Read a linear calibration curve
Understand the fitted line, its intercept, residuals and inverse estimates.
Fit the measured response
Put known standard concentrations x on the horizontal axis and measured absorbance y on the vertical axis. Ordinary least squares finds the slope m and intercept b that minimise squared vertical residuals. The intercept is fitted; it is not automatically removed as a blank correction.
Look beyond R²
Residuals show how each reading differs from the line. A curved pattern or changing spread deserves investigation even when R² is high. Keep replicate rows and examine unusual readings; this workspace does not silently average or delete them.
The fit treats standard concentrations as fixed/exact and assumes a suitable linear response with reasonably comparable measurement variability. It does not model uncertainty in the standards. A high R² is not evidence that a laboratory method is valid.
Invert the same fitted line
Synthetic teaching data x = [0, 1, 2, 3] µM and y = [0.05, 0.26, 0.44, 0.65] give m = 0.198 µM⁻¹ and b = 0.053. For an unknown A = 0.55, x = (0.55 − 0.053) / 0.198 ≈ 2.5101 µM.
An estimate outside 0–3 µM is extrapolation. A negative estimate remains an arithmetic result, but is not a physically meaningful concentration in this model. A zero or numerically unstable slope cannot support a reliable inverse estimate. No uncertainty interval is calculated.
Sources & further reading
- NIST — Data analysis and model validation
- NIST — Calibration of future measurements
- NIST — Least squares
Original educational material. Content review records a source and consistency check; it is not specialist peer review or laboratory method validation.