ABSTRACT
In the first chapter we gave an intuitive explanation as to how the mismeasurement phenomenon arises, i.e., how measurement error in a continuous explanatory variable typically attenuates the associated regression coefficient. Now we mathematically elucidate this attenuation, first in the simple scenario of Chapter 1 and then in more complex scenarios. There is no attempt yet to adjust estimators to account for measurement error; this is taken up in Chapter 4. Rather, the goal of this chapter is to quantify the degradation of naive inference in various settings. It can be very useful to develop some intuition in this regard, as in some scenarios not enough is known about the mismeasurement process to attempt a formal adjustment.
