14 Measurement errors & calibration problem

The regression model treats the regressors as known exactly; all the randomness is in \(y\). In practice regressors are often measured with error: a person’s usual salt intake is recorded from a single day’s recall, a soil’s nitrogen from one sample, a temperature by an imperfect instrument. This section asks what such errors do to least squares and how to allow for them. It then turns to a closely related question that runs regression backwards: calibration, in which a fitted line is used to estimate the value of \(x\) that produced an observed \(y\).

Questions on this section

Stuck on something here? Ask below and it stays attached to this topic.