Statistics

R-squared Calculator: Coefficient of Determination

Easily calculate the R-squared value to understand the goodness of fit for your regression model. Input your data and predicted values for instant results and insightful visualizations.

Data Inputs

Enter your data sets to calculate the R-squared value. Ensure both datasets are comma-separated and of equal length.

Comma-separated numerical values.

Comma-separated predicted numerical values.

Result

Explained Variance

R-squared Value:

The R-squared value, also known as the coefficient of determination, ranges from 0 to 1. It represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

  • R-squared = 1: Perfect fit. The model explains all the variance in the dependent variable.
  • R-squared = 0: No fit. The model explains none of the variance.
  • 0 < R-squared < 1: Indicates the extent to which the variance in the dependent variable is predictable from the independent variable(s).
Formula: $$R^2 = 1 - \frac{SS_{res}}{SS_{tot}} = 1 - \frac{\sum_{i}(y_i - \hat{y}_i)^2}{\sum_{i}(y_i - \bar{y})^2}$$

Understanding R-squared

R-squared, or 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. In simpler terms, it shows how well the data points fit a regression line.

It's a crucial metric in evaluating the performance of regression models. A higher R-squared value generally indicates a better fit, suggesting that the model is effective at predicting the dependent variable. However, R-squared doesn\'t tell the whole story and should be considered alongside other metrics and domain knowledge.

For further reading, you can explore resources like:

Frequently Asked Questions

What is the R-squared Calculator: Coefficient of Determination?
The R-squared Calculator: Coefficient of Determination is an online Statistics calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the R-squared Calculator: Coefficient of Determination?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the R-squared Calculator: Coefficient of Determination for professional Statistics projects?
Yes. The math behind it is standard Statistics, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the R-squared Calculator: Coefficient of Determination instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the R-squared Calculator: Coefficient of Determination?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.