Mathematical Formulas:

1. Slope: \( A = \frac{N \sum_{i=1}^{N} x_i y_i - \sum_{i=1}^{N} x_i \sum_{i=1}^{N} y_i}{N \sum_{i=1}^{N} x_i^2 - (\sum_{i=1}^{N} x_i)^2} \)

2. Intercept: \( B = \frac{\sum_{i=1}^{N} y_i \sum_{i=1}^{N} x_i^2 - \sum_{i=1}^{N} x_i \sum_{i=1}^{N} x_i y_i}{N \sum_{i=1}^{N} x_i^2 - (\sum_{i=1}^{N} x_i)^2} \)

3. Uncertainty in Slope: \( \sigma_A = \sqrt{\frac{N}{N \sum_{i=1}^{N} x_i^2 - (\sum_{i=1}^{N} x_i)^2} \cdot \frac{\sum_{i=1}^{N} (y_i - (Ax_i + B))^2}{N-2}} \)

4. Uncertainty in Intercept: \( \sigma_B = \sqrt{\frac{\sum_{i=1}^{N} x_i^2}{N \sum_{i=1}^{N} x_i^2 - (\sum_{i=1}^{N} x_i)^2} \cdot \frac{\sum_{i=1}^{N} (y_i - (Ax_i + B))^2}{N-2}} \)

5. Coefficient of Determination: \( r^2 = \left(\frac{N \sum_{i=1}^{N} x_i y_i - \sum_{i=1}^{N} x_i \sum_{i=1}^{N} y_i}{\sqrt{(N \sum_{i=1}^{N} x_i^2 - (\sum_{i=1}^{N} x_i)^2)(N \sum_{i=1}^{N} y_i^2 - (\sum_{i=1}^{N} y_i)^2)}}\right)^2 \)