L}$, which can be written, once we retain only the terms depending on the model parameter $r_0$, as $$S=2\int^{r_{\rm max}}_{r_{\rm min}} h(r)dr -2\sum_i^{N_p}    
\ln[h(r_i)]\ .$$

The integral in the previous equation is computed over the range of scales where the fit is made. The minimum scale is set by the smallest scale at which we find QSO pairs ($r_{\rm min}=3 h^{-1}$ Mpc), while for the maximum scale we adopt $r_{\rm max}=30 h^{-1}$ Mpc. The latter choice is made to avoid possible biases from large angular scales, where the signal is weak.

By minimizing $S$ one can obtain the best-fitting parameter $r_0$. The confidence level is defined by computing the increase $\Delta S$ with respect to the minimum value of $S$. In particular, assuming that $\Delta S$ is distributed as a $\chi^2$ with one degree of freedom, $\Delta S=1$ corresponds to 68.3 per cent confidence level. It should be noted that by assuming a Poisson distribution the method considers all pairs as independent, neglecting their clustering. Consequently the resulting error bars can be underestimated \[see the discussion by [@croft]\].

In Fig. \[totlog\] the lines represent the 1$\sigma$ confidence region computed with the MLE method previously described, varying only the correlation length 