Let's start again but use design of experiments this time. With an experimental design, you plan a set of experiments where all the factors are varied in a systematic and balanced manner. In a simple factorial design, for example, each factor is ascribed a low and a high level and you carry out all combinations of all factors at the two levels. Hence, two factors describe a square array of experiments, three describe a cube and four or more a hypercube.
As before, the experiments are marked on the contour plot (red dots). This time, the design allows the effects of the two factors and their interaction to be calculated using a multiple regression model, making part of the map visible.