Question: Dependent features in linear regression] Consider the setting of multiple linear regression with d = 2 . Imagine that the second feature has the value

Dependent features in linear regression]

Consider the setting of multiple linear regression with d = 2 . Imagine that the second feature has the value exactly twice as the first one for each training example. In other words, xi = (xi1, xi2), with xi2 = 2 xi1, for all i {1, . . . , N}. Consider the matrix XT X, which needs to be inverted for computing the closed-form optimal solution. What is the rank of XT X(Xtranspose X)? Is the matrix invertible?

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