Regression and curve fitting are statistical methods for modeling relationships between variables by finding the best-fitting curve through a set of data points. The core objective is to minimize the difference between observed and predicted values. The Key Regression Approaches are:

1. Least Squares Method
   • Minimizes the sum of squared vertical distances between data points and the regression line
   • Provides an optimal line that represents the underlying data trend
   • Assumes errors are normally distributed and independent
2. Weighted Least Squares
   • Extends least squares by incorporating weights to account for varying data point reliability
   • Allows differential emphasis on different data points
   • Useful when data points have inherent measurement uncertainties The implemented regression calculator demonstrates three primary curve-fitting techniques:
3. Linear Regression

• Simple model representing a straight line (y = mx + b)
• Captures linear relationships between variables
• Lowest complexity among regression types

2. Polynomial Regression

• Allows capturing non-linear relationships
• Second-degree polynomial enables more complex curve fitting
• Increases model flexibility compared to linear regression

3. Exponential Regression

• Models relationships with exponential growth or decay
• Transforms data to linear space for coefficient estimation
• Suitable for processes with multiplicative changes

R-squared (Coefficient of Determination) are:

• Indicates the proportion of variance explained by the regression model
• Ranges from 0 to 1
• Higher values suggest better model fit
• Quantifies the model's predictive power Implementation Strategies are:
• Robust error handling
• Flexible input mechanisms
• Visual representation of results
• Support for weighted and unweighted regressions Computational Approach
• Uses matrix solving techniques (LU decomposition)
• Handles transformation for exponential regression
• Implements comprehensive error calculation Strengths of the Approach are:

1. Supports multiple regression types
2. Allows custom data point weighting
3. Provides visual and numerical results
4. Handles various data distributions
5. User-friendly interface for regression analysis
6. Minimal advanced statistical diagnostics Regression and curve fitting are powerful techniques for understanding data relationships. The implemented web application demonstrates a practical, accessible approach to statistical modeling, enabling users to explore different regression methodologies with ease.