Statistics Toolbox

Exploring Graphs of Multidimensional Polynomials

The function rstool is useful for fitting response surface models. The purpose of rstool is larger than just fitting and prediction for polynomial models. This GUI provides an environment for exploration of the graph of a multidimensional polynomial.

You can learn about rstool by trying the commands below. The chemistry behind the data in reaction.mat deals with reaction kinetics as a function of the partial pressure of three chemical reactants: hydrogen, n-pentane, and isopentane.

• load reaction
  rstool(reactants,rate,'quadratic',0.01,xn,yn)
  

You will see a "vector" of three plots. The dependent variable of all three plots is the reaction rate. The first plot has hydrogen as the independent variable. The second and third plots have n-pentane and isopentane respectively.

Each plot shows the fitted relationship of the reaction rate to the independent variable at a fixed value of the other two independent variables. The fixed value of each independent variable is in an editable text box below each axis. You can change the fixed value of any independent variable by either typing a new value in the box or by dragging any of the three vertical lines to a new position.

When you change the value of an independent variable, all the plots update to show the current picture at the new point in the space of the independent variables.

Note that while this example only uses three inputs (reactants) and one output (rate), rstool can accommodate an arbitrary number of inputs and outputs. Interpretability may be limited by the size of the monitor for large numbers of inputs or outputs.

The GUI also has two pop-up menus. The Export menu facilitates saving various important variables in the GUI to the base workspace. Below the Export menu there is another menu that allows you to change the order of the polynomial model from within the GUI. If you used the commands above, this menu will have the string Full Quadratic. Other choices are:

• Linear - has the constant and first order terms only.
• Pure Quadratic - includes constant, linear and squared terms.
• Interactions - includes constant, linear, and cross product terms.

The rstool GUI is used by the rsmdemo function to visualize the results of a designed experiment for studying a chemical reaction. See The rsmdemo Demo.

Quadratic Response Surface Models

Stepwise Regression