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Example 5.1 Computing the Pearson Measure of Association in Single-Machine Mode

The `Fitness`

data set created in the section Getting Started: HPCORR Procedure contains measurements from a study of physical fitness of 31 participants. The following statements request the Pearson measure
of association for the variables `Weight`

, `Oxygen`

, and `Runtime`

:

title 'Measures of Association for a Physical Fitness Study';
proc hpcorr data=Fitness pearson;
var Weight Oxygen RunTime;
run;

The "Simple Statistics" table in Output 5.1.1 displays univariate descriptive statistics for the analysis variables. By default, observations that have nonmissing values
for each variable are used to derive the univariate statistics for that variable.

Output 5.1.1: Simple Statistics

31 |
77.44452 |
8.32857 |
2401 |
59.08000 |
91.63000 |

29 |
47.22721 |
5.47718 |
1370 |
37.38800 |
60.05500 |

29 |
10.67414 |
1.39194 |
309.55000 |
8.17000 |
14.03000 |

The "Pearson Correlation Coefficients" table in Output 5.1.2 displays the Pearson correlation statistics for pairs of analysis variables. The Pearson correlation is a parametric measure
of association for two continuous random variables. When the data have missing values, the number of observations used to
calculate the correlation can vary.

Output 5.1.2: Pearson Correlation Coefficients

The table shows that the Pearson correlation between `Runtime`

and `Oxygen`

is 0.86843, which is significant with a p-value less than 0.0001. This indicates a strong negative linear relationship between these two variables. As `Runtime`

increases, `Oxygen`

decreases linearly.