Example 1
\(\text{Points: } (1,2), (2,4), (3,5), (4,4), (5,5) \rightarrow y = 0.6x + 2.2, R^2 = 0.64\)
Calculatrice de régression linéaire
Trouver la droite de meilleur ajustement pour vos données avec visualisation en nuage de points
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
Linear Regression
Linear regression finds the best-fitting straight line through a set of data points. The line is defined by the equation y = mx + b, where:
- Slope (m): The rate of change in y for each unit change in x
- Intercept (b): The value of y when x = 0
- R² (R-squared): Coefficient of determination (0 to 1), indicates how well the line fits the data
- Correlation (r): Measures the strength and direction of the linear relationship (-1 to 1)
The regression line minimizes the sum of squared differences between observed and predicted values (least squares method). An R² value close to 1 indicates a strong linear relationship, while a value close to 0 suggests a weak relationship.
\(y = mx + b, m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}, b = \bar{y} - m\bar{x}\)
Worked Examples
Example 2
\(\text{Study hours vs test scores} \rightarrow \text{Find relationship and predict outcomes}\)