1. What is Sum of Squares Error (SSE)?

The Sum of Squares Error (SSE) measures the variation between observed values and predicted values in regression analysis. It quantifies how well the regression line fits the data points.

2. How Does the Calculator Work?

The calculator uses the SSE formula:

Where:

• \( Y_i \) — Observed value (unitless)
• \( \hat{Y}_i \) — Predicted value (unitless)

Explanation: For each data point, calculate the difference between observed and predicted value, square it, and sum all these squared differences.

3. Importance of SSE in Statistics

Details: SSE is fundamental in regression analysis. It's used to calculate R-squared, assess model fit, and compare different regression models. Lower SSE indicates better model fit.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SSE and RMSE?
A: Root Mean Square Error (RMSE) is the square root of (SSE/n), making it on the same scale as the original data.

Q2: Can SSE be negative?
A: No, because it's a sum of squared values which are always non-negative.

Q3: How does SSE relate to R-squared?
A: R-squared = 1 - (SSE/SST), where SST is total sum of squares. It shows proportion of variance explained by the model.

Q4: What's a "good" SSE value?
A: There's no absolute threshold - it depends on your data scale. Compare SSE values between models for the same dataset.

Q5: Why square the errors instead of using absolute values?
A: Squaring emphasizes larger errors and makes the function differentiable, which is important for optimization algorithms.