1. What is MSE?

Mean Squared Error (MSE) is a commonly used measure of the average squared difference between the estimated values (predictions) and the actual values. It's a risk function, corresponding to the expected value of the squared error loss.

2. How Does the Calculator Work?

The calculator uses the MSE formula:

Where:

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

Explanation: The MSE is calculated by taking the average of the square of the difference between the original and predicted values of the data.

3. Importance of MSE

Details: MSE is widely used in regression analysis to measure the quality of an estimator. It's always non-negative, and values closer to zero are better. MSE gives more weight to larger differences, which can be both an advantage and disadvantage.

4. Using the Calculator

Tips: Enter comma-separated actual and predicted values. Both lists must have the same number of values. Example format: "1, 2, 3" or "1.5, 2.8, 3.2".

5. Frequently Asked Questions (FAQ)

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

Q2: What is a good MSE value?
A: There's no universal "good" MSE value - it depends on your data scale and problem domain. Lower values indicate better fit, but the threshold depends on context.

Q3: Why square the errors in MSE?
A: Squaring ensures all values are positive, gives more weight to larger errors, and is mathematically convenient for differentiation.

Q4: When shouldn't I use MSE?
A: Avoid MSE when your data has many outliers (use MAE instead) or when you need error interpretation in original units (use RMSE).

Q5: Can MSE be negative?
A: No, since all errors are squared, MSE is always non-negative. A value of 0 means perfect prediction.