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| regression dilution ： ウィキペディア英語版 |
regression dilution
Regression dilution, also known as regression attenuation, is the biasing of the regression slope towards zero (or the underestimation of its absolute value), caused by errors in the independent variable.
Consider fitting a straight line for the relationship of an outcome variable ''y'' to a predictor variable ''x'', and estimating the slope of the line. Statistical variability, measurement error or random noise in the ''y'' variable cause uncertainty in the estimated slope, but not bias: on average, the procedure calculates the right slope. However, variability, measurement error or random noise in the ''x'' variable causes bias in the estimated slope (as well as imprecision). The greater the variance in the ''x'' measurement, the closer the estimated slope must approach zero instead of the true value.
It may seem counter-intuitive that noise in the predictor variable ''x'' induces a bias, but noise in the outcome variable ''y'' does not. Recall that linear regression is not symmetric: the line of best fit for predicting ''y'' from ''x'' (the usual linear regression) is not the same as the line of best fit for predicting ''x'' from ''y''.
==How to correct for regression dilution==
(詳細はウィキペディア（Wikipedia）』
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