Home
Back
R² Formula:
| From: | To: |
R-squared (R²), also known as the coefficient of determination, is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.
The calculator uses the simple formula:
Where:
Explanation: R-squared is simply the square of the correlation coefficient, representing how much of the variance in the dependent variable is predictable from the independent variable.
Details: R-squared is crucial in regression analysis as it indicates the goodness-of-fit of a model. Higher R-squared values (closer to 1) indicate that the model explains a large portion of the variance in the dependent variable.
Tips: Enter the Pearson correlation coefficient (r) value between -1 and 1. The calculator will compute R-squared, which ranges from 0 to 1.
Q1: What does R-squared value of 0.8 mean?
A: An R-squared 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 R-squared be negative?
A: No, R-squared ranges from 0 to 1. Negative values would indicate that the model performs worse than simply using the mean of the dependent variable.
Q3: Is higher R-squared always better?
A: Not necessarily. While higher R-squared indicates better fit, it doesn't guarantee that the model is appropriate or that the relationship is causal.
Q4: What's the difference between R and R-squared?
A: R is the correlation coefficient (-1 to 1) measuring the strength and direction of linear relationship, while R-squared (0 to 1) measures the proportion of variance explained.
Q5: When should I use adjusted R-squared?
A: Use adjusted R-squared when comparing models with different numbers of predictors, as it penalizes for adding irrelevant variables.