The relationship between the user perceived Quality of Experience (QoE) with Internet applications and the Quality of Service (QoS) of the underlying network and applications is complex. Unveiling statistical relations between QoE and QoS can boost the prediction and diagnosis of QoE. In this paper, we shed light on the relationship between QoE and QoS for a popular application: YouTube video streaming. We conducted a controlled study where we asked users to rate their perceived quality of YouTube videos under different network conditions. During this experiments, we also captured network QoS and application QoS. We then analyze the resulting dataset with SES, a feature selection algorithm that identifies minimal-size, statistically-equivalent signatures with maximal predictive power for a target variable (e.g., QoE). We found that we can build optimal QoE predictors using a minimal signature of only three features from application or network QoS metrics compared to four when we consider features from both layers.