Computing error bars for decay.
The decay error bars are based on the scatter of the points about
the least squares fit plotted in the bampqc.ps file. The variance
in decay is computed from the deviations about the line. In general,
for any least squares solution of the form , the slope,
m, is given by,
|
(15) |
Here, N is the number of (x,y) pairs. We can estimate the variance
in y from
|
(16) |
The variance in the slope, m, follows from the equation used to compute
m, equation(15), and the variance in the y values (which
will be taken to be a constant given by equation(16)). For
uncorrelated errors, the variance in the slope is given by
|
(17) |
which reduces to the following
|
(18) |
The slope, m, for our problem is of course the decay factor (dB/m).
Conversion to 1/m units follows by dividing by 8.68589 in the usual
way.
pm
2018-04-08