The R Squared value, also known as the coefficient of determination, is a statistical measure that assesses the proportion of the variance in the dependent variable explained by the independent variables in a regression model. It ranges from 0 to 1, where 0 indicates no explanatory power, and 1 indicates perfect explanatory power.
Formula: The R Squared value is calculated using the formula: �2=1−Residual Sum of SquaresTotal Sum of SquaresR2=1−Total Sum of SquaresResidual Sum of Squares
How to Use:
- Enter the observed values separated by commas in the “Observed Values” field.
- Enter the predicted values separated by commas in the “Predicted Values” field.
- Click the “Calculate” button to obtain the R Squared value.
Example: Suppose you have observed values [5, 10, 15, 20] and predicted values [6, 9, 14, 19]. Entering these values into the calculator will yield an R Squared value.
FAQs:
- Q: What is the R Squared value? A: The R Squared value is a statistical measure that indicates the proportion of the variance in the dependent variable explained by the independent variables in a regression model.
- Q: What does an R Squared value of 0.8 mean? A: An R Squared value of 0.8 indicates that 80% of the variability in the dependent variable is explained by the independent variables in the regression model.
- Q: Can the R Squared value be negative? A: Yes, the R Squared value can be negative if the model performs worse than a simple average of the dependent variable.
Conclusion: The R Squared value is a valuable metric for assessing the goodness of fit in regression models. This calculator provides a simple tool to compute the R Squared value based on observed and predicted values, aiding in the evaluation of the model’s performance.