What is the most essential metric used by a regression model?

Mean squared error (MSE) is a crucial metric for evaluating the performance of a regression model. It measures the average of the squares of the errors, which are the differences between predicted values and actual values. By squaring the errors, MSE amplifies the impact of larger errors and provides a clear indication of how well the model is performing overall.

One of the reasons MSE is commonly used is its mathematical properties, which make it particularly useful in optimization during the training of regression models. For example, MSE is differentiable, which allows for efficient calculation of gradients necessary for gradient descent optimization methods.

Additionally, the concept of MSE aligns with the principle of least squares, which is foundational in many regression techniques. This ensures that when minimizing the MSE, you are typically improving the model's predictive performance on the training data.

Other metrics like absolute error or root mean squared deviation also provide insights into model performance but may not be as effective in capturing the influence of larger errors as MSE does, which is an essential consideration in regression analysis. Variance, while important in understanding model behavior, does not specifically measure the accuracy of predictions directly.