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Choosing the Next Feature

Machine Learning•Aquatic CapitalHardFree

Question

A multiple linear regression has already been fitted on a set of features, and the residual vector is ee. Three further candidate features are available. After the component of each candidate already explained by the current features is removed, call the residualised candidate zjz_j. The inner products are as follows.

Candidate 11:

zj⊤e=15,zj⊤zj=25.z_j^{\top} e = 15, \qquad z_j^{\top} z_j = 25.

Candidate 22:

zj⊤e=18,zj⊤zj=18.z_j^{\top} e = 18, \qquad z_j^{\top} z_j = 18.

Candidate 33:

zj⊤e=20,zj⊤zj=50.z_j^{\top} e = 20, \qquad z_j^{\top} z_j = 50.

Which candidate should be added to produce the largest reduction in the residual sum of squares? Enter the candidate number.

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