Example 1
\(\text{Study hours: } [2,3,4,5,6], \text{ Test scores: } [65,75,80,90,95] \rightarrow r = 0.99\)
Calculatrice de corrélation
Calculer le coefficient de corrélation de Pearson pour mesurer les relations linéaires
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
Pearson Correlation Coefficient
The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1:
- r = +1: Perfect positive linear relationship
- r = -1: Perfect negative linear relationship
- r = 0: No linear relationship
- 0.7 ≤ |r| < 1: Strong correlation
- 0.5 ≤ |r| < 0.7: Moderate correlation
- 0.3 ≤ |r| < 0.5: Weak correlation
- |r| < 0.3: Very weak or no correlation
Important: Correlation does not imply causation. A high correlation between two variables does not mean that one causes the other. Always consider other factors and the context of your data.
\(r = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum(x_i - \bar{x})^2 \sum(y_i - \bar{y})^2}}, R^2 = r^2\)
Worked Examples
Example 2
\(\text{Temperature: } [10,15,20,25,30], \text{ Ice cream sales: } [100,150,200,250,300]\)