Question: (a) Using the original data sets \(\mathbf{X}_{1}\) and \(\mathbf{X}_{2}\) given in Example 11.7, calculate \(\overline{\mathbf{x}}_{i}, \mathbf{S}_{i}\) \(i=1,2\), and \(S_{\text {pooled }}\), verifying the results provided for these quantities in the example.

(b) Using the calculations in Part a, compute Fisher's linear discriminant function, and use it to classify the sample observations according to Rule (11-25). Verify that the confusion matrix given in Example 11.7 is correct.

(c) Classify the sample observations on the basis of smallest squared distance \(D_{i}^{2}(\mathbf{x})\) of the observations from the group means \(\bar{x}_{1}\) and \(\bar{x}_{2} .\) [See \(\left.(11-54) .\right]\) Compare the resort sults with those in Part b. Comment.

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