1. What is Squared Error?

Squared Error (SE) is a measure of the difference between an observed value and its predicted value. It's calculated by squaring the difference between the observed (y) and predicted (ŷ) values.

2. How Does the Calculator Work?

The calculator uses the Squared Error formula:

Where:

• \( y \) — Observed value (actual measurement)
• \( ŷ \) — Predicted value (estimated value)

Explanation: The formula squares the difference between observed and predicted values, which has the effect of penalizing larger errors more heavily than smaller ones.

3. Importance of Squared Error

Details: Squared Error is fundamental in statistics and machine learning for evaluating model performance. It's the building block for Mean Squared Error (MSE) and Root Mean Squared Error (RMSE), common metrics for regression problems.

4. Using the Calculator

Tips: Enter both observed and predicted values in the same units. The calculator will output the squared error in squared units (units²).

5. Frequently Asked Questions (FAQ)

Q1: Why square the error instead of using absolute value?
A: Squaring emphasizes larger errors and has nice mathematical properties (differentiability) that make it useful for optimization.

Q2: What's the difference between SE and MSE?
A: MSE (Mean Squared Error) is the average of squared errors across multiple observations, while SE is for a single observation.

Q3: Can squared error be negative?
A: No, because squaring always produces a non-negative result, regardless of the direction of the error.

Q4: What are typical units for squared error?
A: The units are the square of the original measurement units (e.g., if measuring in meters, SE is in meters²).

Q5: When should I use squared error versus absolute error?
A: Use squared error when you want to penalize large errors more heavily, and absolute error when all errors should be treated equally regardless of size.