Shavuot is the biblical feast the Apostles celebrated when the Holy Spirit was poured out. It marked the giving of the Mosaic Law on Mount Sinai. And it foreshadows that day when God inscribes His Law on our hearts - through His Holy Spirit.
On Yom Kippur, the High Priest chose a goat to carry the sins of the people into the wilderness. Isaiah 53 tells us that one day, God will put our sin on the true scapegoat who will bear our sin.