Name: using a calibration line to find unknowns
Uploaded: 2024-04-04T10:51:12.000Z
Duration: 1 min 20 s
Channel: JoVE

A calibration curve is a mathematical relationship between the instrument&#39;s signal and known analyte concentrations. This curve equation predicts the unknown concentration of a sample.
The experimental data may not lie perfectly on a straight line due to random errors. So, the linear least squares method - a regression analysis is used to obtain a straight line that best fits the different points.
LLS is based on two assumptions. Firstly, a linear relationship exists between the instrument&#39;s signal and the analyte concentration. Secondly, the errors are attributed to random error, not human error.
The best-fitting line is drawn by minimizing the sum of the squared differences between the estimated and the actual values.
The recorded plot yields the equation of the line. Here, y is the instrument&#39;s signal, x is the analyte concentration, m is the slope of the line, and c is the y-intercept. The unknown concentration of the sample is determined by measuring its instrumental signal and substituting the appropriate values in the equation.

calibration curves: linear least squares

A calibration curve is a plot of the instrument&#39;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 &#39;y = mx + c.&#39; Here, y is the instrument&#39;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.

Calibration Curves: Linear Least Squares

A calibration curve is a mathematical relationship between the instrument&#39;s signal and known analyte concentrations. This curve equation predicts the ...

Education

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Analytical Chemistry

Unit 1

Chemical Applications of Statistical Analyses

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KEY TERMS AND CONCEPTS

using a calibration line to find unknowns

A calibration curve links an instrument's signal to known concentrations of a substance. Scientists use it to set response levels with standards. They can also fit an equation to the curve and use it to find the concentration of unknown samples.

When the data make a straight line, the linear least-squares method is the standard way to fit the curve. This method finds the line that best matches the points by minimizing the sum of the squared differences between the predicted and actual values. The result is a best-fit line that represents the calibration data reliably.

In this method, concentration is plotted on the x-axis and the measured analytical response is plotted on the y-axis. The line is written as y = mx + c. Here, y is the instrument's signal, x is the analyte concentration, m is the slope, and c is the y-intercept. Once the equation is known, an unknown concentration can be determined by solving for x.

Using a Calibration Line to Find Unknowns

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A calibration curve links an instrument's signal to known concentrations of a substance. Scientists use it to set response levels with standards. They can also fit an equation to the curve and use it to find the concentration of unknown samples. When the data make a straight line, the linear least-squares method is the standard way to fit the curve. This method finds the line that best matches the points by minimizing the sum of the squared differences between the predicted and actual values.

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key terms and concepts

Learn how calibration curves use known standards, a best-fit line, and the equation y = mx + c to calculate unknown concentrations from instrument signals.

Using a Calibration Line to Find Unknowns | JoVE K12

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Using a Calibration Line to Find Unknowns

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