The Proof of the Structure Stability of the Polynomial Curve Fitting Model When the Time Variable t Takes Equidistant Values

The polynomial curve fitting models are among the most common trend extrapolation prediction models. The time‐independent variable can take on various values during model construction, and it is a theoretical question whether different value selections will affect the model’s structure. This study proves that when the time‐independent variable t is sampled equidistantly, the least‐squares error (SSE) of the established polynomial curve fitting model remains constant, the model validation F ‐statistic is equal, and the polynomial degree of the model is consistent. The demonstration that equidistant sampling of the time‐independent variable maintains structural stability in the model will provide theoretical support for the modeling and application of this model.