Chapter 3, Problem 3.1P

Discuss the differences between an error and a residual.

To determine

By discussing the difference between an error and a residual.

Explanation of Solution

The term error is defined as the difference between the observed value and its true value. Formula to obtain the error is $E=X-\overline{X}$

Where, $X$ is the observed value and $\overline{X}$ is the true value of the observation.

The term residual is defined as the difference between the observed value of quantity and its most probable value.

Formula to obtain the residual is

  $v=\overline{M}-M$

Where, $\overline{M}$ is the most probable value of the quantity and $M$ is the observed value.