Binary Logistic regression

HW 4: Binary Logistic regression
Banks – Spring
2023.xlsx
Financial Condition of Banks. The file Banks.xlsx 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:
1.
TotLns&Lses/Assets is the ratio of total loans and leases to total assets, and
2.
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 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:
i.
The logit as a function of the predictors. Note that,
Logit is the natural logarithm of odds, i.e. Logit of the logistic regression model =
ii.
The odds as a function of the predictors.
Odds is:
iii.
The probability as a function of the predictors.
The equation relating the outcome variable to the predictors in terms of probability p is
b. Consider a new bank whose total loans and leases/assets ratio = 0.6 and total expenses/assets ratio = 0.11.
From your logistic regression model, estimate the following four quantities for this bank (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 = 0.5).
c. Interpret the estimated coefficient for Y=TotLns&Lses/Assets (i.e. the total loans & leases to total assets ratio) 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?