Nonsensical Excel and Statistica Default Output and Algorithm for an Adequate Display

TL;DR

This paper introduces an algorithm to determine the optimal number of significant digits in polynomial trend coefficients, improving the accuracy and clarity of default software outputs like Excel, Statistica, and Mathematica.

Contribution

It presents a novel algorithm for selecting significant digits in polynomial coefficients to ensure desired precision in data fitting results.

Findings

The algorithm effectively identifies necessary significant digits.

Default outputs in Excel and Statistica may misrepresent data precision.

Mathematica's default output handles precision better, but sometimes shows excess digits.

Abstract

The purpose of this paper is to present an algorithm that determines the necessary and sufficient number of significant digits in the coefficients of a polynomial trend to achieve a pre-specified precision for the polynomial trend. Thus, the obtained coefficients should be presented in the default output when fitting the experimental data with the polynomial trend. Namely, when finding the best fitting function for a certain type of data, there is a real possibility of making significant errors when using the default output of the Excel 2003, 2007, 2010, and 2013 and Statistica for Windows 2007-2012 software packages. Conversely, the software package Mathematica (version 6) has been very good at dealing with precision problems, although the default output sometimes shows more significant digits than necessary.