PSYC 316 Lecture Notes - Lecture 8: Homoscedasticity, General Linear Model, Tikhonov Regularization
10 May 2016
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Imagine a situation with 3 variables: a partial correlation is a correlation between variable 1 and 2, with variable 3 being held constant (or controlled for or partialed out ): i. Thus, the influence of x3 is removed from both x1 and x2: What is the linear relationship between x1 and x2 independent of the linear influence of x3: formula (with 3 variables): a) r12. 3 = : i. ii. Notice that xs are not shown for simplicity. The dot indicates variables preceding it are correlated and the variable following it is partialed out. b) In the example, the relationship between height and weight isn"t as strong after you control for age. Imagine some extremes: both r13 and r23 equal zero, then r12 = r12. 3: i. If the variable partialled out is not correlated with the other two, the partialling out process will not have any effect. b) If r13 or r23 equals one, r12. 3 cannot be defined:
