The effects of errors in measuring the independent variable in least-squares regression analysis |
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Authors: | Louis Meites H.C Smit G Kateman |
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Affiliation: | Laboratorium voor Analytische Scheikunde, Universiteit van Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam The Netherlands;Laboratorium voor Analytische Scheikunde, Universiteit van Nijmegen, Toernooiveld, 6525ED Nijmegen The Netherlands |
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Abstract: | It is well known that linear regression analysis gives unbiased estimates of the slope and intercept of a straight line if the dependent variable y is subject to random errors of measurement while the independent variable x is not. It is much less well known that, if x is also subject to random errors of measurement, linear regression analysis yields an underestimate of the slope and a correspondingly biased estimate of the intercept. These errors cannot be removed by weighted regression. Similar errors arise in non-linear regression when the independent variable is afflicted by random errors of measurement. |
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