Regressing structure function against bin separation

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

Forward-difference scheme regression

1. If $D_{ll}(n,\delta )$ 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 $D_{ll}(n,\delta )$ values for each separation distance will be the number of bins in the range less 1 for $\delta$ = 1, reducing by 1 for each increment in $\delta$, with the regression ultimately yielding a single $\epsilon$ value for the data segment

Bin-centered difference scheme regression

1. If $D_{ll}(n,\delta )$ was evaluated using a bin-centered difference scheme, the regression can either be done:
   • for each bin individually, with a single $D(n,\delta )$ for each separation distance, ultimately yielding an $\epsilon$ for each bin; or
   • by combining the data for all of the bins, with each separation distance having a $D_{ll}(n,\delta )$ value for each bin, with the regression again ultimately yielding a single $\epsilon$ value for the data segment.

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