Scientists and Engineers (LWR)
Scientists
XCOM starts with 10 scientists and may acquire more throughout the campaign.
Each scientist increases the speed of research by 2% (stacks additively).
An exact formula for research speed can be found here: Research
Scientists are also required in order to build laboratories. The first laboratory requires 20 scientists. Each laboratory requires double the number of scientist from the previous laboratory (e.g. the 4th lab requires 160 scientists).
Engineers
XCOM starts with 10 engineers and may acquire more throughout the campaign.
The speed to produce an item is reduced with more engineers. An exact formula can be found here: Engineering - Item Production Speed
Engineers are also required in order to build workshops and satellite uplinks/nexus' (15 engineers per workshop and 20 engineers per satellite uplink/nexus).