Linear least squares fit when both variables are affected by equal uncorrelated errors

A solution for the least-squares fit of a straight line to measurements in two dimensions is presented for the case where measurements have uncorrelated errors in both variables, while all errors in a given variable are taken from the same probability distribution. The straight line solution is parametrized either by the intercept and the slope or by the impact parameter relative to the origin and the angle with respect to one axis. Simple formulas are presented for both the estimated fit parameters and their standard errors.