Linearity validation study

ICH Q2(R2) treats linearity as a demonstration, not an assumption: the response must be shown to be proportional to analyte concentration across the range the method claims. The guideline recommends a minimum of five concentration levels spanning that range, and asks for the regression line itself to be reported — slope, y-intercept and the coefficient of determination — together with a plot of the data and an evaluation of the residuals.

This tool fits an ordinary least-squares line to the mean response at each level, with every individual replicate shown on the plot so the within-level spread stays visible. The residual plot is the diagnostic that r² is not: a run of residual signs like + + − − + means the response is curved and the straight line under-reads through the middle of the range, however good r² looks. The detection and quantitation limits come from the same curve, by the two σ routes the guideline offers for calibration data — the standard error of the y-intercept and the residual standard deviation — at the fixed factors 3.3σ/S and 10σ/S.

The guideline requires linearity to be reported; the numeric acceptance limit belongs to the study protocol. The verdicts here use the conventional assay defaults — r² of at least 0.99, and detection and quantitation limits reported by at least one σ route — judged with inclusive bounds, so a study that lands exactly on its limit meets it. In the full validation suite these criteria are per study: a lab working in a difficult matrix sets its own limits, and the report records the limits it was judged against.

Every number on this page is traceable. The back-calculated concentration table shows what the fitted curve says each standard was, statistics are displayed at your chosen significant figures while every calculation runs at full precision, and the exported JSON is byte-stable — the same record always serialises to the same bytes, so two exports can be diffed or hashed.

This page opens the AssayProof study workbench on its linearity tab. A study can also carry an accuracy section and a repeatability section, and a detection-limit section for LOD and LOQ that came from somewhere other than this curve — switch tabs inside the workbench to add them to this same study, or reopen a saved study's ?study= link to come back to it. Following the links above starts a new study instead. One record, one append-only audit trail, and one PDF report with an overall verdict across every criterion. The statistics engine is the same one behind the free calculators, validated against NIST certified reference datasets.