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;
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
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
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 p-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
.