The CORR procedure in SAS calculates several types of correlation between variables: - Pearson product-moment correlation for linear relationships - Rank correlations including Spearman and Kendall's tau-b - Hoeffding's measure of dependence - Partial correlations can also be calculated to assess the relationship between two variables while controlling for other variables. The procedure syntax allows specification of variables, frequency and ID variables, use of weights, and generation of correlation and scatter plots. Examples demonstrate its use for correlation and partial correlation analysis of datasets.

1. CORR procedure
2013/3/6

2. The CORR procedure gives you
• Pearson product-moment correlation
• Rank correlation:
• Spearman rank-order correlation
• Kendall’s tau-b coefficient
• Hoeffding’s measure of dependence, D
• Partial correlations for Pearson, Spearman, and Kendall’s
measurement

3. Syntax
PROC CORR <options> ;
BY variables ;
FREQ variable ;
指定計算淨相
關時的control ID variables ;
variable
PARTIAL variables ;
VAR variables ;
WEIGHT variable ;
WITH variables ;
RUN; proc corr;
var x1 x2;
with y1 y2 y3;
run;

4. Example 1
data example1;
do i=1 to 200;
x=10*rannor(100);
y=x+10*rannor(3);
output;
end;
drop i;
;
proc corr plots=scatter spearman;
run;

5. Example 2 (SAS 9.2 guide)
不指定var
Without control
data Fitness;
input Age Weight Oxygen RunTime @@;
datalines;
44 89.47 44.609 11.37
…
;
proc corr data=Fitness plots=matrix(histogram); With control
var RunTime Weight;
partial Oxygen Age;
run;

6. Questions ?

7. Why correlation?

8. Pearson’s r (for linear correlation)
Var X

9. Correlation does not “imply” causation
• Tufte:
• "Empirically observed covariation is a necessary but not sufficient condition for
causality."
• "Correlation is not causation but it sure is a hint."
• If Y and X correlate significantly, then one of the following may be true:
• X causes Y
• Y causes X
• X and Y are consequences of a common cause other than X or Y
• Just coincidence
• What does “cause” mean actually?
• It is a philosophical question