Solution 2.11 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

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Education Article

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

1. A mixture diagram is as follows. The new triangle is indicated. Note how there are binary mixtures of components 1 and 2 (points A and B on the triangle), since the sum of the lower and upper limits for each of these components equal 1, but ternary mixtures when component 3 is at its upper limit. A triangle is possible because the sum of lower limits for any two components and upper limit for the third component is always 1.

2.  The true design matrix is as follows.

x1

x2

x3

x1x2

x1x3

x2x3

x1x2x3

0.9

0.1

0

0.09

0

0

0

0.2

0.8

0

0.16

0

0

0

0.2

0.1

0.7

0.02

0.14

0.07

0.014

0.55

0.45

0

0.2475

0

0

0

0.55

0.1

0.35

0.055

0.1925

0.035

0.01925

0.2

0.45

0.35

0.09

0.07

0.1575

0.0315

0.4333

0.3333

0.2333

0.1444

0.1011

0.0778

0.0337

3.  The model is

y = 2.713 x1-1.040 x2-1.072 x3+18.245 x1x2+15.775 x1x3
+16.041 x2x3-83.878 x1x2x3

Note that the quite large terms for the higher order interactions are not necessarily very significant. The range of variation for x1 is 0.7 (maximum-minimum) whereas for x1x2x3 it is 0.0337 or almost 20 times less.

4. The predicted conductivity when the salts are in proportions 0.209, 0.146 and 0.645 is 2.27 W -1cm-1.

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