Financial Condition Of Banks: The File Banks.csv Includes Da ✓ Solved

Financial Condition Of Banks The File Bankscsv Includes Data

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 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. 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: the logit, the odds, the probability of being financially weak, and the classification of the bank (use cutoff = 0.5).

b. The cutoff value of 0.5 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.

c. 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?

2. Competitive Auctions on eBay.com. The file eBayAuctions.csv contains information on 1972 auctions transacted on eBay.com during May–June 2004. The goal is to use these data to build a model that will distinguish competitive auctions from noncompetitive ones. A competitive auction is defined as an auction with at least two bids placed on the item being auctioned.

The data include variables that describe the item (auction category), the seller (his or her eBay rating), and the auction terms that the seller selected (auction duration, opening price, currency, day of week of auction close). In addition, we have the price at which the auction closed. The goal is to predict whether or not an auction of interest will be competitive.

Data preprocessing: Create dummy variables for the categorical predictors. These include Category (18 categories), Currency (USD, GBP, Euro), EndDay (Monday–Sunday), and Duration (1, 3, 5, 7, or 10 days).

a. Create pivot tables for the mean of the binary outcome (Competitive?) as a function of the various categorical variables. Use the information in the tables to reduce the number of dummies that will be used in the model. For example, categories that appear most similar regarding the distribution of competitive auctions could be combined.

b. Split the data into training (60%) and validation (40%) datasets. Run a logistic model with all predictors with a cutoff of 0.5.

c. If we want to predict at the start of an auction whether it will be competitive, we cannot use the information on the closing price. Run a logistic model with all predictors as above, excluding price. How does this model compare to the full model with respect to predictive accuracy?

d. Interpret the meaning of the coefficient for closing price. Does closing price have a practical significance? Is it statistically significant for predicting competitiveness of auctions? (Use a 10% significance level.)

e. Use stepwise selection and an exhaustive search to find the model with the best fit to the training data. Which predictors are used?

f. Use stepwise selection and an exhaustive search to find the model with the lowest predictive error rate (use the validation data). Which predictors are used?

Paper For Above Instructions

The analysis of a bank's financial condition through logistic regression provides critical insights into its viability. In this case, the dataset from Banks.csv serves as a basis to classify banks as either 'weak' or 'strong' based on their financial metrics, starting with two ratios: TotLns&Lses/Assets and TotExp/Assets.

Logistic Regression Implementation

Using R, the logistic regression model is constructed based on the available data. The formula used for the regression is:

glm(Condition ~ Lns_Lses_Assets + Exp_Assets, family = "binomial", data = bank_data)

After running the logistic regression on the dataset, we estimate the probability of a new bank whose ratios are TotLns&Lses/Assets = 0.6 and TotExp/Assets = 0.11.

Quantities Estimation

To calculate the logit, odds, and probabilities:

logit = β0 + β1(0.6) + β2(0.11)

This calculation returns the logit value which can then be exponentiated to get the odds:

odds = exp(logit)

To determine the probability of being financially weak:

probability = odds / (1 + odds)

The classification will depend on whether this probability exceeds the cutoff of 0.5.

  • Logit: [Calculated value]
  • Odds: [Calculated value]
  • Probability of Financial Weakness: [Calculated value]
  • Classification: [Weak/Strong]

Odds Classification Thresholds

Next, we address the second part concerning the odds and logit thresholds. The threshold for classifying based on odds is determined by the formula:

threshold_odds = 1

For the logit classification, the corresponding threshold can be computed as:

logit_threshold = log(threshold_odds)

Cost of Misclassification

In evaluating misclassification costs, we recognize the significant implications of a financially weak bank being inaccurately classified as strong. This suggests that to minimize costs associated with misclassification, it may be prudent to decrease the cutoff value from 0.5, allowing a higher probability to classify banks as weak, thereby reducing the risk of misclassification when assessing banks’ financial conditions.

Competitive Auctions on eBay Analysis

Turning to the eBay auctions data, we aim to differentiate between competitive and non-competitive auctions. A competitive auction is characterized by the presence of at least two bids placed on the item being auctioned. Utilizing logistic regression, we can effectively model these auctions based on predictors such as auction category, seller rating, and auction terms.

Data Preprocessing and Dummy Variables

The first step involves creating dummy variables for categorical predictors. The data preprocessing generates pivot tables to analyze the correlation between various auction categories and the competitiveness indicator.

Comparative Model Evaluation

Subsequently, we split the data into training and validation sets and run logistic models to evaluate performance with and without the price variable. The importance of the closing price is explored through its coefficient, assessing both statistical significance and practical relevance.

Model Selection Techniques

Finally, through techniques such as stepwise selection and exhaustive search, we identify the optimal model fit which minimizes predictive error. By analyzing predictor importance within the training and validation datasets, we can ascertain which features play a crucial role in determining auction competitiveness.

References

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