Analysing measurement data using regression analysis and error calculation

Purpose of the work

During this presentation I will discuss different methods of regression analysis and error calculation with regard to the review of the measurement standard ISO 9972. I will explain these methods and the ideas behind the formulas.

Method of approach

I will present examples and charts to explain the different methods and evaluate them on the basis of theoretical considerations.

Content of the contribution

I will describe the calculation methods according to the current edition of ISO 9972, the national Annex NC of ISO 9972 and the proposed WLOC (weighted line of organic correlation). This entails three work steps: The method of regression analysis, weighting during regression analysis and error calculation.

When applying the standard regression method with the "least square deviation", the result depends on which of the two variables is considered to be independent. This asymmetry is avoided by using the LOC (line of organic correlation) method.

Logarithmization has the effect that test points under a small pressure difference will have a greater impact on the result than test points under a large pressure difference. This phenomenon can be compensated by using weighting with the square of the air flow. Another option is to use weighting based on the "reliability" of the respective test point which is inversely proportional to its measurement uncertainty.

During test result evaluations the statistical error is usually either calculated and stated, or the inaccuracy of the result is derived from the inaccuracy of the various parameters according to error propagation law. When measuring air permeability it will be initially unclear as to which of these two errors will predominate.

Results and assessment of their significance

The "line of organic correlation" method seems to make sense, yet its effect on the flow exponent only ranges around one per mille.
Weighting is necessary and at the very least has to compensate for logarithmization.

Conclusions

Is does make sense to improve the regression calculation compared to the current version in the international part of ISO 9972. The informative annex covering the regression calculation should be retained to ensure that legacy software can still be used for a certain period of time.

For further information please contact Joachim Zeller at: joachim.zeller@t-online.de