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This white paper delves into the critical role of residuals analysis in validating linear regression models for analytical method validation under GMP. It elucidates how residuals—differences between observed and predicted values—serve as diagnostics for model adequacy, uncovering hidden systematic biases or curvature unaccounted for by linear models. Through detailed examples and figures, it illustrates truly random versus quadratically biased residuals, emphasizing their implications for linearity assessment. The paper introduces studentized residuals, standardized by leverage, to identify influential data points and potential outliers robustly. It further presents quadratic fitting of residuals as a formal tool to evaluate systematic deviation, with practical acceptance criteria based on confidence intervals. Statistical significance evaluation via p-values ensures scientific rigor in decision-making. This comprehensive guide empowers analysts to confirm model validity, refine calibration ranges, and fulfill regulatory expectations for method accuracy, precision, and reliability—fortifying the analytical foundations that underpin pharmaceutical product quality and patient safety.
This white paper delves into the critical role of residuals analysis in validating linear regression models for analytical method validation under GMP. It elucidates how residuals—differences between observed and predicted values—serve as diagnostics for model adequacy, uncovering hidden systematic biases or curvature unaccounted for by linear models. Through detailed examples and figures, it illustrates truly random versus quadratically biased residuals, emphasizing their implications for linearity assessment. The paper introduces studentized residuals, standardized by leverage, to identify influential data points and potential outliers robustly. It further presents quadratic fitting of residuals as a formal tool to evaluate systematic deviation, with practical acceptance criteria based on confidence intervals. Statistical significance evaluation via p-values ensures scientific rigor in decision-making. This comprehensive guide empowers analysts to confirm model validity, refine calibration ranges, and fulfill regulatory expectations for method accuracy, precision, and reliability—fortifying the analytical foundations that underpin pharmaceutical product quality and patient safety.