# Solution 5.3 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

## Education Article

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

1. The labelled scores and loadings plots are as follows.

*c* variables

x variables

The *x* variables are easy to interpret, the loadings simply represent a mixture triangle (see Chapter 2), with the scores indicating the blends. For example, sample 1 contains the highest proportion of milk, sample 3 the highest proportion of sugar and sample 8 cocoa. In addition, samples 5 and 6 are replicates and so identical.

The sign of PC2 is inverted in the *c* and *x* PC calculations, this cannot be controlled, but otherwise the two scores plots can almost be superimposed, suggesting very good evidence that taste and texture relate closely to blends. By looking at the variables in the *c* loadings plot and comparing to the *x* loadings plot, it is easy to see which constituents result in different sensory perceptions, for example, sweetness is clustered close to sugar, and cocoa odour and colour to cocoa.

2. The predictions are below, using standardised data and 2 PLS components. If you do not obtain these results, check your calculations carefully.

Lightness |
Colour |
Cocoa-odour |
Smooth-txtr |
Milk-taste |
Sweetness |

44.79 |
1.47 |
5.85 |
8.35 |
6.24 |
8.42 |

42.69 |
3.72 |
6.60 |
8.64 |
5.12 |
9.73 |

41.64 |
4.86 |
6.98 |
8.79 |
4.56 |
10.39 |

42.56 |
4.94 |
7.73 |
6.55 |
4.27 |
6.80 |

41.04 |
7.03 |
7.95 |
6.41 |
2.76 |
7.04 |

41.04 |
7.03 |
7.95 |
6.41 |
2.76 |
7.04 |

39.31 |
9.49 |
9.95 |
4.92 |
1.76 |
5.88 |

38.13 |
11.83 |
11.45 |
2.98 |
0.35 |
3.61 |

3. The percentage root mean square errors of prediction are as follows.

Lightness |
Colour |
Cocoa-odour |
Smooth-text |
Milk-taste |
Sweetness |

7.20 |
19.41 |
16.233 |
23.85 |
30.42 |
10.94 |

4. The correlation coefficients are as follows.

Lightness |
Colour |
Cocoa-odour |
Smooth-text |
Milk-taste |
Sweetness |

0.9981 |
0.9865 |
0.9905 |
0.9795 |
0.9664 |
0.9957 |

The graph is given below. The two graphs are monotonically related, the higher the error the lower the correlation coefficient. Both parameters can be used as indicators of goodness-of-fit. However, many of the correlation coefficients are close to 1, despite high percentage errors, and can give a falsely optimistic answer.

5. The root mean square errors for PLS2 are as follows.

Lightness |
Colour |
Cocoa-odour |
Smooth-text |
Milk-taste |
Sweetness |

14.61 |
25.18 |
16.76 |
25.07 |
40.28 |
15.32 |

They are somewhat higher than for PLS1, this is often the case.

6. Simply swap the "x" and "c" blocks around.