"the bigger RegSS, the better the estimated model performs" are we sure? Wikipedia here says "the bigger ESS (or RegSS, SSR, etc), the better the estimated model performs". Surely this is wrong. ESS is the sum of the squared distances between the fitted values and the sample mean. $$ESS = \sum (\hat{y}_i-\bar{y})^2$$Surely the smaller ESS is, the closer the fitted values are to the sample mean, which is a good sign! On the other hand, if we have a large ESS, it means that the fitted values are very distant from the sample mean, which is bad. > Is Wikipedia wrong or is there a flaw in my reasoning? **EDIT** Here I want to know: if I am given some data $(x_i,y_i)$ and I want to model them using a linear model and I calculate $RegSS$..... should I think my model is good when $RegSS$ is large or small?

Suppose your linear model predicted $\hat{y_i} = \overline{y}$ for each sample point $x_i$. Then the ESS would be zero, but the linear model would be a terrible fit! (unless the actual underlying distribution was actually a point mass which is unlikely).

Basically, the goal in simple linear regression is to draw the line through the points that minimizes RSS, or, in other words, maximizes ESS. So your model is "good" when you have a small RSS, or RegSS.