Practice R-Squared (Coefficient of Determination) in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

R-squared (the coefficient of determination) is the proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model. It ranges from 0 to 1, where 0 means the model explains none of the variability and 1 means it explains all of it.

R^2 = 0.80 means the model explains 80% of why Y values differ. The other 20% is unexplained variation. Higher R^2 = better predictions.

Example 1

hard
A regression model has R^2 = 0.85. Interpret this value.

Example 2

hard
If the correlation coefficient is r = -0.9, find R^2 and interpret both values.

Example 3

hard
Two models are compared: Model A has R^2 = 0.72 and Model B has R^2 = 0.58. Which model provides a better fit and why?

Example 4

hard
A linear model has R^2 = 0.64. What percentage of the variation is not explained by the model?
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