The growing use of machine learning in healthcare requires careful consideration of patient privacy, particularly when models are trained on small medical datasets where the risk of re-identification is heightened. This study analyzes how regression models operate under privacy-preserving constraints and assesses their susceptibility to privacy leakage. A stability-based membership-inference framework quantifies how much model outputs reveal about individual training samples. Noise-injection techniques are applied to reduce this risk, and their effects on privacy and predictive accuracy are evaluated. Experiments on a small real-world medical dataset show a trade-off between model utility and privacy, identifying conditions in which regression models remain reliable while limiting exposure to membership-inference attacks.