This might be a really basic question but I'm calculating ANOVA tables for tables of design points and one of the calculations I need to do is: $Y^TY-N\bar{y}^2$ and I'm not sure what $\bar{y}$ means.
$Y$ is the matrix: $\begin {pmatrix} 0 \\ 1 \\ -1 \\ 1 \\ -1 \end{pmatrix}$
$N$ is given to me in the question and I know $Y^T$ is the transpose of $Y$, I'm just not sure what $\bar{y}$ is, if anyone can let me know it would be much appreciated.
Thanks in advance.
I think it means the mean value of variable $y$. $\bar y =\frac 1N\sum_i y_i$. $y_i$ means the i th element in your vector $Y$
I think your formula $Y^TY - N\bar y^2$ is calculating the total sum of squares of $y$ right ( https://en.wikipedia.org/wiki/Partition_of_sums_of_squares) $$ Y^TY - N\bar y^2 = \sum_i y_i^2 - N \bar y^2 = \sum_i(y_i^2 - \bar y ^2) = \sum_i(y_i - \bar y )^2 $$