Standard Curve Linear Regression and Back-Calculation of Unknown Samples (BCA / Bradford / ELISA)

Protein quantification, ELISA, and qPCR standard curves all reduce to the same operation: fit a line y = a + b·x through a set of standards with known concentrations, then use that line to back-calculate concentrations from the readings of unknown samples.

The method is ordinary least squares (OLS):

b = Σ(xᵢ−x̄)(yᵢ−ȳ) / Σ(xᵢ−x̄)²
a = ȳ − b·x̄

Interpreting R²: R² is the fraction of variance explained by the regression. Quantitative assays generally require R² ≥ 0.99. Values below this indicate problems with standard preparation, pipetting, or plate reading — do not force a fit and proceed.

Three things you must not overlook:

1. No extrapolation. Unknown sample readings must fall within the range covered by your standards. If a sample reads outside that range, dilute and re-measure — concentrations back-calculated beyond the calibrated range are meaningless. This tool explicitly flags any out-of-range samples.
2. BCA and Bradford assays lose linearity at high concentrations. If the high-concentration standards visibly curve downward, narrow the working range rather than switching to a higher-order fit.
3. Run a fresh standard curve on every plate. Batch-to-batch variation and differences in color development time both shift the slope.