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Coefficient of Determination Formula:
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The coefficient of determination (R²) is a statistical measure that represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It ranges from 0 to 1, with higher values indicating better model fit.
The calculator uses the simple formula:
Where:
Explanation: The coefficient of determination is simply the square of the correlation coefficient, representing how much of the variance in one variable is explained by the other.
Details: R² is crucial for evaluating the goodness of fit in regression models, assessing predictive power, and comparing different statistical models.
Tips: Enter the correlation coefficient (r) value between -1 and 1. The calculator will compute R² by squaring the input value.
Q1: What does R² = 0.8 mean?
A: An R² of 0.8 means that 80% of the variance in the dependent variable is explained by the independent variable(s) in the model.
Q2: Can R² be negative?
A: No, R² ranges from 0 to 1. Negative values are not possible as it represents a proportion of variance explained.
Q3: What's the difference between R and R²?
A: R is the correlation coefficient (-1 to 1), while R² is the coefficient of determination (0 to 1) that represents the proportion of variance explained.
Q4: Is a higher R² always better?
A: Generally yes, but context matters. Very high R² values might indicate overfitting, and the practical significance should be considered.
Q5: What are typical R² values in social sciences vs. physical sciences?
A: Social sciences often have lower R² values (0.1-0.3), while physical sciences typically have higher values (0.7-0.9) due to more precise measurements.