MSE Calculator — Mean Squared Error
Calculate Mean Squared Error, Sum of Squared Errors, and evaluate prediction accuracy
Calculate MSE and SSE
Observed Values
Predicted Values (Auto)
Predicted values will be set to the sample mean
MSE Results
Enter at least 2 observed values to calculate MSE
Example: MSE Calculation
Sample Data
Observed values: 3, 15, 6, 3, 44, 8, 15, 9, 7, 25, 24, 5, 88, 44, 3, 21
Sample size: n = 16
Sample mean: μ = 320/16 = 20
Calculation Steps
Step 1: Calculate residuals (xi - μ)
Step 2: Square each residual
Step 3: Sum all squared residuals: SSE = 7590
Step 4: Divide by n: MSE = 7590/16 = 474.375
Results
MSE: 474.375
SSE: 7590
RMSE: √474.375 ≈ 21.78
Interpretation: Higher values indicate larger prediction errors
MSE Components
MSE
Mean of squared errors
SSE
Sum of squared errors
RMSE
Root mean squared error
MAE
Mean absolute error
MSE Tips
Lower MSE = better predictions
MSE penalizes large errors more than MAE
Perfect predictions have MSE = 0
RMSE returns to original units
Understanding Mean Squared Error (MSE)
What is MSE?
Mean Squared Error (MSE) measures the average squared differences between predicted and observed values. It quantifies prediction accuracy by penalizing larger errors more heavily due to the squaring operation.
Why Square the Errors?
- •Eliminates negative values from cancelling positive ones
- •Gives more weight to larger errors
- •Provides mathematical convenience for optimization
- •Connects to least squares regression
Key Formulas
MSE = (1/n) × Σ(xi - yi)²
SSE = Σ(xi - yi)²
RMSE = √MSE
MAE = (1/n) × Σ|xi - yi|
Applications:
- Machine Learning: Model evaluation metric
- Regression: Line of best fit optimization
- Forecasting: Prediction accuracy assessment
- Quality Control: Measurement error analysis
Note: MSE units are squared; use RMSE to return to original units