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.
Weighted least-squares methods place higher weight on information from regions of low noise and less weight on less certain information from regions of high noise. However, if experimental studies are confined to the region of the optimum, then in many cases the assumption of homoscedastic noise is appropriate, and special statistical techniques are not required. Authors, Frederick H. Walters, Lloyd R. Parker, Jr., Stephen L. Morgan and Stanley N. Deming.