Question 3 Use the data (a sample of 20 banks) given below to answer the following question(s). Obs financial condition TotCap/Assets TotExp/Assets TotLnsLses/Assets 1 1 9.7 0.12 0.65 2 1 1 0.11 0.62 3 1 6.9 0.09 1.02 4 1 5.8 0.1 0.67 5 1 4.3 0.11 0.69 6 1 9.1 0.13 0.74 7 1 11.9 0.1 0.79 8 1 8.1 0.13 0.63 9 1 9.3 0.16 0.72 10 1 1.1 0.16 0.57 11 1 11.1 0.08 0.43 12 1 20.5 0.12 0.8 13 0 9.8 0.07 0.69 14 0 7.9 0.08 0.53 15 0 9.6 0.09 0.73 16 0 12.5 0.09 0.3 17 0 18.3 0.08 0.49 18 0 7.2 0.11 0.55 19 0 14 0.08 0.44 20 0 8.3 0.08 0.51 The “Financial Condition” column records the judgment of an expert on the financial condition of each bank. This dependent variable takes one of two possible values--weak or strong ---according to the financial condition of the bank. The predictors are two ratios used in the financial analysis of banks: TotLnsLses/Assets is the ratio of total loans and leases to total assets, and TotExp/Assets is the ratio of total expenses to total assets. The target is to use the two ratios for classifying the financial condition of a new bank. Run a logistic regression (on the entire dataset) that models the status of a bank as a function of the two financial measures provided. Specify the success class as weak (this is similar to creating a dummy that is 1 for financially weak banks and 0 otherwise), and use the default cutoff value of 0.5. a) Write the estimated equation that associates the financial condition of a bank with its two predictors in three formats: logit as a function of the predictors: ___________________ odds as a function of the predictors:____________________ probability as a function of the predictors: ______________________ b) Consider a new bank whose total loans and leases/assets ratio = 0.7 and total expenses/assets ratio = 0.09. From your logistic regression model, estimate the following four quantities for this bank: the logit__________, the odds________, the probability of being financially weak ________, and the classification of the bank (use cutoff = 0.5) _____________. c) Interpret the estimated coefficient for the total loans and leases to total assets ratio (TotLns&Lses/Assets) in terms of the odds of being financially weak. ______________ d) When a bank that is in poor financial condition is misclassified as financially strong, the misclassification cost is much higher than when a financially strong bank is misclassified as weak. To minimize the expected cost of misclassification, should the cutoff value for classification (which is currently at 0.5) be increased or decreased?__________________
Question 3
Use the data (a sample of 20 banks) given below to answer the following question(s).
|
Obs |
financial condition |
TotCap/Assets |
TotExp/Assets |
TotLnsLses/Assets |
|
1 |
1 |
9.7 |
0.12 |
0.65 |
|
2 |
1 |
1 |
0.11 |
0.62 |
|
3 |
1 |
6.9 |
0.09 |
1.02 |
|
4 |
1 |
5.8 |
0.1 |
0.67 |
|
5 |
1 |
4.3 |
0.11 |
0.69 |
|
6 |
1 |
9.1 |
0.13 |
0.74 |
|
7 |
1 |
11.9 |
0.1 |
0.79 |
|
8 |
1 |
8.1 |
0.13 |
0.63 |
|
9 |
1 |
9.3 |
0.16 |
0.72 |
|
10 |
1 |
1.1 |
0.16 |
0.57 |
|
11 |
1 |
11.1 |
0.08 |
0.43 |
|
12 |
1 |
20.5 |
0.12 |
0.8 |
|
13 |
0 |
9.8 |
0.07 |
0.69 |
|
14 |
0 |
7.9 |
0.08 |
0.53 |
|
15 |
0 |
9.6 |
0.09 |
0.73 |
|
16 |
0 |
12.5 |
0.09 |
0.3 |
|
17 |
0 |
18.3 |
0.08 |
0.49 |
|
18 |
0 |
7.2 |
0.11 |
0.55 |
|
19 |
0 |
14 |
0.08 |
0.44 |
|
20 |
0 |
8.3 |
0.08 |
0.51 |
The “Financial Condition” column records the judgment of an expert on the financial condition of each bank. This dependent variable takes one of two possible values--weak or strong ---according to the financial condition of the bank. The predictors are two ratios used in the financial analysis of banks: TotLnsLses/Assets is the ratio of total loans and leases to total assets, and TotExp/Assets is the ratio of total expenses to total assets. The target is to use the two ratios for classifying the financial condition of a new bank.
Run a logistic regression (on the entire dataset) that models the status of a bank as a function of the two financial measures provided. Specify the success class as weak (this is similar to creating a dummy that is 1 for financially weak banks and 0 otherwise), and use the default cutoff value of 0.5.
a) Write the estimated equation that associates the financial condition of a bank with its two predictors in three formats:
- logit as a function of the predictors: ___________________
- odds as a function of the predictors:____________________
- probability as a function of the predictors: ______________________
b) Consider a new bank whose total loans and leases/assets ratio = 0.7 and total expenses/assets ratio = 0.09. From your logistic regression model, estimate the following four quantities for this bank: the logit__________, the odds________, the probability of being financially weak ________, and the classification of the bank (use cutoff = 0.5) _____________.
c) Interpret the estimated coefficient for the total loans and leases to total assets ratio (TotLns&Lses/Assets) in terms of the odds of being financially weak. ______________
d) When a bank that is in poor financial condition is misclassified as financially strong, the misclassification cost is much higher than when a financially strong bank is misclassified as weak. To minimize the expected cost of misclassification, should the cutoff value for classification (which is currently at 0.5) be increased or decreased?__________________
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