Procedure for Testing Partial Correlation Coefficients

The partial correlation coefficient testing can be accomplished via the standard six-step method. Let us hold Xi constant and measure the contribution of X2, the humidity, as presented in Example 4.1 (Table 4.5 and Table 4.6). 

Step 3 Write out the computation and test statistic in the sum-of-squares format. We are evaluating X2, so the test statistic is 

As noted earlier, the multiple partial coefficient of determination, r, usually is more of interest than the multiple partial correlation coefficient, because of its direct applicability. That is, an = 0.83 explains 83% of the variability. An r = 0.83 cannot be directly interpreted, except the closer to 0 the value is, the smaller the association the closer r is to 1, the greater the association. The coefficient of determination computation is straightforward. From the model, F = /3o + IB Xi + 2 2 + 3X3 + 4X4, suppose that the researcher wants to compute x x, X2 y or the joint contributiOTi of X3 and X4 to the model with Xi and X2 held constant. The form would be 

However, the multiple partial coefficient of determination generally is not as useful as the F-test. If the multiple partial F-test is used to evaluate the multiple contribution of independent predictor values, while holding the others (in this case Xi, X2) constant, the general formula is 

USED TO DETERMINE HOW MANY x, VARIABLES TO INCLUDE IN THE MODEL 

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