# Solution 2.10 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

## Education Article

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

1. A dummy factor is employed because the total number of factors must be one less than a multiple of four. Two level fractional factorials must consist of a number of experiments equal to a power of two, or 16 in this case. The design reduces the number of experiments necessary, which may be important if experiments are time consuming or expensive.

2. A simple way of doing this is by calculating the correlation coefficients between each possible pair of columns, using a correlation matrix. These should equal 0, except for autocorrelation.

3. The design matrix is exactly as the experimental matrix, except with a first column of "+"s added to account for the intercept. The coefficients are as follows.

 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 47.00 8.33 -2.33 0.50 8.83 -8.17 -2.17 1.33 4.17 7.67 9.00 4.83

4. This can be shown for b1.
b1 = (-15+42-3+57-38-37-74+54+56+64-65+59)/12 = 8.33
which is the same as in question 3.

5. Apart from b0, there five coefficients that are larger in magnitude than the dummy variable, namely b1, b4, b5, b9 and b10. Hence the key factors are (a) %NaOH (b) Stirring (c) Reaction time (d) Catalyst / substrate ratio and (e) Reagent / substrate ratio. Note that the sign of each factor is useful indication also, and reliable as the data is coded and there are no interaction or squared terms.

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