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In the terminology used in ESL, a vector is a column vector. Let output be a $k$-vector, i.e.$$Y=(Y_1,Y_2,\cdots,Y_K)^T$$Now please refer to following line on pg 12.

In general $\hat{Y}$ can be a $K$-vector, in which case $\beta$ would be a $p \times K$ matrix

Q1: Am I correct that the matrix representation of the linear model in above situation will be ${\hat{Y}}^T =X^T.\hat{\beta}$

Q2: Why is there a hat i.e. ^ over $\beta$, what is the significance on that?

Thanks

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