ABSTRACT
Since the values in same States are more certain than in others, it makes sense for the more certain estimates to influence the regression more. There are all manner of ad hoc procedures for weighting some points more than others, and these can help. To incorporate measurement error, recognize that people can replace the observed data for divorce rate with a distribution. In other words, typical "data" is just a special case of a probability distribution for which all of the mass is piled up on a single value. In the divorce data, the measurement error for the marriage rate predictor variable also comes as standard error. Also note that since there is not much association between divorce and marriage rates, there is less movement of the marriage rate estimates. That is to say that there is not much information in divorce rate to help people improve estimates of marriage rate.
