**7.3 Linear Fits When Both Variables Have Errors**

In the previous examples, it was assumed that the independent
variables *x _{i}* were completely free of errors. Strictly
speaking, of
course, this is never the case, although in many problems the errors
on x are small with respect to those on y so that they may be
neglected. In cases where the errors on both variables are comparable,
however, ignoring the errors on

where _{x} and
_{y}, are the errors on
*x* and *y* respectively. Since the
derivative is normally a function of the parameters
*a _{j}*,