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Above is part of an examination paper. I am not sure how to understand this SAS output. Especially what is there in the last table which looks to me like two discriminant functions. Can someone help me understand this? And how do I use this to classify given some observation say $X_1=94$, $X_2=491$? Thanks

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  • $\begingroup$ @ttnphns One way I know is checking the sign of b'x-k and depending on the sign the population is chosen. Is this the same or different? $\endgroup$
    – Heisenberg
    Commented Jun 28, 2014 at 8:03
  • $\begingroup$ Was that homework or solving textbook exercises? If yes, please add self-study tag. $\endgroup$
    – ttnphns
    Commented Jun 28, 2014 at 9:38
  • $\begingroup$ This was from a past paper on Multivariate data analysis. I will add the tag $\endgroup$
    – Heisenberg
    Commented Jun 28, 2014 at 9:40

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The last table shows Fisher's discrimination & classification coefficients. Here is how they are computed (see the bottom section). When groups are only 2, LDA is called "Fisher's LDA", and extracting discriminant function and then classifying by it can be done in one stage: there is no actual need to extract the discriminant function bodily and then classify by it, - the equivalent pass is to compute Fisher's coefficients, which allow to classify data directly by the original variables.

So no, the table is not two discriminant functions. For 2 groups, only one disriminant function exist. That function is actually not shown anywhere in your output: it is implied.

To assign an observation with the help of the Fisher's coefficients, compute classA = .36*X1+.39*X2-101.70 and classB = .49*X1+.34*X2-97.43. Compute classA-classB. If the value is positive, assign to A; if negative, assign to B.

Nowadays, Fisher's coefficients are rarely used, mostly for didactic reasons, for they conceal the computation of the discriminant function(s) as a latent variable(s). LDA is theoretically two-stage analysis: extract discriminants, then classify by them via Bayes' approach.

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  • $\begingroup$ Thanks a lot. In addition what do you think of the question asking whether this is an accurate classification rule? any ideas? $\endgroup$
    – Heisenberg
    Commented Jun 28, 2014 at 9:29
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    $\begingroup$ (39+44)/90=92% correct rate is high for me. $\endgroup$
    – ttnphns
    Commented Jun 28, 2014 at 9:34
  • $\begingroup$ @Heisenberg I have a question regarding LDA/FDA. Let say, original dataset: 100 features/dimensions; 2 classes; 50 samples/examples. We start with n dimensions and end with k dimensions, where k < n. and is not restricted to only 2 output value. Is that correct? $\endgroup$
    – aan
    Commented May 6, 2020 at 19:53

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