change. Suppose the change in x is known under some new circumstance: to estimate the likely change in an outcome variable y, the slope of the regression of y on x is needed, not y on w. This arises in epidemiology. To continue the example in which x denotes blood pressure, perhaps a large clinical trial has provided an estimate of the change in blood pressure under a new treatment; then the possible effect on y, under the new treatment, should be estimated from the slope in the regression of y on x. Another circumstance is predictive modelling in which future observations are also variable, but not (in the phrase used above) "similarly variable". For example, if the current data set includes blood pressure measured with greater precision than is common in clinical practice. One specific example of this arose when developing a regression equation based on a clinical trial, in which blood pressure was the average of six measurements, for use in clinical practice, where blood pressure is usually a single measurement. Caveats All of these results can be shown mathematically, in the case of simple linear regression assuming normal distributions throughout (the framework of Frost & Thompson). It has been discussed that a poorly executed correction for regression dilution, in particular when performed without checking for the underlying assumptions, may do more damage to an estimate than no correction. Further reading Regression dilution was first mentioned, under the name attenuation, by Spearman (1904). Those seeking a readable mathematical treatment might like to start with Frost and Thompson (2000). See also Errors-in-variables models Quantization (signal processing) – a common source of error in the explanatory or independent variables References Regression models