Statistics Toolbox

Exploring Graphs of Multidimensional Polynomials

The function rstool performs an interactive fit and plot of a multidimensional response surface (RSM). Note that, in general, 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)
  

rstool displays 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, and is marked by a vertical dashed blue line. 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 your monitor for large numbers of inputs or outputs.

Exporting Variables to the Workspace

Click Export to save variables in the GUI to the base workspace.

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Fitted parameters, i.e., coefficients, appear in the following order. Some polynomial models use a subset of these terms but keep them in this order.

1. Constant term
2. Linear terms
3. Interaction terms formed by taking pairwise products of the columns of the input matrix
4. Squared terms

Changing the Order of the Polynomial

Below the Export button, there is a pop-up menu that enables you to change the polynomial model. If you use the commands above, this menu has the string Full Quadratic already selected. The choices are:

• Linear - includes constant and linear terms.
• Pure Quadratic - includes constant, linear and squared terms.
• Interactions - includes constant, linear, and cross product terms.
• Full Quadratic - includes interactions and squared terms.
• User Specified - available only if you provide a matrix of model terms as the third argument to rstool. See the rstool and x2fx function reference pages for details.)

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

Quadratic Response Surface Models

Stepwise Regression