Regression diagnostics and robust regression in geothermometer/geobarometer calibration: the garnet‐clinopyroxene geothermometer revisited

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<jats:p><jats:bold>Abstract </jats:bold> The calibration of geothermometers and geobarometers should involve not only the determination of the parameters in the equation used, but also the uncertainties on, and the correlations between, these parameters. This necessitates the use of a technique such as least squares. Given the poor performance of least squares in the presence of outliers in the data, techniques for identifying outliers for exclusion—regression diagnostics, and techniques for handling data which include outliers—robust regression and jackknifing, are essential. These techniques are summarized and their importance is emphasized, and they are applied to the calibration of the garnet‐clinopyroxene Fe‐Mg exchange geothermometer.</jats:p><jats:p>The experimental data of Raheim & Green (1974) and Ellis & Green (1979) are explored using regression diagnostics to discover outliers in the data. After exclusion of the two influential outliers found, a new geothermometer equation for garnet‐clinopyroxene Fe‐Mg exchange is derived using robust regression and based on all the data: thus, <jats:italic>T</jats:italic>(K) = 2790 + 10<jats:italic>P</jats:italic>+ 3140x<jats:sub>ca,g</jats:sub>/1.735 + In <jats:italic>K</jats:italic><jats:sub><jats:italic>D</jats:italic></jats:sub> where <jats:italic>T</jats:italic> is in Kelvin and <jats:italic>P</jats:italic> is in kbar. This equation, as might be hoped, is essentially identical to that of Ellis & Green (1979). Equations for calculating the uncertainty in a calculated temperature, contributed by uncertainties in the calibration, are also derived.</jats:p>

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