How else can you get rid of the minus sign? We could square our differences, that is, we take our predictions, subtract the true values ​​from them and square them, thereby obtaining the squared deviation. Now we can sum all the squared deviations and divide by their number of objects. This value shows how much our predictions deviate from the truth squared. It is called the mean square error or MSE. When the MSE goes to zero, in this case, all true values ​​match our predictions perfectly.

We can calculate it:

Output: 
0.2838275324435149

Or just use the similar to the previous chapter method:

But there is a small snag here. It is important to note that when calculating the error, the MSE units do not match the original units of the predicted target value. We predict the number of phenols squared, which is sometimes a bit difficult to use for estimation. You can get rid of this square quite simply by taking the square root of MSE. It calls the root mean squared error (RMSE). Thus, it may be common to use the MSE loss to train a regression prediction model and use the RMSE to evaluate and report its performance.

The formula:

Ideally, all the metrics that we considered (MSE, RMSE, MAE) tend to zero when all true values are very close to predictions. But these metrics do not have a right border above which we consider metrics to be useless. Is our prediction good if MSE=13 or not?

Let’s look at an example:

In both cases MSE = 13. For the first table, this is a very large value. We are more than twice wrong in our forecasts. At the same time, for the second sample, this is a fairly good estimate.