In linear regression problem, suppose we have the data matrix X ERN x (d + 1), the model coefficient vector w ER(d+1) x 1, and the target vector y ERN x 1. The linear regression can be solved by minimizing the loss function || X w – y || 2 , i.e., setting its gradient to zero, and then solve for w. Please derive the closed-form solution for model parameter w .

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In linear regression problem, suppose we
have the data matrix X ERN x (d + 1), the
model coefficient vector w ER(d+1) x 1,
and the target vector y ERN x 1. The linear
regression can be solved by minimizing the
loss function || X w – y || 2 , i.e., setting its
gradient to zero, and then solve for w. Please
derive the closed-form solution for model
parameter w .
Transcribed Image Text:In linear regression problem, suppose we have the data matrix X ERN x (d + 1), the model coefficient vector w ER(d+1) x 1, and the target vector y ERN x 1. The linear regression can be solved by minimizing the loss function || X w – y || 2 , i.e., setting its gradient to zero, and then solve for w. Please derive the closed-form solution for model parameter w .
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