For a model predicting house prices, which loss function measures how far off its prediction is from the real price by looking at squared differences?

The loss function that measures how far off a model's prediction is from the real price by looking at squared differences is Mean Squared Error. Mean Squared Error, commonly abbreviated as MSE, is a standard loss function used in regression analysis, which involves predicting a continuous value like house prices. A loss function quantifies the discrepancy between the values predicted by a model and the true, observed values. In the context of predicting house prices, the prediction is the estimated price the model outputs, and the real price is the actual sale price of the house. To calculate MSE, the first step is to find the difference between each predicted house price and its corresponding real price. This difference represents the error for that specific prediction. Next, each of these individual errors is squared. Squaring the errors serves two primary purposes: it ensures that all errors contribute positively to the total loss, preventing positive and negative errors from neutralizing each other, and it penalizes larger errors more heavily than smaller ones, making the model sensitive to significant deviations from the actual price. Finally, all these squared errors are summed up, and this sum is then divided by the total number of predictions to obtain the average. This average of the squared differences is the Mean Squared Error. A lower MSE value indicates that the model's predictions are, on average, closer to the actual real prices.