Neliöhäviö

Neliöhäviö, also known as mean squared error (MSE), is a common metric used to measure the accuracy of a regression model. It quantifies the average of the squares of the errors, where an error is the difference between an observed value and the value predicted by the model. A lower MSE indicates a better fit of the model to the data.

The calculation of neliöhäviö involves summing the squared differences between the actual values and the predicted values for each data point, and then dividing this sum by the number of data points. Mathematically, if $y_i$ represents the actual value and $\hat{y}_i$ represents the predicted value for the i-th data point, and $n$ is the total number of data points, the neliöhäviö is calculated as:

MSE = $\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$

Due to the squaring of the errors, neliöhäviö penalizes larger errors more heavily than smaller errors. This can be advantageous when large deviations are particularly undesirable. However, it also means that outliers can significantly inflate the MSE.

Neliöhäviö is widely used in machine learning and statistics for model evaluation and hyperparameter tuning. It provides a single numerical value that summarizes the overall performance of a regression model. While MSE is sensitive to outliers, its mathematical properties make it convenient for optimization algorithms. For datasets with significant outliers, other metrics like Mean Absolute Error (MAE) might be considered as they are less sensitive to extreme values.