Standard Curve Regression Tool

A best-in-class, offline tool for students, researchers, and lab technicians to perform linear regression on calibration data, calculate unknown concentrations, and assess method quality. Supports scientific notation, dynamic unit conversion, and uncertainty propagation.

Educational only. Follow your lab SOPs and SDS.

Calibration Data

Precision:

Standard (x) Response (y) Weight (optional)

Unknowns

Force regression through zero (y = mx)

Use only when the method and instrument justify it. Increases uncertainty if intercept is truly non-zero.

Regression Results

Enter calibration data to see results.

Correlation (r)

—

R²

—

Slope (m)

—

Intercept (b)

—

Unknown	Response	Concentration	95% CI

Quality Checks

Enter data to see checks.

Why Standard Curves Matter

A standard curve (calibration curve) transforms instrument response into meaningful concentration values. This tool performs weighted or unweighted linear regression, calculates confidence intervals for unknowns, and highlights potential outliers—critical for analytical methods like HPLC, GC, spectrophotometry, and ELISA.

Step‑by‑Step Usage

Enter standards: Known concentrations (x) and their instrument responses (y). Use consistent units.
Optionally weight: If higher concentrations have higher variance, enter weights (e.g., 1/variance).
Add unknowns: Enter response values from your samples.
Review results: Check R² (>0.99 is typical for good methods), intercept significance, and unknown confidence intervals.
Export: Copy results for your lab notebook or report.

Realistic Examples

Example 1: Simple UV‑Vis calibration

Standards: 0, 2, 4, 6, 8, 10 µM with Absorbance: 0.02, 0.145, 0.305, 0.448, 0.601, 0.749. Unknown Abs = 0.420 → Concentration ≈ 5.6 µM.

Example 2: Forced‑through‑zero (enzymatic assay)

Standards: 0, 20, 40, 60, 100 ng/mL with RFU: 0, 450, 920, 1380, 2310. Unknown RFU = 1200 → Concentration ≈ 52 ng/mL.

Common Mistakes Checklist

Using too few standards (less than 5).
Ignoring non‑linearity at high concentrations.
Forcing through zero when intercept is statistically significant.
Extrapolating beyond the highest standard.
Not checking for outliers (e.g., Cook's distance > 1).

What‑If: LOD/LOQ Estimator

Estimate Limit of Detection (LOD) and Limit of Quantification (LOQ) from the standard curve's residual standard deviation (Sy/x).

Residual SD (Sy/x)

Slope (m)

LOD ≈ — (3.3×Sy/x/m)

LOQ ≈ — (10×Sy/x/m)

Frequently Asked Questions

What R² value is acceptable?

For quantitative analysis, R² > 0.99 is often required. However, always inspect residuals—systematic patterns indicate model failure even with high R².

Should I force the regression through zero?

Only if your analytical method and instrument truly give zero response at zero concentration. If the intercept is statistically significant, forcing through zero biases results.

How do I handle non‑linear data?

This tool is for linear regression. For non‑linear curves (e.g., sigmoidal), transform the data or use a different model (e.g., 4‑ or 5‑parameter logistic).

What are the units for weights?

Weights should be proportional to the inverse of the variance at each concentration. Common choices: 1, 1/x, 1/x², or 1/(standard deviation)².

Formulas & Assumptions

Linear Regression (weighted)

y = mx + b
m = Σ[wᵢ(xᵢ - x̄)(yᵢ - ȳ)] / Σ[wᵢ(xᵢ - x̄)²]
b = ȳ - m x̄
r = Σ[wᵢ(xᵢ - x̄)(yᵢ - ȳ)] / √[Σ[wᵢ(xᵢ - x̄)²] Σ[wᵢ(yᵢ - ȳ)²]]

Assumptions & Constants

Errors in x are negligible compared to y.
Variance is homogeneous (unless weighted).
Confidence intervals use t‑distribution (95%, df = n‑2).
LOD factor = 3.3, LOQ factor = 10 (IUPAC).

For informational and educational purposes only. Estimates depend on your inputs and simplifying assumptions. This tool does not replace professional judgment, lab SOPs, or safety procedures. Always follow SDS guidance and institutional policies.

Sources: Common chemistry constants: R, NA, F; Standard unit conversions and lab measurement best practices; General analytical chemistry and uncertainty concepts; IUPAC recommendations on detection limits; Laboratory safety basics and SDS principles.

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Standard Curve Regression Tool

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