Load packages library(tidyverse) Properties of the arithmetic mean The stuff presented here is far from new, that’s all well-known and basic. See here for a source. The arithmetic mean has a number of properties … Residuals cancel out … such as that the residuals cancel out, i.e, the sum of the deviations from the mean (the residuals) sum up to zero: [\sum (x_i - \bar{x}) = \sum x_i - \sum \bar{x} = n \cdot \bar{x} - n \cdot \bar{x} = …