Example 1
\(\text{Study hours: } [2,3,4,5,6], \text{ Test scores: } [65,75,80,90,95] \rightarrow r = 0.99\)
Calcolatrice correlazione
Calcola il coefficiente di correlazione di Pearson per misurare relazioni lineari
Risultati
Inserisci i valori e clicca Calcola per vedere il risultato.
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
\(\text{Temperature: } [10,15,20,25,30], \text{ Ice cream sales: } [100,150,200,250,300]\)