1. What Is R Squared?

R squared (R²), also known as 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.

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: R² quantifies how well the independent variables explain the variability of the dependent variable, with values ranging from 0 to 1 (or 0% to 100%).

3. Importance Of R Squared

Details: R squared is a key metric in regression analysis that helps evaluate the goodness of fit of a model. Higher R² values indicate that the model explains more of the variability in the dependent variable.

4. Using The Calculator

Tips: Enter the residual sum of squares (SS_res) and total sum of squares (SS_tot). Both values must be positive numbers, and SS_res cannot exceed SS_tot.

5. Frequently Asked Questions (FAQ)

Q1: What is a good R squared value?
A: This depends on the field of study, but generally, values above 0.7 are considered good, while values above 0.9 are excellent. However, context matters greatly.

Q2: Can R squared be negative?
A: In ordinary least squares regression, R² ranges from 0 to 1. Negative values typically indicate that the model performs worse than simply using the mean of the dependent variable.

Q3: What are the limitations of R squared?
A: R² always increases when adding more variables, which can lead to overfitting. It doesn't indicate whether the regression coefficients are statistically significant.

Q4: What's the difference between R and R squared?
A: R is the correlation coefficient measuring the strength and direction of a linear relationship, while R squared measures the proportion of variance explained by the model.

Q5: When should adjusted R squared be used instead?
A: Adjusted R squared should be used when comparing models with different numbers of predictors, as it penalizes for adding unnecessary variables.