1. What is Least Square Error (SSE)?

Definition: SSE measures the discrepancy between observed data and the values predicted by a model.

Purpose: It's a key metric in regression analysis to evaluate model fit - lower SSE indicates better fit.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( SSE \) — Sum of squared errors
• \( y_i \) — Observed values
• \( ŷ_i \) — Predicted values from model

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

3. Importance of SSE in Statistics

Details: SSE is fundamental in regression analysis, model comparison, and optimization algorithms like gradient descent.

4. Using the Calculator

Tips: Enter comma-separated observed and predicted values of equal length. Values can be integers or decimals.

5. Frequently Asked Questions (FAQ)

Q1: How is SSE different from MSE?
A: MSE (Mean Squared Error) is SSE divided by number of observations - it averages the squared errors.

Q2: What's a good SSE value?
A: There's no universal "good" value - it depends on your data scale. Compare SSE between models on same data.

Q3: Why square the errors?
A: Squaring emphasizes larger errors, ensures positive values, and makes the function differentiable.

Q4: Can I use this for multiple regression?
A: Yes, as long as you have observed values and model predictions, the calculation method is the same.

Q5: How does this relate to R-squared?
A: R-squared is calculated using SSE - it's 1 - (SSE/SST), where SST is total sum of squares.