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Related Concept Videos

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...
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
Instrument Calibration01:12

Instrument Calibration

Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
Analytical Balance Calibration
An analytical balance measures mass and requires regular calibration to...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...

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Related Experiment Video

Updated: Jun 1, 2026

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

Maximum likelihood multivariate calibration.

P D Wentzell1, D T Andrews, B R Kowalski

  • 1Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, NS, Canada B3H 4J3.

Analytical Chemistry
|June 7, 2011
PubMed
Summary
This summary is machine-generated.

Two new multivariate calibration methods, maximum likelihood principal components regression (MLPCR) and maximum likelihood latent root regression (MLLRR), incorporate measurement uncertainties for improved accuracy. These methods outperform conventional techniques like PCR and PLS, especially with non-uniform error structures.

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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Last Updated: Jun 1, 2026

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Area of Science:

  • Analytical Chemistry
  • Chemometrics
  • Statistical Modeling

Background:

  • Multivariate calibration is crucial for analyzing complex chemical mixtures.
  • Existing methods like PCR and PLS do not adequately account for measurement uncertainties.
  • Non-uniform error structures can significantly degrade calibration model performance.

Purpose of the Study:

  • To introduce novel multivariate calibration methods that integrate measurement uncertainty information.
  • To develop statistically sound approaches for enhancing calibration accuracy.
  • To compare the performance of new methods against established techniques.

Main Methods:

  • Development of maximum likelihood principal components regression (MLPCR) and maximum likelihood latent root regression (MLLRR).
  • Utilizing maximum likelihood parameter estimation and principal component analysis.
  • Incorporating estimates of measurement error variance into the calibration models.

Main Results:

  • MLPCR and MLLRR demonstrated superior predictive ability compared to PCR and PLS with non-uniform errors.
  • The new methods reduce to PCR and LRR under uniform noise assumptions.
  • MLLRR generally showed slightly better performance than MLPCR.

Conclusions:

  • Maximum likelihood approaches offer a statistically robust way to include measurement uncertainties in multivariate calibration.
  • MLPCR and MLLRR provide enhanced performance, particularly in the presence of non-uniform measurement errors.
  • These novel methods represent a significant advancement in chemometric modeling for chemical analysis.