Breast cancer remains one of the leading causes of cancer-related mortality among women worldwide. Early and accurate differentiation between benign and malignant tumors is critical for improving patient outcomes. This paper presents a complete machine-learning pipeline for binary classification of breast masses using the Wisconsin Breast Cancer Diagnostic (WBCD) dataset. Features describing cell nuclei morphology (mean, standard error, and worst values of radius, texture, perimeter, area, smoothness, compactness, concavity, concave points, symmetry, and fractal dimension) are extracted from digitized fine-needle aspirate (FNA) images. After rigorous preprocessing that includes standardization and exploratory correlation analysis, a logistic regression classifier is trained. The model achieves 94.73% accuracy on the training set and 92.11% accuracy on an independent 20% hold-out test set, together with balanced precision, recall, and F1-score. Comprehensive mathematical formulations of the sigmoid hypothesis, binary cross-entropy loss, gradient-based parameter estimation, and standard evaluation metrics are provided. Comparative experiments against support-vector machines, random forests, and k-nearest neighbors confirm that logistic regression offers an attractive trade-off between predictive performance, interpretability, and computational efficiency. Feature-importance analysis highlights mean concave points, worst radius, and worst perimeter as the most discriminative attributes. The proposed framework is fully reproducible, clinically interpretable, and suitable for integration into computer-aided diagnosis systems.