ESL - Linear Model where output is a vector. Ch 2 Pg 11
$begingroup$
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
linear-algebra machine-learning linear-regression
edited Dec 29 '18 at 12:30
Saad
19.7k92352
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
$endgroup$
add a comment |
$begingroup$
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
linear-algebra machine-learning linear-regression
edited Dec 29 '18 at 12:30
Saad
19.7k92352
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
$endgroup$
add a comment |
$begingroup$
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
linear-algebra machine-learning linear-regression
edited Dec 29 '18 at 12:30
Saad
19.7k92352
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
$endgroup$
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
linear-algebra machine-learning linear-regression
linear-algebra machine-learning linear-regression
edited Dec 29 '18 at 12:30
Saad
19.7k92352
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
edited Dec 29 '18 at 12:30
Saad
19.7k92352
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
edited Dec 29 '18 at 12:30
Saad
19.7k92352
edited Dec 29 '18 at 12:30
Saad
19.7k92352
edited Dec 29 '18 at 12:30
Saad
19.7k92352
19.7k92352
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
asked Dec 29 '18 at 12:09
aman_ccaman_cc
588
588
add a comment |
add a comment |
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