Figure 2.7 shows homoscedastic noise, noise that is constant everywhere across the factor domain. In the upper graph, the smooth underlying response surface can be imagined with uniform noise superimposed. Figure 2.7 Graphs showing a homoscedastic response surface. In the upper graph, the smooth underlying response surface can be imagined beneath the varying amount of noise. Figure 2.8 Graphs showing a heteroscedastic response surface.
Most real systems exhibit heteroscedastic noise when viewed over a large factor domain.
One reason for this was considered in the discussion of Figures 1.5 and 1.6. For a given amount of variation in a factor x , the steepness of the response surface determines the amount of noise transformed into the response y . In the region of an optimum, the slope of the response surface is close to zero, so random fluctuations in the factor induce very little noise in the response. When viewed over a smaller factor domain, many real systems appear to exhibit homoscedastic noise. Most statistical procedures assume homoscedastic noise structures.