Data Modeling and Curve Fitting Techniques

📋 Course Outline

1. Model Selection Criteria
2. Point Cloud Representation
3. Curve Fitting Methods
4. Affine and Polynomial Models
5. Logarithmic and Exponential Fits
6. Goodness of Fit (R2)
7. Adjusting and Interpolating
8. Extrapolation Techniques
9. Practical Example: Car Consumption

📖 1. Model Selection Criteria

🔑 Key Concepts & Definitions

• Model Fit: The process of choosing a mathematical model that best describes the relationship between variables in a dataset, minimizing the distance between the model and the data points.
• Nuage de points (Scatter Plot): A graphical representation of data points (xi, yi) in a two-variable dataset, visualizing their distribution and potential relationships.
• Coefficient of Determination (R²): A statistical measure indicating the proportion of variance in the dependent variable explained by the model; values close to 1 suggest a good fit.
• Ajustement (Fitting): The process of determining the parameters of a model (e.g., line, parabola) that best align with the data points.
• Types of Models:
  • Affine (Linear): y = a + bx, with a > 0 or < 0.
  • Polynomial: Includes quadratic (degree 2), cubic (degree 3), etc., e.g., y = a2 + bx + c.
  • Logarithmic: y = log(a x) + b.
  • Exponential: y = a × q^bx, with a, q ≠ 1.
• Interpolation & Extrapolation:
  • Interpolation: Estimating a value within the range of data points.
  • Extrapolation: Estimating a value outside the data range,…