1. What is Mean Squared Error (MSE)?

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

2. How Does the Calculator Work?

The calculator uses the MSE equation:

Where:

• \( Y_i \) — Actual observed values
• \( \hat{Y_i} \) — Forecasted/predicted values
• \( n \) — Number of observations

Explanation: The equation squares each forecast error (difference between actual and predicted), sums them up, and then takes the average.

3. Importance of MSE in Forecasting

Details: MSE is particularly useful because it penalizes larger errors more severely than smaller ones (due to squaring), making it sensitive to outliers. It's commonly used to compare different forecasting models.

4. Using the Calculator

Tips: Enter comma-separated lists of actual values and corresponding forecast values. Both lists must be of equal length and contain numeric values.

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. RMSE is in the same units as the original data, while MSE is in squared units.

Q2: What is a good MSE value?
A: There's no universal "good" MSE - it depends on your data scale. Lower values indicate better fit. Always compare MSE values between models for the same dataset.

Q3: Why square the errors instead of using absolute values?
A: Squaring emphasizes larger errors and is differentiable everywhere (important for optimization), but MAE (Mean Absolute Error) is an alternative that doesn't square errors.

Q4: Can MSE be negative?
A: No, since all errors are squared, MSE is always ≥0, with 0 representing perfect prediction.

Q5: When shouldn't I use MSE?
A: Avoid MSE when your data has many outliers (it will be heavily influenced by them) or when you need error metrics in the original units (use RMSE instead).