This paper presents the first study in a series of proxemics experiments concerned with the role of personal spatial zones in human-robot interaction. In the study 40 participants approached a NAO robot positioned approximately at participants' eye level and entered different social zones around the robot (personal and intimate space). When the robot perceived the approaching person entering its personal space, it started gazing at the participant, and upon the intrusion of its intimate space it leaned back. Our research questions were: (1) given the small size of the robot (58 cm tall), will people expect its social zones to shrink by its size? (2) Will the robot behaviors be interpreted as appropriate social behaviors? We found that the average approach distance of the participants was 48 cm, which represents the inner limit of the human-size personal zone (45-120 cm), but is outside of the personal zone scaled to robot size (16-42 cm). This suggests that most participants did not (fully) scale down the extent of these zones to the robot size. We also found that the leaning back behavior of the robot was correctly interpreted by most participants as the robot's reaction to the intrusion of its personal space; however, our implementation of the behavior was often perceived as "unfriendly". We will discuss this and other limitations of the study in detail. Additionally we found positive correlations between participants' personality traits, Godspeed Questionnaire subscales, and the average approach distance. The technical contribution of this work is the real-time perception of 25 keypoints on the human body using a single compact RGB-D camera and the use of these points for accurate interpersonal distance estimation and as gazing targets for the robot.