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Generate confidence ellipses for bivariate normal data

PURPOSE:

The %CONELIP macro generates confidence ellipses for bivariate normal data. It can either create ellipses for the data or ellipses about the mean.

REQUIREMENTS:

The %CONELIP macro requires Version 6.06 or later of Base SAS software and SAS/GRAPH.

USAGE:

Follow the instructions in the Downloads tab of this sample to save the %CONELIP macro definition. Replace the text within quotes in the following statement with the location of the %CONELIP macro definition file on your system. In your SAS program or in the SAS editor window, specify this statement to define the %CONELIP macro and make it available for use:

   %inc "<location of your file containing the CONELIP macro>";

Following this statement, you may call the %CONELIP macro. See the Results tab for an example.

The macro parameters are described below:

DATA=

SAS data set that contains the variables that you want to generate the ellipses for.

X1=

Variable 1 of interest. This variable will be plotted on the horizontal axis.

X2=

Variable 2 of interest. This variable will be plotted on the vertical axis.

MEAN=YES | NO

Tells the macro if you want the confidence ellipse on the mean (YES) or not (NO).

CONF=

Tells the macro at what alpha level you want the ellipse to be computed.

LIMITATIONS:

No error checking is done. The macro assumes that dataset names and variable names entered are valid. The user must also specify the MEAN= and CONF= options.

EXAMPLE:

This data is from Applied Multivariate Statistical Analysis, Third Edition by Johnson and Wichern, pp. 189-191.

      data a;
      input x y id;
      cards;
      .62233    0.74008     1
      .54772    0.54772     1
      .65136    0.74008     1
      .56234    0.56234     1
      .47287    0.56234     1
      .58857    0.58857     1
      .53183    0.54772     1
      .47287    0.56234     1
      .53183    0.54772     1
      .56234    0.56234     1
      .51437    0.51437     1
      .37606    0.47287     1
      .31623    0.31623     1
      .56234    0.81904     1
      .56234    0.58857     1
      .56234    0.66874     1
      .37606    0.44721     1
      .56234    0.56234     1
      .31623    0.31623     1
      .79527    0.88011     1
      .56234    0.58857     1
      .47287    0.56234     1
      .41618    0.47287     1
      .47287    0.47287     1
      .62233    0.62233     1
      .56234    0.74008     1
      .62233    0.62233     1
      .54772    0.54772     1
      .53183    0.54772     1
      .65136    0.72743     1
      .56234    0.56234     1
      .66874    0.56234     1
      .57590    0.56234     1
      .74008    0.74008     1
      .37606    0.58857     1
      .66874    0.70711     1
      .66874    0.66874     1
      .74008    0.79527     1
      .74008    0.75793     1
      .79527    0.75212     1
      .74008    0.58857     1
      .47287    0.58857     1
      ;

      /* Define the CONELIP macro */
      %inc "<location of your file containing the CONELIP macro>";
      
      *95% Conf Ellipse about the mean vector;
      %conelip(data=a, x1=x, x2=y, mean=yes,conf=.95)

      *95% Conf Ellipse about the data;
      %conelip(data=a, x1=x, x2=y, mean=no, conf=.95)

RESULTS:

The above statements produce a confidence ellipse for the mean and a confidence ellipse for the data.

Right-click on the link below and select Save to save the %CONELIP macro definition to a file. It is recommended that you name the file conelip.sas.

Download and save conelip.sas

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