CORRELATION Procedure

(View the complete code for this example.)

This example creates a data table and then uses PROC CORRELATION to produce Pearson correlations.

The following statements create the mylib.Fitness data table. These data have been altered to contain some missing values:

*----------------- Data on Physical Fitness -----------------*
| These measurements were made on men involved in a physical |
| fitness course at N.C. State University.                   |
| The variables are Age (years), Weight (kg),                |
| Runtime (time to run 1.5 miles in minutes), and            |
| Oxygen (oxygen intake, ml per kg body weight per minute)   |
| Certain values were changed to missing for the analysis.   |
*------------------------------------------------------------*;
data mylib.Fitness;
   input Age Weight Oxygen RunTime @@;
   datalines;
44 89.47 44.609 11.37    40 75.07 45.313 10.07
44 85.84 54.297  8.65    42 68.15 59.571  8.17
38 89.02 49.874   .      47 77.45 44.811 11.63
40 75.98 45.681 11.95    43 81.19 49.091 10.85
44 81.42 39.442 13.08    38 81.87 60.055  8.63
44 73.03 50.541 10.13    45 87.66 37.388 14.03
45 66.45 44.754 11.12    47 79.15 47.273 10.60
54 83.12 51.855 10.33    49 81.42 49.156  8.95
51 69.63 40.836 10.95    51 77.91 46.672 10.00
48 91.63 46.774 10.25    49 73.37   .    10.08
57 73.37 39.407 12.63    54 79.38 46.080 11.17
52 76.32 45.441  9.63    50 70.87 54.625  8.92
51 67.25 45.118 11.08    54 91.63 39.203 12.88
51 73.71 45.790 10.47    57 59.08 50.545  9.93
49 76.32   .      .      48 61.24 47.920 11.50
52 82.78 47.467 10.50
;

These statements assume that your CAS engine libref is named mylib, but you can substitute any appropriately defined CAS engine libref.

The following statements invoke the CORRELATION procedure and request a correlation analysis:

proc correlation data=mylib.Fitness;
run;

The "Simple Statistics" table in Figure 1 displays univariate statistics for the analysis variables.

By default, all numeric variables not listed in other statements are used in the analysis. Observations that have nonmissing values for each variable are used to derive the univariate statistics for that variable.

The "Pearson Correlation Coefficients" table in Figure 2 displays the Pearson correlation, the p-value under the null hypothesis of zero correlation, and the number of nonmissing observations for each pair of variables.

By default, Pearson correlation statistics are computed from observations that have nonmissing values for each pair of analysis variables. Figure 2 displays a correlation of –0.86843 between Runtime and Oxygen, which is significant with a p-value less than 0.0001. That is, an inverse linear relationship exists between these two variables. As Runtime (time in minutes to run 1.5 miles) increases, Oxygen (oxygen intake in milliliters per kilogram body weight per minute) decreases.