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Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
Systematic Error: Methodological and Sampling Errors01:15

Systematic Error: Methodological and Sampling Errors

In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...
Data Validation01:15

Data Validation

Method validation is a crucial process in analytical chemistry designed to confirm that a given method consistently produces reliable and high-quality results. This process is essential when a method is applied to different sample matrices or when procedural modifications are made, ensuring that the results meet acceptable standards across various applications.
Key parameters for method validation include:
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Random and Systematic Errors01:20

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
Random and Systematic Errors01:20

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

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Related Experiment Video

Updated: Jun 1, 2026

Methods of Soil Resampling to Monitor Changes in the Chemical Concentrations of Forest Soils
09:16

Methods of Soil Resampling to Monitor Changes in the Chemical Concentrations of Forest Soils

Published on: November 25, 2016

Assessing the accuracy of analytical methods using linear regression with errors in both axes.

J Riu1, F X Rius

  • 1Departament de Química, Universitat Rovira i Virgili, Pl. Imperial Tàrraco, 1, 43005-Tarragona, Catalonia, Spain.

Analytical Chemistry
|May 31, 2011
PubMed
Summary

A new linear regression technique enhances analytical method accuracy assessment by using bivariate least-squares regression (BLS) to calculate joint confidence intervals, accounting for uncertainties in both axes.

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Area of Science:

  • Analytical Chemistry
  • Statistical Modeling

Background:

  • Assessing analytical method accuracy is crucial for reliable scientific results.
  • Traditional methods often use ordinary or weighted least-squares regression, which may not fully account for uncertainties.

Purpose of the Study:

  • To introduce a novel technique for evaluating analytical method accuracy using linear regression.
  • To develop a test based on the joint confidence interval for slope and intercept, incorporating uncertainties from both axes.

Main Methods:

  • Bivariate least-squares regression (BLS) was employed to calculate slope, intercept, and associated variances.
  • The new technique was validated using simulated data (Monte Carlo simulations with 100,000 datasets) and real-world datasets.

Main Results:

  • The BLS-based joint confidence interval method was validated for correctness.
  • Application to real data revealed differences compared to ordinary and weighted least-squares regression methods.
  • The new technique demonstrated improved detection of discrepancies in analytical method accuracy.

Conclusions:

  • The proposed BLS-based joint confidence interval technique offers a more robust assessment of analytical method accuracy.
  • This method provides a valuable alternative for validating analytical procedures by accounting for dual-axis uncertainties.