1. What is MSE?

MSE (Mean Squared Error) is a common metric used to measure the average squared difference between estimated values and actual values. It's widely used in statistics and machine learning to assess model performance.

2. How Does the Calculator Work?

The calculator uses the MSE formula:

Where:

• \( errors_i \) — The error for each observation (actual - predicted)
• \( n \) — Number of observations

Explanation: Each error is squared (to eliminate negative values and emphasize larger errors), then averaged across all observations.

3. Importance of MSE

Details: MSE is particularly useful because it penalizes larger errors more heavily than smaller ones (due to squaring), making it sensitive to outliers. It's widely used in regression analysis and model evaluation.

4. Using the Calculator

Tips: Enter your errors as comma-separated values. Errors can be positive or negative. The calculator will automatically square them, sum them, and divide by the count.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between MSE and RMSE?
A: RMSE (Root Mean Squared Error) is simply the square root of MSE, bringing the units back to the original scale.

Q2: When should I use MSE vs MAE?
A: Use MSE when you want to penalize large errors more heavily. Use MAE (Mean Absolute Error) when all errors should be weighted equally.

Q3: Can MSE be negative?
A: No, since all errors are squared before averaging, MSE is always ≥0.

Q4: What's a good MSE value?
A: There's no universal "good" value - it depends on your data scale. Lower is better, with 0 being perfect prediction.

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).