1. What is R-Squared?

R-squared (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.

2. How Does the Calculator Work?

The calculator uses the R-squared formula:

Where:

• \( SS_{res} \) — Residual sum of squares (sum of squared differences between observed and predicted values)
• \( SS_{tot} \) — Total sum of squares (sum of squared differences between observed values and their mean)

Explanation: R-squared measures how well the regression predictions approximate the real data points, with values ranging from 0 to 1.

3. Importance of R-Squared

Details: R-squared is crucial for evaluating the goodness of fit of a regression model. Higher values indicate that the model explains a greater proportion of the variance in the dependent variable.

4. Using the Calculator

Tips: Enter both SS_res and SS_tot values. Both must be positive numbers, and SS_res cannot exceed SS_tot. The calculator will compute R-squared automatically.

5. Frequently Asked Questions (FAQ)

Q1: What is a good R-squared value?
A: Generally, higher values are better, but acceptable values depend on the field of study. Values above 0.7 are often considered good in social sciences, while physical sciences may require higher values.

Q2: Can R-squared be negative?
A: In ordinary least squares regression, R-squared ranges from 0 to 1. Negative values may occur in other contexts but indicate that the model performs worse than simply using the mean.

Q3: What are the limitations of R-squared?
A: R-squared doesn't indicate whether the regression coefficients are statistically significant, and it can be artificially inflated by adding more variables to the model.

Q4: How is R-squared different from adjusted R-squared?
A: Adjusted R-squared accounts for the number of predictors in the model and penalizes excessive variables, providing a more accurate measure for multiple regression.

Q5: When should I use R-squared?
A: Use R-squared to compare the explanatory power of regression models and to understand how well your model fits the data, particularly in linear regression analysis.