Figure 2. Comparison of the statistical power to detect coreferentiality, dependency in multiple regression, and classic correlation.

The power of each method was tested in 100 respectively simulated data sets, all with a sample size of 200 and different reference data dependency degrees δ. Multiple regression was tested for a given test variable X in dependency on the scores of either 10 or 50 PCA factors derived from the 130 reference variables. Bivariate correlation was tested for simulations with X₂ depending on X₁ with the degree δ, and tested by simple linear regression.