This paper evaluates the influence of crude oil (vacuum residue) properties, the processing of fluid catalytic cracking slurry oil, and recycle of hydrocracked vacuum residue diluted with fluid catalytic cracking heavy cycle oil, and the operating conditions of the H-Oil vacuum residue hydrocracking on the quality of the H-Oil liquid products. 36 cases of operation of a commercial H-Oil® ebullated bed hydrocracker were studied at different feed composition, and different operating conditions. Intercriteria analysis was employed to define the statistically meaningful relations between 135 parameters including operating conditions, feed and products characteristics. Correlations and regression equations which related the H-Oil® mixed feed quality and the operating conditions (reaction temperature, and reaction time (throughput)) to the liquid H-Oil® products quality were developed. The developed equations can be used to find the optimal performance of the whole refinery considering that the H-Oil liquid products are part of the feed for the units: fluid catalytic cracking, hydrotreating, road pavement bitumen, and blending.