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4. (LS) Consider the vector b є R. We would like to project this onto the line/subspace through the all-ones vector a E Rm, and we would like to understand this in terms of least squares. To do so, l...
4. (LS) Consider the vector b є R. We would like to project this onto the line/subspace through the all-ones vector a E Rm, and we would like to understand this in terms of least squares. To do so, let's solve the m equations ax-: b in one unknown x є R by least squares. (a) Solve aTax = aTb to show that the solution x is the mean, i.e., the average, of the (b) Find e b- aâ, and from this find the variance llell and the standard deviation llell2 (Hint: Remember that a and b are vectors, not scalars.) elements of b.
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