1. What is MSE?

The Mean Squared Error (MSE) is a measure of the average squared difference between the estimated values and the actual value. It's a common metric used in statistics and machine learning to evaluate the performance of models.

2. How Does the Calculator Work?

The calculator uses the MSE formula:

Where:

• \( n \) — Number of observations
• \( y_i \) — Actual values
• \( \hat{y}_i \) — Predicted values

Explanation: The MSE calculates the average of the squares of the errors between predicted and actual values.

3. Importance of MSE

Details: MSE is widely used because it gives more weight to larger errors, making it useful when large errors are particularly undesirable. It's always non-negative, and values closer to zero are better.

4. Using the Calculator

Tips: Enter the number of observations, then comma-separated lists of actual and predicted values. All values must be numeric and the lists must be of equal length.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between MSE and RMSE?
A: RMSE (Root Mean Squared Error) is the square root of MSE. RMSE is in the same units as the original values, while MSE is in squared units.

Q2: What are good MSE values?
A: There's no universal threshold - it depends on your data scale. Lower values are better, with 0 being perfect prediction.

Q3: When shouldn't I use MSE?
A: MSE is sensitive to outliers. For data with many outliers, consider Mean Absolute Error (MAE) instead.

Q4: Can MSE be negative?
A: No, MSE is always non-negative since it's the average of squared values.

Q5: How does MSE relate to variance?
A: MSE can be decomposed into variance of the estimator plus the square of its bias (bias-variance decomposition).