Evaluation of Calibration Equations by Using Regression Analysis: An Example of Chemical Analysis

Area of Science:

• Analytical Chemistry
• Instrumental Analysis

Background:

• Calibration curves are essential for quantifying analytes using instrumental methods.
• Traditional linear and polynomial equations often fail to accurately represent complex instrument responses.
• Accurate calibration equations are critical for ensuring reliable instrument performance.

Purpose of the Study:

• To evaluate the performance of various calibration equation types for chemical analysis.
• To identify the most suitable calibration models for diverse datasets.
• To assess the impact of outliers on calibration accuracy and predictive ability.

Main Methods:

• Comparison of linear, polynomial, exponential, and power calibration equations.
• Application of constant variance tests and residual plots for model assessment.
• Utilizing standard error of the estimate (s) and Prediction Sum of Squares (PRESS) for performance evaluation.
• Investigating the effect of outlier removal on calibration model fitting and prediction.

Main Results:

• Linear and higher-order polynomial equations showed limitations in accurately fitting many datasets.
• Nonlinear equations, including exponential and power models, demonstrated superior suitability for most datasets.
• Logarithmic transformation of response data effectively stabilized non-constant variance.
• Outlier removal substantially enhanced both the fit and prediction capabilities of calibration equations.

Conclusions:

• Nonlinear calibration equations are generally more appropriate than linear models for chemical instrument analysis.
• Data preprocessing, including outlier identification and removal, is crucial for improving calibration accuracy.
• The choice of calibration equation is dataset-dependent; no universal model exists.
• The proposed methodology can be adapted to optimize calibration for various chemical instruments.