1. What is Sum of Squares Regression (SSR)?

The Sum of Squares Regression (SSR) measures the variation in the dependent variable that is explained by the regression model. It quantifies how well your model fits the data by comparing predicted values to the overall mean.

2. How Does the Calculator Work?

The calculator uses the SSR formula:

Where:

• \( \hat{Y}_i \) — Predicted values from the regression model (unitless)
• \( \bar{Y} \) — Mean of the observed values (unitless)

Explanation: The formula calculates the squared differences between each predicted value and the overall mean, then sums these squared differences.

3. Importance of SSR in Regression Analysis

Details: SSR is a key component in ANOVA tables and helps assess model goodness-of-fit. Higher SSR values (relative to total variation) indicate a better fitting model.

4. Using the Calculator

Tips: Enter all predicted values (separated by commas or spaces) and the observed mean. The calculator will compute the SSR by summing the squared differences between each predicted value and the mean.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SSR and SSE?
A: SSR measures explained variation (predicted vs mean), while SSE (Sum of Squared Errors) measures unexplained variation (observed vs predicted).

Q2: How is SSR used in R-squared calculation?
A: R² = SSR/SST (total sum of squares), representing the proportion of variance explained by the model.

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

Q4: What does a high SSR value indicate?
A: A high SSR (relative to SST) suggests the regression model explains much of the variability in the data.

Q5: Is SSR affected by sample size?
A: Yes, SSR generally increases with more data points, which is why we often look at proportions (like R²) rather than absolute values.