Solution 5.2 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

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  • Published: Jan 1, 2000
  • Channels: Chemometrics & Informatics

1.

 Hence, 

So, a1 = 1/b1 and a0 = - b0/b1

2. The dimensions of the matrices are as follows.

10 ´ 1, X 10 ´ 2, b 2 ´ 1

10 ´ 1, C 10 ´ 2, a 2 ´ 1

The coefficients are and

3.
a1 = 0.0995 » 1/b1 = 1/9.9867 = 0.10013
a0 = 0.0019 » - b0/b1 = -0.00103
(note both intercepts are close to 0).

This equality is not exact since each model has a different assumption about errors.

4. The classical model assumes that the errors are all in the x direction and the inverse model assumes they are in the c direction. Providing there are no strong outliers the equalities and also the best fit straight lines using both methods should be fairly similar.

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