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 Calculation

Details: R-squared is crucial for evaluating the goodness of fit of regression models, helping researchers understand how much of the variability in the outcome can be explained by the model.

4. Using the Calculator

Tips: Enter both residual sum of squares (SS_res) and total sum of squares (SS_tot) as positive values. SS_res must be less than or equal to SS_tot.

5. Frequently Asked Questions (FAQ)

Q1: What is a good R-squared value?
A: This depends on the field of study. In social sciences, 0.3 might be acceptable, while in physical sciences, 0.7+ is often expected.

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

Q3: What's the difference between R and R-squared?
A: R is the correlation coefficient (-1 to 1), while R-squared is the square of R (0 to 1) representing the proportion of variance explained.

Q4: Are there limitations to R-squared?
A: Yes, R-squared increases with more predictors added to the model, even if they're irrelevant. Adjusted R-squared addresses this issue.

Q5: When should I use R-squared?
A: Use R-squared to compare models with the same dependent variable and to understand how well your model explains the variability in the data.