Abstract
Vdgraph: A Package for Creating Variance Dispersion Graphs
Highlights
Response surface methods consist of (1) experimental designs for collecting data to fit an approximate relationship between the factors and the response, (2) regression analyses for fitting the model and (3) graphical and numerical techniques for examining the fitted model to identify the optimum
The model normally used in response surface analysis is a second order polynomial, as shown in Equation (1)
The fitted equation is examined in order to predict the factor coordinates of the maximum or minimum response within the experimental region, or to explore the relationship between the factors and response
Summary
Response surface methods consist of (1) experimental designs for collecting data to fit an approximate relationship between the factors and the response, (2) regression analyses for fitting the model and (3) graphical and numerical techniques for examining the fitted model to identify the optimum. The fitted equation is examined in order to predict the factor coordinates of the maximum or minimum response within the experimental region, or to explore the relationship between the factors and response. Since it is not known in advance what neighborhood will be of most interest in the design space, a desirable response surface design will be one that makes the variance of a predicted value as uniform as possible throughout the experimental region. For the face-centered cube design, or 32 design shown, Figure 1 is a contour plot of the scaled variance of a predicted value in the range of −1.5 ≤ x1 ≤ 1.5, −1.5 ≤ x2 ≤ 1.5. The scaled variance of a predicted value is NVar[y(x)]/σ2, where N is the number of points in the experimental design
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