SOME EFFECTS OF ERRORS OF MEASUREMENT ON LINEAR REGRESSION.
HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS
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When y has a linear regression on X, which is subject to an error of measurement h, there is reason to believe that the regression of y on the fallible x Xh will not in general satisfy Lindleys conditions for linearity. However, a linear component of this regression can be defined in terms of the low moments of the joint distribution of X and h, and this component satisfies the usual elementary results given in the literature. Working out the exact regression of y on x in a few simple cases suggests i that the linear component often dominates even for measurements of only moderate reliability ii good approximations to the exact regression can be obtained by quadratics or cubics in x. Author
- Statistics and Probability