Consider the following data on bankrupt firms (G) and non-bankrupt firms (G): Row CF NI x = X = X = TD TA Firm 1 -0.45 -0.41 1.09 G 2 -0.56 -0.31 1.51 G 3 0.06 0.02 1.01 G 4 -0.07 -0.09 1.45 G 5 -0.10 -0.09 1.56 G 6 -0.14 -0.07 0.71 G 7 0.04 0.01 1.50 G 8 -0.06 -0.06 1.37 G 9 0.07 -0.01 1.37 G 10 -0.13 -0.14 1.42 G 11 -0.23 -0.30 0.33 G 12 0.07 0.02 1.31 G 13 0.01 0.00 2.15 G 14 -0.28 -0.23 1.19 G 15 0.15 0.05 1.88 G 16 0.37 0.11 1.99 G 17 -0.08 -0.08 1.51 G 18 0.05 0.03 1.68 G 19 0.01 0.00 1.26 G 20 0.12 0.11 1.14 G 21 -0.28 -0.27 1.27 G 1 0.51 0.10 2.49 G 2 0.08 0.02 2.01 G 3 0.38 0.11 3.27 G 4 0.19 0.05 2.25 G 5 0.32 0.07 4.24 G 6 0.31 0.05 4.45 G 7 0.12 0.05 2.52 G 8 -0.02 0.02 2.05 G 9 0.22 0.08 2.35 G 10 0.17 0.07 1.80 G 11 0.15 0.05 2.17 G 12 -0.10 -0.01 2.50 G 13 0.14. -0.03 0.46 G 14 0.14 0.07 2.61 G 15 0.15 0.06 2.23 G 16 0.16 0.05 2.31 G 17 0.29 0.06 1.84 G 18 0.54 0.11 2.33 G 19 -0.33 -0.09 3.01 G 20 0.48 0.09 1.24 G 21 0.56 0.11 4.29 G 22 0.20 0.08 1.99 G 23 0.47 0.14 2.92 G2 24 0.17 0.04 2.45 G 25 0.58 0.04 5.06 G 1. Suppose an indicator variable Y takes the value 1 for a bankrupt firm and, 0 for a non- bankrupt firm. Then fit a logistic regression of Y on X1, X2 and X3 of the form () Jog1-(x)=Bo+ B+ BX+ BX3 And assign a firm to be a bankrupt or non-bankrupt one if the estimated (X) > 0.5 or 0.5. Hence find the aperant error rate APER of miss-allocation with the above regression rule. 2. Considering that X = (X1, X2, X) follow normality, derive an optimal discriminating rule for the two types of firms once assuming (a) homoscedasticity for two types of firms, and once (b) without assuming homoscedasticity for two types of firms. Hence find the APER of misclassification for either rules. Also estimate the asymptotic Total Probability of Misclassification for case (a). 3. Assign a new firm with X = (0.10, -0.02, 2.00) as a feature bankrupt' or 'feature non-bankrupt as per part (1) and part (2) (a). (b)