Semi-partial correlation

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In multiple linear regression, semi-partial correlations indicate the unique relation between a predictor (IV) and a response variable (DV).

What do the areas mean?[edit]

This is a Venn diagram representing the variance and correlations involved in a multiple linear regression analysis.

Question 1: Which areas represent the squared semi-partial correlations between the IVs and DV?
Question 2: What do the other labelled areas represent?

Partial correlation.svg

Answer 1: a and c
Answer 2:

  • a = squared semi-partial correlation between IV1 and DV (with the effect of IV2 removed)
  • b = variance in the DV which is explained by both IV1 and IV2
  • c = squared semi-partial correlation between IV2 and DV (with the effect of IV1 removed)
  • d = variance in DV which is not explained by IV1 and IV2

See also[edit]