POLYPARCI calculates confidence intervals for parameters estimated by ‘polyfit’.
Updated 4 Jan 2024

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POLYPARCI uses the procedures outlined in the ‘polyfit’ documentation to calculate the covariance matrix, and uses ‘betainc’ and ‘fzero’ to calculate the cumulative t-distribution and the inverse t-distribution for a given probability and degrees-of-freedom. It uses only core MATLAB functions and does not require the Statistics Toolbox.
The t-distribution and t-statistic calculations have a relative error of about 1E-012 compared to the Statistics Toolbox functions ‘tcdf’ and ‘tinv’. The relative error of the confidence intervals is about 1E-005 compared to those calculated by ‘nlinfit’ and ‘nlparci’ with the same model on the same data.
POLYPARCI Version 2.0 includes options for 1- or 2-tailed t-statistics (default 2), and the probability that a paramerer is different from zero as an additional optional output, in addition to the parameter confidence intervals already provided. It also incorporates the option to use the default value of ‘alpha’ by defining it as [ ], when choosing to define a specific value for the fourth argument, ‘tails’. All outputs are row vectors or a two-row matrix, matching the input parameter vector, required to be a row vector (the default output for ‘polyfit’).
As with the earlier version, it is self-contained, requires only MATLAB, and does not requre any additional Toolboxes. It is written with 2023b, however it should be backward-compatible to at least R2012b, since it uses ‘bsxfun’ rather than implicit expansion.

Cite As

Star Strider (2024). polyparci (https://www.mathworks.com/matlabcentral/fileexchange/39126-polyparci), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2023b
Compatible with R2012b and later releases
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Major upgrade with improved efficiency, t-distribution options, and an additional optional probability output.

Update 02 2014 — Now works with 2013b. Corrected typo. Added internal documentation. Inverted CI output matrix to 2xN so columns correspond to elements in 1xN parameter vector returned by polyfit.