Calibration Curve
Data Entry
Each row is one standard measurement; enter replicates as separate rows with the same concentration. At least three (preferably five) distinct levels are required.
Unknown samples (optional)
Enter the measured response; the concentration is obtained from the curve by inverse prediction. If the replicate count (m) is empty, 1 is assumed; if the response is the mean of several measurements, enter m and the confidence interval narrows.

What it does

Fits a straight line (response = a + S·concentration) to calibration standards by ordinary least squares, reports the slope and intercept with confidence intervals, r², the residual standard deviation sy/x, and derives the detection and quantitation limits from the curve. Every standard is back-calculated so that accuracy per level can be checked.

Typical uses
  • UV/Vis, HPLC or fluorescence calibration for assay, content uniformity and dissolution testing
  • Linearity and range sections of an ICH Q2(R2) validation report
  • Checking day-to-day curves: slope drift, intercept bias, RSD of replicate standards
How to read the output
  • r² alone is not linearity. Look at the residual-% plot: a systematic curve means the range is too wide or the detector saturates. r² ≥ 0.99 is a common acceptance value, not a proof.
  • Intercept test: if the intercept differs significantly from zero, single-point calibration or "response factor" quantitation will be biased at low concentrations.
  • LOD = 3.3·σ/S, LOQ = 10·σ/S with σ = sy/x (ICH Q2(R2) "standard deviation of the response and the slope"). They are estimates; ICH expects the LOQ to be confirmed by analysing standards at that level with acceptable precision and accuracy. The intercept standard deviation may be used as σ instead; the residual SD is used here because it does not depend on the concentration spacing.
  • Back-calculated accuracy: the FDA/EMA bioanalytical limits (±15%, ±20% at the lowest standard) are used to highlight levels; pharmacopoeial assay methods usually require tighter agreement.
  • Replicate RSD per level flags precision problems at individual standards.
Prerequisites and limitations
  • At least three, preferably five or more concentration levels spanning 80–120 % of the working range (ICH Q2(R2)); replicates entered as separate rows
  • Constant variance across the range. If the residual-% plot shows a funnel, weighted (1/x, 1/x²) regression is more appropriate; this tool fits unweighted OLS only
  • Do not extrapolate below the lowest or above the highest standard

References: ICH Q2(R2) Validation of Analytical Procedures (2023); Miller J.N., Miller J.C. (2018) Statistics and Chemometrics for Analytical Chemistry, 7th ed., Pearson; Shrivastava A., Gupta V.B. (2011) Chron. Young Sci. 2:21–25, doi:10.4103/2229-5186.79345.

Parameters
Ordinary least squares; LOD = 3.3·σ/S and LOQ = 10·σ/S (σ = residual standard deviation s_y/x, S = slope; ICH Q2(R2)).
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