Generally the work was of a good standard.  Question 1 is hard, not least since the data are on a topic beyond most of your general knowledge (which is of course why I selected it). Most made a good attempt at the analysis itself but several were deficient in their verbal description.  'Describe the main sources of variation' requirs a stage more than saying the first PC is a contrast between home and opp variables, at least say that high scores on this are obtained with low values of the home and high values of the opp variables and so the greatest source of variation is that some teams have high opp abd low home while others have the opposite feature.  This then helps you identify the characteristics of teams appearing in different parts of the scatter plots of the PC scores.   There is more practice on this in Exercises 2 and I know this information would have been better before you submit Exs2 but the timings of sheets are are rather constrained to even the spread though the semester and are outside my control (6011 does benefit from other aspects of timings).

In the second question the sample correlation must be around zero irrespective of what the plot looks like --- the eye is easily deceived. They key point about the final part is that one of the groups clearly divides into two subgroups with the other group 'in between them' --- the PCA plots shew all there is to know about the data so clearly it will not be possible to separate the two groups with a single line/plane/hyperplane and so the advice has to be that lda is unlikely to be useful until the two subgroups are investigated first. It might be possible to use a non-linear classification rule (e.g. a neural net) but that is not sensible since clearly the scientist hasn't appreciated that there are two very distinct variants of type 2 and this is important information to feed back to her before proceeding further.

The commonly occuring mistakes sheet also contains ones which I am sure many of you would have made on Q3 and I have included these because you need to make sure you never make them --- not least in other courses, this sort of matrix manipulation underlies multivariate analysis but the emphasis in this course is more on the practical implementation and interpretation of multivariate techniques.  In lectures I did outline why the question is of importance --- it provides a Union-Intersection Test of a single outlier and shows that all statstical information on a multivairae otlieris held in a single dimension which I call an outlier displaying component.  This can be exploited in assessing and interpreting the outlier's influence on suibsequent analysis.