R2 (correlation coefficient)
One of the most widely recognized measures of dependence between two quantities is the Pearson product-moment correlation coefficient, commonly referred to as "Pearson's correlation coefficient". It assesses the strength of the relationship between the relative movements of two variables, with values ranging from -1.0 to 1.0. A correlation less than -1.0 or greater than 1.0 suggests a measurement error. A correlation of -1.0 indicates a perfect negative correlation, while 1.0 signifies a perfect positive correlation. A correlation of 0.0 indicates no relationship between the variables. Widely utilized across various scientific fields, the correlation coefficient was pioneered by Karl Pearson, building on earlier work by Francis Galton and Auguste Bravais. Pearson's correlation coefficient is represented as R, while R2 denotes the square of Pearson's correlation coefficient.
- r = The Correlation coefficient
- n = number in the given dataset
- x = first variable in the context
- y = second variable
The interpretation of the Pearson correlation coefficient (r) depends on its magnitude:
- |r| < 0.2: Indicates a very weak or negligible correlation. The variables have little to no linear relationship.
- 0.2 > |r| < 0.4: Suggests a weak correlation. The relationship between the variables is present but still relatively small.
- 0.4 > |r| < 0.7: Represents a moderate correlation. The variables exhibit a noticeable linear relationship, but it may not be strong.
- 0.7 > |r| < 0.9: Indicates a strong correlation. The variables have a clear linear relationship.
- |r| > 0.9: Represents a very strong correlation. The variables are highly linearly related.
Additionally, the sign of the correlation coefficient (positive or negative) indicates the direction of the relationship.
How To Cite
Please provide the data in a two-column format (observed vs. simulated). You can copy from Excel, text, or any other format, separated by space.
Correlation Coefficient (R2):