Coefficient of Determination Calculator

Sum of Squares of Residuals:


Total Sum of Squares:



Calculate Coefficient of Determination

 

Coefficient of Determination Calculator

When analyzing the goodness of fit of a regression model, the coefficient of determination (R²) plays a crucial role in understanding the variance explained by the model. R² measures the proportion of the variance in the dependent variable that can be predicted from the independent variables. To simplify the process of calculating R², we’ve created an interactive Coefficient of Determination Calculator.

Understanding the Calculator

Our Coefficient of Determination Calculator offers a straightforward way to compute R² by inputting two essential values: the sum of squares of residuals and the total sum of squares. These values are integral to quantifying the quality of a regression model’s fit to the data.

1. Sum of Squares of Residuals: The sum of squares of residuals represents the sum of the squared differences between the actual values and the predicted values from the regression model. It quantifies the unexplained variability in the dependent variable.
2. Total Sum of Squares: The total sum of squares represents the sum of the squared differences between the actual values and the mean of the dependent variable. It quantifies the total variability in the dependent variable.

How to Use

1. Enter the sum of squares of residuals and the total sum of squares in the designated input fields.
2. Click the “Calculate Coefficient of Determination” button.
3. The calculator will instantly provide you with the coefficient of determination (R²) which ranges between 0 and 1. A higher R² indicates a better fit of the model to the data.

Interpreting the Result

The result will display the coefficient of determination (R²) with a precision of four decimal places. R² can help you understand the proportion of the variance in the dependent variable that is explained by the independent variables used in your regression model. An R² value closer to 1 indicates that a larger portion of the variability in the dependent variable is accounted for by the model.

Conclusion

Our Coefficient of Determination Calculator simplifies the process of computing R², enabling you to assess the goodness of fit of your regression model effortlessly. By plugging in the sum of squares of residuals and the total sum of squares, you gain insights into the strength of the relationship between your variables. This tool empowers analysts, researchers, and students to make informed decisions based on statistical analysis.

Incorporate this calculator into your data analysis toolkit to enhance your understanding of regression models and their predictive capabilities.