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tokens: with the predictions of Reiners et al. (2010) and Barnes et al. (2011) . Their simulations suggest that the large scatter around the std(RV)– v sin i correlation seen in the left panel of Fig. 3 could be caused by the spot characteristics of the active stars, such as their spot coverage fraction, and their spot-to-photosphere temperature contrast. We also recall that an additional source of scatter could be true orbital motions of these stars due to their as yet undiscovered planetary systems. 5.2 Correlations of RVs with spectral activity indicators After searching for correlations between std(RV) and activity-related stellar parameters of the active RV-loud sample as a whole, we moved on to investigate individual stars of the sample for correlations between their stellar activity indicators and their measured RVs. Finding a parametric function that could translate measurable spectral activity indicators into RV deviations is a great challenge, but at the same time, it holds the promise to enable the modeling of RV time series with a combined model of planetary- and activity-induced signals. Moreover, such a function would obviate simultaneous auxiliary measurements to quantify activity-induced RVs, such as multi-band photometric observations. Unfortunately, no such a function has been proposed so far for M dwarfs. Lacking a physical model to guide our spectral data exploration, we searched our active RV-loud stars for linear correlations between their varying RVs and three ofthe spectral activity indicators that we have chosen to investigate in this paper: CRX, dLW, and log L H α ∕ L bol . To best illustrate the process, we show here a few representative plots for one of the most frequently observed stars in our sample: J22468+443 (EV Lac). In order to demonstrate the CRX definition, we show in the top panel of Fig. 4 the order-by-order RVs from four representative observations of EV Lac: three observations with close-to-median H α emission but different CRX values, and one observation with extremely high H α emission. The latter observation was taken during a strong flare event ( Fuhrmeister et al. 2018 ). The slopes of the best-fit lines to these RV–order scatter plots are related to the CRX values of these four observations ( Zechmeister et al. 2018 ). The locations of activity-induced emission lines are marked at the top panel of Fig. 4 . The bottom panel of Fig. 4 shows the corresponding CARMENES spectra from these four observations, centered on the H α line. Fig. 4 CARMENES VIS measurements of J22468+443 (EV Lac). Top : Order-by-order RVs from four representative observations. Red, green, and blue show three observations with close-to-median H α emission. Black plots an observation with extremely high H α emission, taken during a strong flare event ( Fuhrmeister et al. 2018 ). The corresponding log L H α ∕ L bol values are given in the inset. Dashed lines show the best-fit straight lines to the RV–order scatter plots of each