 A similar example is presented in  Figure 4,  adapted from Kievit, Frankenhuis, Waldorp, and Borsboom (2013). The figure shows the results of coffee intake on performance at an IQ test. Suppose that coffee actually decreases performance slightly because it makes drinkers more nervous and less focused. At the same time, coffee intake co-varies with education level (construction workers are too busy for drinking coffee all the time!) and education level co-varies with test performance. When we measure performance repeatedly for different individuals, we see that their performance is slightly negatively affected by their coffee intake. However, the (unconditional) regression model of performance as a function of coffee intake suggests misleadingly that coffee consumption strongly improves performance! The reason for the confounding is the causal impact of the hidden covariate, education level, on both coffee consumption and performance. Similar to the results from  section 2,  Simpson’s Paradox in linear models can be characterized formally by means of inequalities among regression coefficients (e.g., Pearl 2013), and its occurrence depends on the nature of the causal interaction between the involved variables.