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

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.