uncontrolled data under a noise intensity of 0.2. The Runge-Kutta fourth-order (RK4) method was employed for numerical simulations, and steady-state solutions were derived for equilibrium points. The results demonstrated that the p-vector norm errors (D1, D2, D3, D4) followed a monotonically decreasing sequence, with D3 exhibiting the least error. This study provides a framework for selection, development and validation of the best model for prediction, highlighting the impact of random noise on statistical dispersion metrics such as range, mean, and variance.