Regression Metrics R2

Both mean absolute error and mean squared error, a popular metrics. But they're not bonded in a fixed range, so it's not possible to compare across data sets. Next, we'll introduce another regression metrics called r squared which has a fixed maximum score of 1. Formally, r squared or coefficient of determination is one minus the ratio between MSE and variance. For example, if we have a linear regression model looking like this, the mean square error can be equal to .86, while the variance equals 4.9 and r squared for this particular example is around 0.82, which is considered to be very good. In fact, r squared of 1 indicate the regression is perfectly fits data, while r squared of 0 indicate the line does not fit the data at all.
 
It is important to notice that by this definition, it's possible to have negative values of r squared. Which means the predictive model performed worse than a simple average over the original data. Again, the same visual illustration as we increase the noise level, we can see the r squared value also decreases.