The magenta open circles with the error bar represent the mean UV slope $\beta$ value, standard deviation (left side), and mean error (right side) of the UV slope $\beta$ for each magnitude bin, and they are summarized in table \[tab3\]. []{data-label="fig5"}](Pic2-Official.SEDSBetaMuv+1sig-v1cal.v1BobsMobs.eps){width="80mm"}

Relation between $\beta$ and $M_{UV}$ {#S4S1BM}
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Figure \[fig5\] shows the obtained distribution of the UV slope $\beta$ as a function of the UV absolute magnitude at rest-frame 1500Å ($\beta$–$M_{\mathrm{UV}}$ relation). The UV absolute magnitude for each object is calculated from the best-fit SED model template by integrating the flux from rest-frame 1450Å to 1550Å. The green filled circles show the objects in the area observed with Spitzer and the blue ones show the objects out of the area. There seems to be no notable systematic difference in the distribution of the sample with and without the Spitzer data, and the lack of the information about 3.6$\>\micron$ and 4.5$\>\micron$ does not influence the selection for *z* $\sim$ 4 star-forming galaxies very much. In fact, we conduct the Kolmogorov–Smirnov test (K–S test) for the whole sample and some magnitude sub-samples. The null hypothesis of the K–S test is that the samples with (green) and without (blue) SEDS/Spitzer data are derived 