Calibration lines passing through the origin with errors in both axes |
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Authors: | Vaclav Synek |
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Institution: | (1) Regional Hygiene Station, Moskevska 15, P.O. Box 78/U2, 40078 Usti nad Labem, Czech Republic e-mail: khsusti@mbox.vol.cz Tel.: +420-47-5312205 Fax: +420-47-5209278, CZ |
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Abstract: | Linear regression of calibration lines passing through the origin was investigated for three models of y-direction random errors: normally distributed errors with an invariable standard deviation (SD) and log normally and normally
distributed errors with an invariable relative standard deviation (RSD). The weighted (weighting factor is x
2
i
), geometric and arithmetic means of the ratios y
i
/x
i
estimate the calibration slope for these models, respectively. Regression of the calibration lines with errors in both directions
was also studied. The x-direction errors were assumed to be normally distributed random errors with either an invariable SD or invariable RSD, both
combined with a constant relative systematic error. The random errors disperse the true, unknown x-values about the plotted, demanded x-values, which are shifted by the constant relative systematic error. The systematic error biases the slope estimate while
the random errors do not. They only increase automatically the slope estimate uncertainty, in which the uncertainty component
reflecting the range of the possible values of the systematic error must be additionally included.
Received: 9 May 2000 Accepted: 7 March 2001 |
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Keywords: | Calibration Heteroscedastic data Ordinary least squares method Uncertainty of measurement x-direction error |
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