Sign In

1.17 : 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 least-squares method. This method minimizes the sum of the squared differences between the predicted and actual values.

The linear least square method plots the data points with the concentration on the x-axis and the measured analytical response on the y-axis. The equation of the line that best fits these data points is 'y = mx + c.' Here, y is the instrument's signal, x is the analyte concentration, m is the slope of the line, and c is the y-intercept. Once the best-fit equation has been determined, unknown concentrations can be determined with this equation by solving for x.

Tags
Calibration CurveInstrument ResponseKnown ConcentrationsLinear Least squares MethodData FittingPredicted ValuesAnalytical ResponseBest fit EquationUnknown ConcentrationsSlopeY intercept

From Chapter 1:

article

Now Playing

1.17 : Calibration Curves: Linear Least Squares

Chemical Applications of Statistical Analyses

701 Views

article

1.1 : SI Units: 2019 Redefinition

Chemical Applications of Statistical Analyses

674 Views

article

1.2 : Degrees of Freedom

Chemical Applications of Statistical Analyses

2.6K Views

article

1.3 : Statistical Analysis: Overview

Chemical Applications of Statistical Analyses

3.4K Views

article

1.4 : Types of Errors: Detection and Minimization

Chemical Applications of Statistical Analyses

700 Views

article

1.5 : Systematic Error: Methodological and Sampling Errors

Chemical Applications of Statistical Analyses

765 Views

article

1.6 : Random Error

Chemical Applications of Statistical Analyses

401 Views

article

1.7 : Standard Deviation of Calculated Results

Chemical Applications of Statistical Analyses

3.2K Views

article

1.8 : Introduction to <em>z</em> Scores

Chemical Applications of Statistical Analyses

142 Views

article

1.9 : Uncertainty: Overview

Chemical Applications of Statistical Analyses

154 Views

article

1.10 : Propagation of Uncertainty from Random Error

Chemical Applications of Statistical Analyses

247 Views

article

1.11 : Propagation of Uncertainty from Systematic Error

Chemical Applications of Statistical Analyses

147 Views

article

1.12 : Uncertainty: Confidence Intervals

Chemical Applications of Statistical Analyses

2.3K Views

article

1.13 : Significance Testing: Overview

Chemical Applications of Statistical Analyses

3.0K Views

article

1.14 : Identifying Statistically Significant Differences: The <em>F</em>-Test

Chemical Applications of Statistical Analyses

714 Views

See More

JoVE Logo

Privacy

Terms of Use

Policies

Research

Education

ABOUT JoVE

Copyright © 2025 MyJoVE Corporation. All rights reserved