Social Assistive Robotics is increasingly being used in care settings to provide psychosocial support and interventions for the elderly with cognitive impairments. Most of these social robots have provided timely stimuli to the elderly at home and in care centres, including keeping them active and boosting their mood. However, previous investigations have registered shortcomings in these robots, particularly in their ability to satisfy an essential human need: the need for companionship. Reports show that the elderly tend to lose interests in these social robots after the initial excitement as the novelty wears out and the monotonous familiarity becomes all too familiar. This paper presents our research facilitating conversations between a social humanoid robot, Nadine, and cognitively impaired elderly at a nursing home. We analysed the effectiveness of human-humanoid interactions between our robot and 14 elderly over 29 sessions. We used both objective tools (based on computer vision methods) and subjective tools (based on observational scales) to evaluate the recorded videos. Our findings showed that our subjects engaged positively with Nadine, suggesting that their interaction with the robot could improve their well-being by compensating for some of their emotional, cognitive, and psychosocial deficiencies. We detected emotions associated with cognitively impaired elderly during these interactions. This study could help understand the expectations of the elderly and the current limitations of Social Assistive Robots. Our research is aligned with all the ethical recommendations by the NTU Institutional Review Board.