Calibration Curve and Linearity: Online Regression Analysis
What is a Calibration Curve?
A calibration curve establishes the quantitative relationship between an instrument response (peak area, absorbance) and concentration, and is the foundation of chromatographic, spectroscopic and electrochemical quantitation. The tool fits y = a + bx by least squares and reports the regression equation, slope, intercept, correlation coefficient R² and regression standard deviation, judging how linear the method is across its concentration range. Curve quality directly drives the accuracy of quantitative results, so it is a routine focus of method validation and QC.
When to Use It
Use it during method validation and routine quality control of quantitative methods, when checking linear range against industry criteria (commonly R ≥ 0.995 or R² ≥ 0.99), after instrument changes that require recalibration, and when auditing whether standard-point accuracy still meets requirements such as 85–115% back-calculated recovery.
How to Use It (Step by Step)
Enter the standard concentrations and responses, and the tool fits the regression, outputs the equation, R², slope and intercept, draws the residual plot, and calculates each standard point's back-calculated concentration and relative deviation. Points with large standardized residuals are flagged: confirm the cause (preparation error, injection problem, drift), remove confirmed bad points, refit, and re-verify the linear range — but never delete points repeatedly just to force linearity.
Key Formulas / Example
Least squares: b = Σ(xᵢ−x̄)(yᵢ−ȳ)/Σ(xᵢ−x̄)², a = ȳ − b·x̄, and R² = 1 − SS_res/SS_tot. Keep at least 5–6 concentration points spanning the sample range, and accept back-calculated accuracy within, for example, 85–115% when defining the linear range.