Fitting the Line y = ax when Errors of Observation are Present in Both Variables

Note that E :E(di-d)2/n(n-1) var(d) + 1(8j8) 2/n (n1) so if 8i / 8, var(d) = (di d) 2/ n(n-1) tends to overestimate var(i). This relation holds in general. Furthermore, 71 var (d) /2> 18J gives an upper limit to the numerical value of 8 if ui and vi are normal and is an approximate guide in more general cases. d provides a very simple estimate of log(a), that in a sense is distribution free. Whether or not it is a useful estimate in any particular application depends entirely on the actual data. Thus, if u* and vi are normal, with var(ui) = var(v*) = 0,2 for all i, then d is the best linear unbiased estimate of log(a). If var(ui) = var (V,) = 2 different for different i, then d is an unweighted linear estimate of log a.