Fitting to specific curves

QtiPlot includes quick access to the most useful functions for fitting.

Fitting to a line

This command is used to fit a curve which has a linear shape.

Figure 6-4. The results of a Fit Linear.

The results will be given in the Log panel:

Fitting to a polynomial

This command is used to fit a polynomial function to data which has a curvilinear shape. Results are be given in the Log panel

If the Apparent Fit option is checked, QtiPlot uses the apparent values for fitting, according to the current axis scales. For example, select this box to fit exponentially decaying data with a straight line fit when data are plotted on a log scale. When this check box is selected and the data has error values associated with it, QtiPlot uses the larger of the positive/negative errors as weight. Apparent Fit is only useful when you fit from a graph and change the plot axis type (from Linear to Log10, for example). If you check this option, QtiPlot will first transform raw data into new data space as specified in the graph axis type, and then fit the curve with the new data. Otherwise, QtiPlot always fits raw data directly, regardless of the axis type. Apparent fit is equivalent to direct fit if you first transform raw data on the worksheet, and leads to completely different results from direct fit if your graph axis is non-linear.

Figure 6-5. The results of a Fit Polynomial..., showing the initial data, the curve added to the plot, and the results in the log panel.

Fitting to a Boltzmann function

This command is used to fit a curve which has a sigmoidal shape. The function used is:

Equation 6-3. Boltzmann equation

in which A1 is the low Y limit, A2 is the high Y limit, x0 is the inflexion (half amplitude) point and dx is the width.

Figure 6-6. The results of a Fit Boltzmann (sigmoidal).

When the X axis is using a logarithmic scale, the Fit Boltzmann (sigmoidal) command uses the Logistical equation for fitting:

Equation 6-4. Logistic dose response equation

where A1 is the initial Y value, A2 is the final Y value, x0 is the inflexion point (center) and p is the power.

Fitting to a Gauss function

This command is used to fit a curve which has a bell shape. The function used is:

Equation 6-5. Gauss equation

in which A is the height, w is the width, xc is the center and y0 is the Y-values offset.

Figure 6-7. The results of a Fit Gaussian.

Fitting to a Lorentz function

This command is used to fit a curve which has a bell shape. The function used is:

Equation 6-6. Lorentz equation

in which A is the area, w is the width, xc is the center and y0 is the Y-values offset.

Figure 6-8. The results of a Fit Lorentzian.

Fitting to a PsdVoigt1 function

This command is used to fit a curve with a Pseudo-Voigt function which is a linear combination of Gaussian and Lorentzian functions:

Equation 6-7. PsdVoigt1 equation

The parameters of the PsdVoigt1 function have the following meaning: y0 is the Y-values offset, A is the area, w is the width (FWHM), xc is the center and mu is a profile shape factor.

Fitting to a PsdVoigt2 function

This command is used to fit a curve with a Pseudo-Voigt function which is a linear combination of Gaussian and Lorentzian functions with different FWHM:

Equation 6-8. PsdVoigt2 equation

The parameters of the PsdVoigt2 function have the following meaning: y0 is the Y-values offset, A is the area, wG is the Gaussian FWHM, wL is the Lorentzian FWHM, xc is the center and mu is a profile shape factor.