The question is from textbook ‘Applied Multivariate Statistical

Analysis 6E by Johnson & Wichern’

I want help for Exercise11.24

The solution on Chegg solved this Exercise by SAS program.

How can i solve this Exercise by using R program?

The data is given below

-0.45 -0.41 1.09 0.45 0

-0.56 -0.31 1.51 0.16 0

0.06 0.02 1.01 0.40 0

-0.07 -0.09 1.45 0.26 0

-0.10 -0.09 1.56 0.67 0

-0.14 -0.07 0.71 0.28 0

0.04 0.01 1.50 0.71 0

-0.07 -0.06 1.37 0.40 0

0.07 -0.01 1.37 0.34 0

-0.14 -0.14 1.42 0.43 0

-0.23 -0.30 0.33 0.18 0

0.07 0.02 1.31 0.25 0

0.01 0.00 2.15 0.70 0

-0.28 -0.23 1.19 0.66 0

0.15 0.05 1.88 0.27 0

0.37 0.11 1.99 0.38 0

-0.08 -0.08 1.51 0.42 0

0.05 0.03 1.68 0.95 0

0.01 0.00 1.26 0.60 0

0.12 0.11 1.14 0.17 0

-0.28 -0.27 1.27 0.51 0

0.51 0.10 2.49 0.54 1

0.08 0.02 2.01 0.53 1

0.38 0.11 3.27 0.35 1

0.19 0.05 2.25 0.33 1

0.32 0.07 4.24 0.63 1

0.31 0.05 4.45 0.69 1

0.12 0.05 2.52 0.69 1

-0.02 0.02 2.05 0.35 1

0.22 0.08 2.35 0.40 1

0.17 0.07 1.80 0.52 1

0.15 0.05 2.17 0.55 1

-0.10 -0.01 2.50 0.58 1

0.14 -0.03 0.46 0.26 1

0.14 0.07 2.61 0.52 1

0.15 0.06 2.23 0.56 1

0.16 0.05 2.31 0.20 1

0.29 0.06 1.84 0.38 1

0.54 0.11 2.33 0.48 1

-0.33 -0.09 3.01 0.47 1

0.48 0.09 1.24 0.18 1

0.56 0.11 4.29 0.44 1

0.20 0.08 1.99 0.30 1

0.47 0.14 2.92 0.45 1

0.17 0.04 2.45 0.14 1

0.58 0.04 5.06 0.13 1

Show transcribed image text 11.24. Annual financial data are collected for bankrupt firms approximately 2 years prior to their bankruptcy and for financially sound firms at about the same time. The data on four vari- ables, X,-CF/TD (cash flow)/(total debt), X2-NUTA = (net income)/(total as- sets), X3-CA/CL (current assets)/(current liabilities), and X4-CANS = (current assets)/(net sales), are given in Table 11.4 (a) Using a different symbol for each group, plot the data for the pairs of observations (x1, x2), (x1, x3) and (x1, x4). Does it appear as if the data are approximately bivariate normal for any of these pairs of variables? (b) Using the n 21 pairs of observations (x1,2) for bankrupt firms and the n2 25 pairs of observations (x1, x2) for nonbankrupt firms, calculate the sample mean vec tors x1 and x2 and the sample covariance matrices S and S2 (c) Using the results in (b) and assuming that both random samples are from bivariate normal populations, construct the classification rule (11-29) with pl = p2 and (d) Evaluate the performance of the classification rule developed in (c) by computing the apparent error rate (APER) from (11-34) and the estimated expected actual error rate E (AER) from (11-36) (e) Repeat Parts c and d, assuming that P1 = .05, p2 .95, and c( 1 12 ) = c(211). Is the results in (b), form the pooled covariance matrix Spooled, and construct le observations and evaluate the APER. Is Fisher's linear discriminant on pairs (x1, x3) and (x1, x4). Do some vari- this choice of prior probabilities reasonable? Explain Fisher's sample linear discriminant function in (11-19). Use this function to c the samp function a sensible choice for a classifier in this case? Explain. (g) Repeat Parts b-e using the observati ables appear to be better classifiers than others? Explain. (h) Repeat Parts b-e using observations on all four variables (X1, X2, X3, X.)

11.24. Annual financial data are collected for bankrupt firms approximately 2 years prior to their bankruptcy and for financially sound firms at about the same time. The data on four vari- ables, X,-CF/TD (cash flow)/(total debt), X2-NUTA = (net income)/(total as- sets), X3-CA/CL (current assets)/(current liabilities), and X4-CANS = (current assets)/(net sales), are given in Table 11.4 (a) Using a different symbol for each group, plot the data for the pairs of observations (x1, x2), (x1, x3) and (x1, x4). Does it appear as if the data are approximately bivariate normal for any of these pairs of variables? (b) Using the n 21 pairs of observations (x1,2) for bankrupt firms and the n2 25 pairs of observations (x1, x2) for nonbankrupt firms, calculate the sample mean vec tors x1 and x2 and the sample covariance matrices S and S2 (c) Using the results in (b) and assuming that both random samples are from bivariate normal populations, construct the classification rule (11-29) with pl = p2 and (d) Evaluate the performance of the classification rule developed in (c) by computing the apparent error rate (APER) from (11-34) and the estimated expected actual error rate E (AER) from (11-36) (e) Repeat Parts c and d, assuming that P1 = .05, p2 .95, and c( 1 12 ) = c(211). Is the results in (b), form the pooled covariance matrix Spooled, and construct le observations and evaluate the APER. Is Fisher's linear discriminant on pairs (x1, x3) and (x1, x4). Do some vari- this choice of prior probabilities reasonable? Explain Fisher's sample linear discriminant function in (11-19). Use this function to c the samp function a sensible choice for a classifier in this case? Explain. (g) Repeat Parts b-e using the observati ables appear to be better classifiers than others? Explain. (h) Repeat Parts b-e using observations on all four variables (X1, X2, X3, X.)