1. What is Error Sum of Squares?

The Error Sum of Squares (SSE) measures the discrepancy between observed data and the values predicted by a regression model. It quantifies the total squared differences between observed (y_i) and predicted (ŷ_i) values.

2. How Does the Calculator Work?

The calculator uses the SSE formula:

Where:

• \( y_i \) — Observed values
• \( \hat{y}_i \) — Predicted values from regression model
• \( n \) — Number of data points

Explanation: The equation sums the squared differences between each observed value and its corresponding predicted value.

3. Importance of SSE in Regression

Details: SSE is a key metric in regression analysis. Lower SSE values indicate better model fit. It's used to calculate R-squared and other goodness-of-fit statistics.

4. Using the Calculator

Tips: Enter matching sets of observed and predicted values. Both lists must have the same number of values. Values can be separated by commas, spaces, or line breaks.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SSE and MSE?
A: MSE (Mean Squared Error) is SSE divided by the number of observations. MSE gives the average squared error.

Q2: Can SSE be negative?
A: No, since it's a sum of squared terms, SSE is always ≥ 0.

Q3: What's a "good" SSE value?
A: There's no absolute threshold - lower is better. Compare SSE values between models for the same dataset.

Q4: How does SSE relate to R-squared?
A: R² = 1 - (SSE/SST), where SST is total sum of squares. R² measures proportion of variance explained.

Q5: When would I use SSE vs other error metrics?
A: SSE is most common in least squares regression. For other contexts, consider MAE (mean absolute error) or RMSE (root mean squared error).