Comparative Evaluation of Residual Diagnostic Measures for Outlier Detection in Linear Regression: An Empirical Study Using Heart Rate Data

Reg No: 410

Abstract

Outliers in medical datasets can substantially distort regression models, leading to biased estimates and unreliable clinical inferences. This study evaluated residual-based diagnostic methods-including standardized residuals, Cook's Distance, DFFITS, DFBETAS, Covariance Ratio, and standardized scores-for detecting influential observations in a simple linear regression model. Using age as the predictor and heart rate as the outcome, data from 30 individuals were analyzed. The initial model (R² = 0.22) revealed one highly influential outlier (heart rate = 290 at age 42), consistently identified across multiple diagnostics. Removal of this case improved model adequacy, yielding a more stable regression (R² = 0.10) with no further significant outliers detected. Findings highlight that even a single outlier can markedly distort regression-based conclusions, underscoring the importance of employing complementary diagnostic tools to ensure valid statistical inference in medical research.