Correlations of the simulated data. Top: result of the partial regression analysis on a synthetic data set with 332 sources together with normally distributed scatter, which was chosen to be similar to the measured values. There is no correlation, as expected. Bottom: method used by Telleschi et al. (2007) and Bustamante et al. (2016) applied to the same data set. The values scatter around a line with a slope of − d∕b and not around a constant, as assumed by Telleschi et al. (2007). The reason is a common response variable, s_y, introduced as an artifact of the analysis method as described in Sect. 3.2.