MSE Calculator — Mean Squared Error

Mean Squared Error (MSE) measures the quality of an estimator or a regression model by calculating the average of the squares of the errors. The mathematical formula is defined as MSE = (1/n) * Sum((Y_i - Y_hat_i)^2), where 'n' represents the total number of data points, 'Y_i' denotes the actual observed values, and 'Y_hat_i' signifies the predicted values generated by your model. Because the errors are squared before being averaged, MSE heavily penalizes larger deviations, making it exceptionally sensitive to outliers.

Imagine you have a simple dataset containing four actual target values and your model's corresponding predictions. Let the actual values (Y) be [3, -5, 2, 7] and the predicted values (Y_hat) be [2, -4, 1, 9]. First, find the errors by subtracting each prediction from its actual value: (3 - 2) = 1, (-5 - (-4)) = -1, (2 - 1) = 1, and (7 - 9) = -2. Next, square each individual error: 1^2 = 1, (-1)^2 = 1, 1^2 = 1, and (-2)^2 = 4. Sum these squared values together to get the Sum of Squared Errors (SSE): 1 + 1 + 1 + 4 = 7. Finally, divide this sum by the number of data points (n = 4): MSE = 7 / 4 = 1.75. Thus, your final Mean Squared Error is 1.75.

When analyzing your results, always keep scale in mind because MSE units are squared relative to your original data. To return to your original units of measurement, take the square root of your MSE to find the Root Mean Squared Error (RMSE). Furthermore, be mindful of outliers; because errors are squared, a single extreme data point can artificially inflate your MSE and misrepresent your overall model performance.