Statistics Toolbox

Quadratic Response Surface Models

Response Surface Methodology (RSM) is a tool for understanding the quantitative relationship between multiple input variables and one output variable.

Consider one output, z, as a polynomial function of two inputs, x and y. The function z = f(x,y) describes a two-dimensional surface in the space (x,y,z). Of course, you can have as many input variables as you want and the resulting surface becomes a hypersurface. You can have multiple output variables with a separate hypersurface for each one.

For three inputs (x₁, x₂, x₃), the equation of a quadratic response surface is

It is difficult to visualize a k-dimensional surface in k+1 dimensional space for k>2. The function rstool is a graphical user interface (GUI) designed to make this visualization more intuitive, as is discussed in the next section.

Example: Multiple Linear Regression

Exploring Graphs of Multidimensional Polynomials