This class contains the methods for performing linear regression and non-linear regression to fit user supplied data either to a user supplied equation or to one of about 50 equations included in this class.
Both unconstrained and constrained non-linear regression methods are available.
All regressions may be performed as either unweighted or classically weighted regressions, i.e. a regression in which the weights are the either the values of or estimates of the standard deviations of the independent variables.
Several of the methods allow a weighted regression in which errors in both the dependent and independent variables may be used to calculate the weights.
The regressions may be performed on sets of x - y data or on a single set of data which is first binned into an histogram.
Full details of Regression plus link to the source code.
This class contains methods for plotting probability plots. It contains methods for
- displaying the plot of ordered data against the relevant order statistic medians
- returning the correlation coefficient of the ordered data and the relevant order statistic medians
- returning the intercept and gradient of the plot
- returning the estimated errors of intercept and gradient of the plot
- returning the best fit estimates of the distribution parameters, e.g. of μ and of σ for a Gaussian distribution
- returning estimates of errors of the distribution parameters
- returning the sum of squares of the ordered data and the relevant order statistic median differences
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This class contains the constructor and methods for fitting immunoassay response curves to one of a range of equations, constructing a standard curve based on the fitting to the equation and obtaining the analyte concentration for a given response, i.e. of a sample of unknown analyte concentration.
A method is available for comparing the goodness of fit to the different equations.
Methods for fitting immunoassay response (r) versus analyte concentration (a) data are available for the following equations and interpolation procedures:
- five parameter logistic function [5PL]: r = top + (bottom - top)/(1 + (a/C50)HillSlope)asymm.
- four parameter logistic function [4PL, EC50 dose response curve]: r = top + (bottom - top)/(1 + (a/C50)HillSlope).
- the best fit polynomial as determined by comparing the extra sum of squares F-ratio probabilities of successive pairs of polynomials of increasing degree.
- a polynomial of user chosen degree, n: r = c0 + c1.a + c2.a2 + . . . + cn.an
- a non-integer polynomial: r = c0 + c1.acn+1 + c2.acn+2 + . . . + cn.ac2n+1
- the sigmoid threshold function: r = Ao/(1 + exp(-α(a - θ))).
- Sips sigmoid function: r = Aoan/(θn + an)
- shifted rectangular hyperbola: r = Aoa/(θ + a) + α
- rectangular hyperbola: r = Aoa/(θ + a)
- ‘Amersham’ mass action model:
- cubic spline interpolation
- linear interpolation
This class provides the methods for fitting complex impedance versus frequency data, as typically obtained in impedance spectroscopy (IS) and in electrochemical impedance spectroscopy (EIS), to a circuit model. Such data is typically obtained using voltage divider in which one impedance is the circuit to be examined, or a system that can be represented by an equivalent circuit (test or model circuit), and the other impedance is the reference impedance, often simply a resistor of known value:
The data may be entered as:
- the magnitudes, Vtest, and phases, φ of the voltage across the test or model circuit as a function of frequency, ω
- the real and imaginary parts of the voltage across the test or model circuit as a function of frequency, ω
- the magnitudes and phases of the impedance of the test or model circuit as a function of frequency, ω
- the real and imaginary parts of the impedance of the test or model circuit as a function of frequency, ω.
Options 3 and 4 allow for the analysis of data obtained using analytical arrangements other than the above.
The test or model circuit may be provided by the user, and is implemented via an interface, ImpedSpecModel, or may be chosen from one of the range of 44 model circuits provided by this class.
The circuit may contain any or all of the following electrical or electrochemical components:
- Resistor [complex impedance: R + j0]
- Capacitor [complex impedance: 0 − j/Cω]
- Inductor [complex impedance: 0 + jLω]