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3.5 Theoretical question

Prove that the maximum number of factors that can be found, is restricted by the product of the two lowest number of factors for any model. Use the equations given in Chapters 1 and 2.

Hint

Take Eq. (4) as a staring point. Rearrange to estimate A in a LS sense. Use that the rank of the problem for solving for A (r1,w1), using estimates of B (r2,w2) and C (r3,w3) limits the number of orthogonal components that can be estimated.

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3.6 Three-way PCR

Use PCR to model the behavior of the y measurements (pH).

Hint

Use the factors in A to make a LS regression to y. Remember to preprocess X and to center y.

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