PsychologyStatisticsUniversity
AQAIB

Coefficient of Determination (R²) Calculator

The proportion of variance in the dependent variable that is predictable from the independent variable.

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
R-Squared

Formula first

Overview

The coefficient of determination represents the proportion of the variance in the dependent variable that is predictable from the independent variable. In simple linear regression, it is calculated by squaring the Pearson correlation coefficient to quantify the strength of the linear relationship.

Symbols

Variables

R^2 = R-Squared, r = Correlation

R-Squared
Correlation

Apply it well

When To Use

When to use: Use this formula when you need to determine the 'effect size' or the shared variance between two continuous variables in psychological research. It is specifically applicable after calculating a Pearson correlation to understand how much of the data's variability is explained by the model.

Why it matters: It transforms abstract correlation coefficients into a more intuitive percentage of explained variance, which is crucial for evaluating the practical significance of a finding. For example, a correlation of 0.7 sounds high, but it only explains 49 percent of the variance, leaving over half to other factors.

One free problem

Practice Problem

A clinical psychologist finds a Pearson correlation of 0.60 between hours of mindfulness practice and a reduction in anxiety scores. What is the coefficient of determination for this relationship?

Correlation0.6

Solve for:

Hint: Square the correlation coefficient to find the coefficient of determination.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Coefficient of determination
  2. Statistical Methods for Psychology by David C. Howell
  3. Britannica: Coefficient of determination
  4. Discovering Statistics Using IBM SPSS Statistics by Andy Field
  5. Statistics for the Behavioral Sciences by Frederick J Gravetter and Larry B Wallnau
  6. Wikipedia: Pearson correlation coefficient
  7. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). Sage Publications.
  8. University Psychology — Statistics