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Issue 14, 2019
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The correlation between regression coefficients: combined significance testing for calibration and quantitation of bias

Abstract

In the analytical sciences regression methods have two main uses – in calibrations in instrumental analysis, and in testing for bias in method comparison studies. In first order (straight line) regression the true values of the intercept α and the slope β are independent of each other but their estimated values [small alpha, Greek, circumflex] and [small beta, Greek, circumflex] are not independent. This can be appreciated visually by considering the straight lines joining all the individual pairs of points; those with a large slope will have a small intercept and vice versa, so the correlation between [small alpha, Greek, circumflex] and [small beta, Greek, circumflex] is negative and possibly substantial. This correlation has important consequences when the estimated coefficients are used for significance testing in the interpretation of the regression line.

Graphical abstract: The correlation between regression coefficients: combined significance testing for calibration and quantitation of bias

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Article information


Submitted
05 Mar 2019
Accepted
05 Mar 2019
First published
27 Mar 2019

Anal. Methods, 2019,11, 1845-1848
Article type
AMC Technical Brief

The correlation between regression coefficients: combined significance testing for calibration and quantitation of bias

Analytical Methods Committee AMCTB No 87, Anal. Methods, 2019, 11, 1845
DOI: 10.1039/C9AY90041A

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