# What is J in while calculating SST in multiple regression?

I am little confused what actually is the J in the formula of the SST and SSR for multiple regression

SST= $$Y^T\left[ 1-\frac{1}{n}J\right]Y$$

SSR=$$Y^T\left[ H-\frac{1}{n}J\right]Y$$

## 1 Answer

$$J$$ is the matrix of all $$1$$s. i.e., let $$\mathbf{1}=(1,1,...,1)^T\in \mathbb{R}^n,$$ then $$J = \mathbf{1}\mathbf{1}^T.$$ While $$\frac{1}{n}J$$ can be called "means generating matrix", namely, for some $$y=(y_1, y_2,...,y_n)^T \in \mathbb{R}^n$$, then $$\frac{1}{n}Jy= (\bar{y}_n, \bar{y}_n, ..., \bar{y}_n)^T,$$ which is an essential part of any sum of squares.