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
The proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model, ranging from 0 to 1.
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
hardA regression model has R^2 = 0.85. Interpret this value.
Example 2
hardIf the correlation coefficient is r = -0.9, find R^2 and interpret both values.
Example 3
hardTwo 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
hardA linear model has R^2 = 0.64. What percentage of the variation is not explained by the model?