Statistics Toolbox

The polytool Demo

The polytool demo is an interactive graphic environment for polynomial curve fitting and prediction.

The polytool demo has the following features:

• A graph of the data, the fitted polynomial, and global confidence bounds on a new predicted value.
• y-axis text to display the predicted y-value and its uncertainty at the current x-value.
• A data entry box to change the degree of the polynomial fit.
• A data entry box to evaluate the polynomial at a specific x-value.
• A draggable vertical reference line to do interactive evaluation of the polynomial at varying x-values.
• Bounds and Method menus to control the confidence bounds and choose between least squares or robust fitting.
• A Close button to end the demonstration.
• An Export list box to store fit results into variables.

You can use polytool to do curve fitting and prediction for any set of x-y data, but, for the sake of demonstration, the Statistics Toolbox provides a data set (polydata.mat) to teach some basic concepts.

To start the demonstration, you must first load the data set.

• load polydata
  who
  Your variables are:
  x         x1        y         y1      
  

The variables x and y are observations made with error from a cubic polynomial. The variables x1 and y1 are data points from the "true" function without error.

If you do not specify the degree of the polynomial, polytool does a linear fit to the data.

• polytool(x,y)
  
  
  

The linear fit is not very good. The bulk of the data with x-values between zero and two has a steeper slope than the fitted line. The two points to the right are dragging down the estimate of the slope.

In the Degree box at the top, type 3 for a cubic model. Then, drag the vertical reference line to the x-value of 2 (or type 2 in the X Values text box).

This graph shows a much better fit to the data. The confidence bounds are closer together indicating that there is less uncertainty in prediction. The data at both ends of the plot tracks the fitted curve.

The following sections explore additional aspects of the tool:

• Confidence Bounds
• Overfitting

The disttool Demo

Confidence Bounds