Mean Squared Error (MSE)

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Measure the average squared difference between estimated and actual values.

Data Input

Actual Values (y)Ground Truth

Predicted Values (ŷ)Model Output

Error Analysis

Mean Squared Error (MSE)0.375

Root Mean Squared Error (RMSE)0.6124Error Root

Mean Absolute Error (MAE)0.5000Absolute Mean

Observations4

About this calculator

Overview

Mean Squared Error (MSE) is a fundamental risk function that measures the average of the squares of the errors. It is a critical metric for evaluating the performance of regression models in machine learning and statistics, where a smaller MSE indicate a better fit.

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Pro Tips

Use MSE as a loss function when you want to strongly discourage large outliers in your predictions.
Compare MSE with Mean Absolute Error (MAE) to see if large errors are dominating your model's performance.
Ensure your actual and predicted datasets are the same length and correspond to the same observations.

Fun Facts

"MSE heavily penalizes larger errors because it squares the difference; an error of 10 is 100 times worse than an error of 1."
"MSE is always non-negative, and a value of 0 indicates that the model predicts the actual values with perfect accuracy."
"The square root of MSE is the Root Mean Squared Error (RMSE), which has the same units as the quantity being estimated."

Formula: MSE = (1/n) Σ(yᵢ - ŷᵢ)²