Regressing structure function against bin separation: Difference between revisions

Revision as of 15:53, 30 May 2022

How the regressions are set up depends on the choice of differencing scheme, these are explained below.

If [math]\displaystyle{ D_{ll}(n,\delta) }[/math] was evaluated using a forward-difference scheme, the regression is done for the combined data from all bins in the selected range, hence the maximum number of [math]\displaystyle{ D_{ll}(n, \delta) }[/math] values for each separation distance will be the number of bins in the range less 1 for [math]\displaystyle{ \delta }[/math] = 1, reducing by 1 for each increment in [math]\displaystyle{ \delta }[/math], with the regression ultimately yielding a single [math]\displaystyle{ \varepsilon }[/math] value for the data segment

If [math]\displaystyle{ D_{ll}(n,\delta) }[/math] was evaluated using a bin-centered difference scheme, the regression is usually done for each bin individually, with a single [math]\displaystyle{ D(n, \delta) }[/math] for each separation distance, ultimately yielding an [math]\displaystyle{ \varepsilon }[/math] for each bin; or

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 == Bin-centered difference scheme regression ==
 <div class="mw-collapsible" id="Bin-center-diff regression" data-collapsetext="Collapse" data-expandtext="Expand">
-# If <math>D_{ll}(n,\delta)</math> was evaluated using a bin-centered difference scheme, the regression can either be done:
+# If <math>D_{ll}(n,\delta)</math> was evaluated using a bin-centered difference scheme, the regression is usually done for each bin individually, with a single <math>D(n, \delta)</math> for each separation distance, ultimately yielding an <math>\varepsilon</math> for each bin; or
-#* for each bin individually, with a single <math>D(n, \delta)</math> for each separation distance, ultimately yielding an <math>\varepsilon</math> for each bin; or
-#* by combining the data for all of the bins, with each separation distance having a <math>D_{ll}(n, \delta)</math> value for each bin, with the regression again ultimately yielding a single <math>\varepsilon</math> value for the data segment.
 </div>