A partial correlation measures the strength of the linear relationship between two variables, while adjusting for the effect of other variables.
The following statements request a partial correlation analysis of variables Height
and Width
while adjusting for the variables Length3
and Weight
. The latter variables, which are said to be “partialled out” of the analysis, are specified with the PARTIAL statement.
ods graphics on; title 'Fish Measurement Data'; proc corr data=fish1 plots=scatter(alpha=.20 .30); var Height Width; partial Length3 Weight3; run; ods graphics off;
Output 2.9.1 displays descriptive statistics for all the variables. The partial variance and partial standard deviation for the variables in the VAR statement are also displayed.
Output 2.9.1: Descriptive Statistics
Fish Measurement Data 
2 Partial Variables:  Length3 Weight3 

2 Variables:  Height Width 
Simple Statistics  

Variable  N  Mean  Std Dev  Sum  Minimum  Maximum  Partial Variance 
Partial Std Dev 
Length3  34  38.38529  4.21628  1305  30.00000  46.50000  
Weight3  34  8.44751  0.97574  287.21524  6.23168  10.00000  
Height  34  15.22057  1.98159  517.49950  11.52000  18.95700  0.26607  0.51582 
Width  34  5.43805  0.72967  184.89370  4.02000  6.74970  0.07315  0.27047 
When you specify a PARTIAL statement, observations with missing values are excluded from the analysis. Output 2.9.2 displays partial correlations for the variables in the VAR statement.
Output 2.9.2: Pearson Partial Correlation Coefficients
Pearson Partial Correlation Coefficients, N = 34 Prob > r under H0: Partial Rho=0 


Height  Width  
Height 



Width 


The partial correlation between the variables Height
and Width
is 0.25692, which is much less than the unpartialled correlation, 0.92632 (in Output 2.9.2). The value for the partial correlation is 0.1558.
The PLOTS=SCATTER option displays (in Output 2.9.3) a scatter plot of the residuals for the variables Height
and Width
after controlling for the effect of variables Length3
and Weight
. The ALPHA=.20 .30 suboption requests and prediction ellipses, respectively.
Output 2.9.3: Partial Residual Scatter Plot
In Output 2.9.3, a standard deviation of Height
has roughly the same length on the X axis as a standard deviation of Width
on the Y axis. The major axis length is not significantly larger than the minor axis length, indicating a weak partial correlation
between Height
and Width
.