The file Banks.csv includes data on a sample of 20 banks. The “Financial Condition” column records the judgment of an expert on the financial condition of each bank. This outcome 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: TotLns&Lses/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 model (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 and use the cutoff value of 0.65.

1. a) Write the estimated equation that associates the financial condition of a bank with its two predictors in three formats:

   1. The logit as a function of the predictors

   2. The odds as a function of the predictors

   3. The probability as a function of the predictors

2. b) Consider a new bank whose total loans and leases/assets ratio = 0.75 and total expenses/assets

   ratio = 0.25. From your logistic regression model, estimate the following four quantities for this bank (use R to do all the intermediate calculations; show your final answers to four decimal places): the logit, the odds, the probability of being financially weak, and the classification of the bank (use cutoff = 0.65).

3. c) The cutoff value of 0.65 is used in conjunction with the probability of being financially weak. Compute the threshold that should be used if we want to make a classification based on the odds of being financially weak, and the threshold for the corresponding logit.

4. d) Interpret the estimated coefficient for the total loans & leases to total assets ratio (TotLns&Lses/Assets) in terms of the odds of being financially weak.

5. e) 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 0.65) be increased or decreased?