Coefficient of Determination (r^2)

Definition

The coefficient of determination, denoted as r^2, measures the proportion of the variation in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect fit.

Analogy

Think of r^2 as a score on a test. If you score a 0, it means you didn't study at all and your performance is completely unrelated to your preparation. On the other hand, if you score a perfect 100%, it means your performance is solely determined by how well you prepared for the test.

Related terms

Correlation Coefficient: A measure that quantifies the strength and direction of the linear relationship between two variables.

Regression Analysis: A statistical technique used to model and analyze relationships between variables.

Goodness-of-Fit Test: A statistical test that assesses how well an observed data set fits with an expected theoretical distribution.