Total sum of squares
In statistical data analysis the total sum of squares (TSS or SST) is a quantity that appears as part of a standard way of presenting results of such analyses. For a set of observations, y i , i ≤ n {\displaystyle y_{i},i\leq n} , it is defined as the sum over all squared differences between the observations and their overall mean y ¯ {\displaystyle {\bar {y}}} .: T S S = ∑ i = 1 n ( y i − y ¯ ) 2 {\displaystyle \mathrm {TSS} =\sum _{i=1}^{n}\left(y_{i}-{\bar {y}}\right)^{2}} For wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares.