Aleppo Population Data Curve Fitting & Regression GUI

A MATLAB-based GUI application designed for statistical data analysis, curve fitting using polynomial functions, and error analysis ($SSE$). The application processes historical population data, allows dynamic polynomial degree adjustments, plots results, and exports analytical tables directly to Excel.

Mathematical Approach & Logic

1. Polynomial Fitting: Computes $n^{\text{th}}$ degree polynomial coefficients: $$p(x) = p_1 x^n + p_2 x^{n-1} + \dots + p_n x + p_{n+1}$$
2. Error Calculation: Evaluates total sum of squares ($SST$) to measure fitting accuracy: $$SSE = \sum (y - \hat{y})^2$$
3. Data Normalization: Normalizes input data using mean values for numerical stability during matrix operations.

Features

• Dynamic Fitting: User-defined polynomial degree input via GUI.
• Interactive Data Table: Displays raw, normalized, fitted, and error residual values in real-time.
• Visual Plotting: Overlay comparison of original data points versus fitted polynomial curves.
• Excel Integration: Imports input dataset (Aleppo_Population_Statistics.xlsx) and exports output analysis (Output.xlsx).

GUI Interface

Prerequisites

• MATLAB R2020b or higher

1. Clone the repository:

   git clone [https://github.com/MAQattan/matlab-population-curve-fitting.git](https://github.com/MAQattan/matlab-population-curve-fitting.git)

2. Open MATLAB and set the working directory to the project folder.
3. Ensure Aleppo_Population_Statistics.xlsx is present in the working directory.
4. Run population_fitting_app.m or type population_fitting_app in the MATLAB Command Window.

License

Distributed under the MIT License. See LICENSE for more information.