The criterion used to select the "best" model may be visualized by showing the surface of the sum of squared errors ${\displaystyle SSE\,\!}$  of each data with respect to its corresponding model approximation. The surface height varies with varying the parameters value ${\displaystyle \theta _{i},\cdots \theta _{j}}$. Where the surface reaches the minimum, the corresponding parameters identify the best model in the sense of least squares.

In the non-linear case, that selection may be more difficult due to the fact that the surface may have multiple local minima. Without exploring the whole surface, there may be no certainty to have reached the global minimum.

The surface shown in the diagram has been translated so that

${\displaystyle \operatorname {mean} (SSE)\equiv \int \limits _{\theta _{i},\theta _{j}}SSE(\theta _{i},\theta _{j})\,d\theta _{i}\,d\theta _{j}\quad {\overset {\underset {\mathrm {def} }{}}{=}}\quad 0}$

${\displaystyle \theta _{i},\theta _{j}\,\!}$