1. What is Regression Sum of Squares?

The Regression Sum of Squares (SSR) measures how well the regression line fits the data. It represents the variation in the dependent variable that is explained by the regression model.

2. How Does the Calculator Work?

The calculator uses the SSR formula:

Where:

• \( \hat{y}_i \) — Predicted value from regression model
• \( \bar{y} \) — Mean of observed values
• \( n \) — Number of observations

Explanation: SSR is calculated by summing the squared differences between each predicted value and the mean of observed values.

3. Importance of SSR in Regression

Details: SSR is a key component in ANOVA tables for regression analysis. It helps assess model fit and is used to calculate R-squared (coefficient of determination).

4. Using the Calculator

Tips: Enter all predicted values from your regression model (separated by commas or spaces) and the mean of observed values. The calculator will compute SSR.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SSR and SSE?
A: SSR (Regression SS) measures explained variation, while SSE (Error SS) measures unexplained variation. SST (Total SS) = SSR + SSE.

Q2: How is SSR related to R-squared?
A: R-squared = SSR/SST. It represents the proportion of variance explained by the model.

Q3: Can SSR be negative?
A: No, SSR is always non-negative as it's a sum of squared terms.

Q4: What does a high SSR value indicate?
A: Higher SSR (relative to SST) indicates more variance is explained by the model.

Q5: When would SSR equal SST?
A: When the regression model perfectly predicts all observations (SSE = 0).