Curve fit models

Calibration curve models

The Analysis module provides a comprehensive range of curve fit models. The following models are available for calibration curves:

Linear.
Linear through origin.
Quadratic.
Quadratic through origin.
Point to point.

Note: The average peak size for all points at a specific level is used to calculate the calibration curve.

Molecular size curve models

The following curve fit models are available for molecular size curves:

Linear.
Linear (log Mw).
Quadratic.
Quadratic (log Mw).
Point to point.
Point to point (log Mw).

Statistics

The Analysis module provides values for the appropriate constants that are used in each curve equation for all models, except for the point to point models. It also provides statistical data that you can use to assess the quality of fit of the curve to the data.

Click the More... button in the Statistics field of the Quantitation table or Mol. size table dialog boxes to view the applied model statistics.

The Linear model

The table below describes the features of the Linear curve fit model.

Feature	Description
Equation.	y = Ax + B
Mathematical model.	The constants A and B are determined by linear least squares regression.
Minimum number of required points.	2 (at least 4 points recommended)
Measuring range for the calibration curve.	Within the highest and lowest values for the points.

Note: A variant of this model is available for the production of a molecular size curve. This uses the logarithm of the molecular size as the x value in the expression above.

The illustration below is an example of the statistical information for an applied Linear curve model:

The Linear through origin model

The table below describes the features of the Linear through origin curve fit model:

Feature	Description
Equation.	y = Ax
Mathematical model.	The constant A is determined by linear least squares regression.
Minimum number of required points.	1 (at least 2 points recommended)
Measuring range for the calibration curve.	From the point with the highest value down to the origin.

The illustration below is an example of the statistical information for an applied Linear through origin curve model:

The Quadratic model

The table below describes the features of the Quadratic curve fit model:

Feature	Description
Equation.	y = Ax2 + Bx + C
Mathematical model.	The constants A, B and C are determined by linear least squares regression.
Minimum number of required points.	3 (at least 6 points recommended)
Measuring range for the calibration curve.	Within the highest and lowest values for the points.

Note: A variant of this model is available for the production of a molecular size curve. This uses the logarithm of the molecular size as the x value in the expression above.

The illustration below is an example of the statistical information for an applied Quadratic curve model:

The Quadratic through origin model

The table below describes the features of the Quadratic through origin curve fit model:

Feature	Description
Equation.	y = Ax2 + Bx
Mathematical model.	The constants A and B are determined by linear least squares regression.
Minimum number of required points.	2 (at least 4 points recommended)
Measuring range for the calibration curve.	From the point with the highest value down to the origin.

The illustration below is an example of the statistical information for an applied Quadratic through origin curve model:

The Point to point model

The table below describes the features of the Point to point curve model.

Feature	Description
Equation.	No single equation.
Mathematical model.	As these curves are not based on a single equation, no statistical data is available. The statistics table only contains information on the number of points in the curve.
Minimum number of required points.	2
Measuring range for the calibration curve.	Within the highest and lowest values for the points.

The illustration below is an example of the statistical information for an applied Point to point curve model:

2005-06-15