多元统计分析课件PART1（谢菲尔德大学）--MVAEXERCISES1FEEDBACK

多元统计 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 课件PART1（谢菲尔德大学）--MVAEXERCISES1FEEDBACK These are some general comments arising from work on Exercises 1 that was marked recently. Generally the work was of a good standard though some of you either did not attempt or blundered early on in the algebraic question 1. 'Totally astray' included those who invented dividing through by a vector or inventing an inverse for a vector. Inverses only exist for square non-singluar matrices though it is possible to define a 'generalized' inverse in some cases for non-square (and singluar square) matrtices and indeed S+ has a function for this. Q1 is not absolutely crucial to completing this course but if you do not understand the algebra used in solving it then you will not be able to understand all the interpretations and derivations of other parts of the course. One of those who did make a serious attempt at Q1 made it rather more difficult than intended (e.g. differentiating ratios of quadratic forms rather than using The Procedure). This of course works in the end but does not display the elegance of using the technique of converting the problem to an eigenproblem where all the quantities needed for the analysis are elements fo the eigenequation and this is obtained with minimal algebra and can readily be implemented numerically with stanadrd algebra or statistical packages. While most avoided the naive mistakes of converting inverses of matrices into fractions and dividing through be vectors a few people produced an ingenious but spurious solution where a key step was to multiply through by {betabeta'}^(-1). However, this doesn't exist for p>1 since it is a rank 1 pxp matrix. It fooled me for a little while though. Some of you made much more of finding the eigenvector and eigenvalue of S^-1xx' than you should --- you only need to verify that x's^-1x and S^-1x satisfy the eigen equation, you don't need to derive them by first principals by trying to evaluate a determinant. Actually this is in fact quite easy using a slicktrick that one of you produced that I hadn't seen before. Thanks. In relation to this area nd it also applies to the material coming up in Chapter 5, keep in mind that this is NOT a course in mathematics but a course in Statistics. The mathematics is used as a tool for understanding and justifying, not as an end in itself. Yes, I am a bit cavalier in skating over precise technical conditions which are indeed important but not at first pass when they would obscure the main point. In the data analysis 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.