The CORR Procedure

Example 2.8 Creating Scatter Plots

The following statements request a correlation analysis and a scatter plot matrix for the variables in the data set Fish1, which was created in Example 2.6.

ods graphics on;
title 'Fish Measurement Data';
proc corr data=fish1 nomiss plots=matrix(histogram);
   var Height Width Length3 Weight3;
run;
ods graphics off;

The “Simple Statistics” table in Output 2.8.1 displays univariate descriptive statistics for analysis variables.

Output 2.8.1: Simple Statistics

Fish Measurement Data

The CORR Procedure

4 Variables:	Height Width Length3 Weight3

Simple Statistics
Variable	N	Mean	Std Dev	Sum	Minimum	Maximum
Height	34	15.22057	1.98159	517.49950	11.52000	18.95700
Width	34	5.43805	0.72967	184.89370	4.02000	6.74970
Length3	34	38.38529	4.21628	1305	30.00000	46.50000
Weight3	34	8.44751	0.97574	287.21524	6.23168	10.00000

The “Pearson Correlation Coefficients” table in Output 2.8.2 displays Pearson correlation statistics for pairs of analysis variables.

Output 2.8.2: Pearson Correlation Coefficients

Height

1.00000

0.92632

<.0001

0.95492

<.0001

0.96261

<.0001

Width

0.92632

<.0001

1.00000

0.92171

<.0001

0.92789

<.0001

Length3

0.95492

<.0001

0.92171

<.0001

1.00000

0.96523

<.0001

Weight3

0.96261

<.0001

0.92789

<.0001

0.96523

<.0001

1.00000

The variables are highly correlated. For example, the correlation between Height and Width is 0.92632.

The PLOTS=MATRIX(HISTOGRAM) option requests a scatter plot matrix for the VAR statement variables in Output 2.8.3.

Output 2.8.3: Scatter Plot Matrix

Note that this graphical display is requested by enabling ODS Graphics and by specifying the PLOTS= option. For more information about ODS Graphics, see Chapter 21: Statistical Graphics Using ODS in SAS/STAT User's Guide.

To explore the correlation between Height and Width, the following statements display (in Output 2.8.4) a scatter plot with prediction ellipses for the two variables:

ods graphics on;
proc corr data=fish1 nomiss
          plots=scatter(nvar=2 alpha=.20 .30);
   var Height Width Length3 Weight3;
run;
ods graphics off;

The PLOTS=SCATTER(NVAR=2) option requests a scatter plot for the first two variables in the VAR list. The ALPHA=.20 .30 suboption requests $80\%$ and $70\%$ prediction ellipses, respectively.

Output 2.8.4: Scatter Plot with Prediction Ellipses

A prediction ellipse is a region for predicting a new observation from the population, assuming bivariate normality. It also approximates a region that contains a specified percentage of the population. The displayed prediction ellipse is centered at the means $(\bar{x},\bar{y})$ . For further details, see the section Confidence and Prediction Ellipses.

Note that the following statements also display (in Output 2.8.5) a scatter plot for Height and Width:

ods graphics on;
proc corr data=fish1
          plots=scatter(alpha=.20 .30);
   var Height Width;
run;
ods graphics off;

Output 2.8.5: Scatter Plot with Prediction Ellipses

Output 2.8.5 includes the point $(13.9,5.1)$ , which was excluded from Output 2.8.4 because the observation had a missing value for Weight3. The prediction ellipses in Output 2.8.5 also reflect the inclusion of this observation.

The following statements display (in Output 2.8.6) a scatter plot with confidence ellipses for the mean:

ods graphics on;
title 'Fish Measurement Data';
proc corr data=fish1 nomiss
          plots=scatter(ellipse=confidence nvar=2 alpha=.05 .01);
   var Height Width Length3 Weight3;
run;
ods graphics off;

The NVAR=2 suboption within the PLOTS= option restricts the number of plots created to the first two variables in the VAR statement, and the ELLIPSE=CONFIDENCE suboption requests confidence ellipses for the mean. The ALPHA=.05 .01 suboption requests $95\%$ and $99\%$ confidence ellipses, respectively.

Output 2.8.6: Scatter Plot with Confidence Ellipses

The confidence ellipse for the mean is centered at the means $(\bar{x},\bar{y})$ . For further details, see the section Confidence and Prediction Ellipses.