Example of a Partial Correlationmain topic interpreting results session command see also
Example of a Partial CorrelationA survey was conducted in restaurants in 19 Wisconsin counties. Variables measured include: Sales (gross sales), Newcap (new capital invested), and Value (estimated market value of the business). All variables are measured in thousands of dollars.
We want to look at the relationship between sales and new capital invested removing the influence of market value of the business. First we calculate the regular Pearson correlation coefficient for comparison. Then we demonstrate calculating the partial correlation coefficient between sales and new capital.
Step 1: Calculate unadjusted correlation coefficients
1 Open the worksheet RESTRNT.MTW.
2 Choose Stat > Basic Statistics > Correlation.
3 In Variables, enter Sales Newcap Value. Click OK.
The remaining steps calculate partial correlation between Sales and Newcap.
Step 2: Regress Sales on Value and store the residuals (Resi1)
1 Choose Stat > Regression > Regression > Fit Regression Model.
2 In Responses, enter Sales. In Continuous predictors, enter Value.
3 Click Storage, and check Residuals. Click OK in each dialog box.
Step 3: Regress Newcap on Value and store the residuals (Resi2)
1 Choose Stat > Regression > Regression > Fit Regression Model.
2 In Responses, enter Newcap. In Continuous predictors, enter Value.
3 Click OK.
Step 4: Calculate correlations of the residual columns
1 Choose Stat > Basic Statistics > Correlation.
2 In Variables, enter Resi1 Resi2. Click OK.
Session window output
Correlation: Sales, Newcap, Value
Sales Newcap Newcap 0.615 0.000
Value 0.803 0.734 0.000 0.000
Cell Contents: Pearson correlation P-Value |
Session window output
Regression Analysis: Sales versus Value
Regression Analysis: Newcap versus Value
Correlation: RESI1, RESI2
Pearson correlation of RESI1 and RESI2 = 0.078 P-Value = 0.261 |
The correlation between the residual columns is 0.078. In other words, after adjusting for the linear effect of Value, the correlation between Sales and Newcap is 0.078 - a value that is quite different from the uncorrected 0.615 value. In addition, the p-value of 0.261 indicates that there is no evidence that the correlation between Sales and Newcap - after accounting for the Value effect -i s different from zero.
You can repeat this example to obtain the partial correlation coefficients between other variables. The partial correlation between Sales and Value is 0.654; the partial correlation between Newcap and Value is 0.502.