Contour Line (Isoline)

An isoline connects all points $(x,y)$ in a contour plot that share the same value of the response $z$ — like the contour lines of a map. The contour plot is thus the two-dimensional top view of a response surface.

• Tightly spaced lines — steep gradient: a small change in the factor moves the response a lot
• Widely spaced lines — flat gradient: the factor barely acts in this region
• Closed contours — a local optimum lies inside the displayed region
• Saddle point — lines meet in a cross: no extremum, but a maximum in one direction and a minimum in the other
• Curved rather than parallel lines — a sign of an interaction between the two factors

The lines are usually computed with the marching-squares algorithm over a fine grid of the model equation. Eight to ten levels is a good compromise: fewer swallows fine structure, more clutters the picture.