Not Nice Square Error
“Not nice” square error is a little silly title to the commonly used mean square error. For those who haven't used mean square error, it is a commonly used estimator in statistics. The simple definition is, the MSE informs you of how close the set of points are to the regression line. It is the preferred estimator because it gives weight to larger values. This estimator is also preferred because it finds the ‘average of the set of errors. This means, the lower the MSE you get from a model or a regression line, the better it performs.
From the formula, we can see we are finding the difference between the observed values and the predicted values. The MSE can reach a small number but it will never result in an extremely smaller number such as zero.
In addition, for certain models, as we begin to increase the number of data points the MSE should begin to decrease. If it does not, it is advised to look over the construct of the model as there may be a flaw. The MSE should typically decrease with more data points.
Root Mean Squared Error
The Root Mean Square Error is the standard deviation of the predicted errors from the model.
The RSME is measured of how spread out the residuals are in the dataset.
This link has a great explanation of RSME.
Hopefully, this was useful to anyone who came across. Any feedback is welcomed!