Context. Current exoplanet surveys are focused on detecting small exoplanets orbiting in the liquid-water habitable zones of their host stars. Despite recent significant advancements in instrumentation, the main limitation in detecting these exoplanets is the intrinsic variability of the host star itself. Aims. Our aim is to investigate the wavelength dependence of high-precision radial velocities (RV), as stellar activity induced RVs should exhibit a wavelength dependence while the RV variation due to an orbiting planet will be wavelength independent. Methods. We used the chromatic index (CRX) to quantify the slope of the measured RVs as a function of logarithmic wavelength of the full CARMENES guaranteed time observations (GTO) data set spanning more than eight years of observations of over 350 stars. We investigated the dependence of the CRX in the full Carmenes GTO sample on 24 stellar activity indices in the visible and near-infrared channels of the CARMENES spectrograph and each star's stellar parameters. We also present an updated convective turnover time scaling for the calculation of the stellar Rossby number for M dwarfs. Results. Our results show that approximately 17% of GTO stars show a strong or a moderate correlation between the CRX and RV. We can improve the measured RVs by a factor of up to nearly 4 in terms of the root mean square (rms) by subtracting the RV predicted by the CRX-RV correlation from the measured RVs. Mid-M dwarfs with moderate rotational velocities and moderate CRX-gradients, with quasi-stable activity features, have the best rms improvement factors. Conclusions. We conclude that the CRX is a powerful diagnostic in mitigation of stellar activity and the search for low mass rocky planets.