value in the previous works for the similar redshift, $-0.13\,\pm\,0.02$ [@Bouw14] and $-0.10\,\pm\,0.03$ [@Kurc14]. We note that our target is the relatively bright LBGs and the dynamic range of $M_{\mathrm{UV}}$ in our study is smaller than that in the previous works, $-22.0 \leq M_{\mathrm{UV}} \leq -15.5$ [@Bouw14] and $-21.0 \leq M_{\mathrm{UV}} \leq -15.0$ [@Kurc14]. When calculating the slope of the $\beta$–$M_{\mathrm{UV}}$ relation, we use *standard deviation of the mean* as an uncertainty of each mean $\beta$ value. The uncertainty is calculated from the standard deviation divided by the number of galaxies in each bin ($= \sigma_{\beta} / N_{\mathrm{obj}}$) described in table \[tab3\], and thus the uncertainty of the slope of the $\beta$–$M_{\mathrm{UV}}$ relation is much smaller than the mean error of $\beta$.

In figure \[fig6\], we show the direct comparison of our result to the results from *z* $\sim$ 4 super luminous stacked LBGs ([@LeeKS11], red diamonds) and *z* $\sim$ 4 faint LBGs ([@Bouw14], green triangles). The red data points are calculated by us from the photometry described in @LeeKS11 since all the $\beta$ values and its uncertainties are not described in their paper. The error bars denotes the typical uncertainty in the $\beta$ value. The error bars of @Bouw14 