Project5

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# Load the dataset from the Downloads folder
bank.df <- read.csv("C:/Users/pulud/Downloads/banks.csv")

# Display the first few rows of the data
head(bank.df)

##   Obs Financial.Condition TotCap.Assets TotExp.Assets TotLns.Lses.Assets
## 1   1                   1           9.7          0.12               0.65
## 2   2                   1           1.0          0.11               0.62
## 3   3                   1           6.9          0.09               1.02
## 4   4                   1           5.8          0.10               0.67
## 5   5                   1           4.3          0.11               0.69
## 6   6                   1           9.1          0.13               0.74

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# Fit the logistic regression model
reg <- glm(Financial.Condition ~ TotExp.Assets + TotLns.Lses.Assets,
           data = bank.df, family = "binomial")

# Display the summary of the model
summary(reg)

## 
## Call:
## glm(formula = Financial.Condition ~ TotExp.Assets + TotLns.Lses.Assets, 
##     family = "binomial", data = bank.df)
## 
## Coefficients:
##                    Estimate Std. Error z value Pr(>|z|)  
## (Intercept)         -14.721      6.675  -2.205   0.0274 *
## TotExp.Assets        89.834     47.781   1.880   0.0601 .
## TotLns.Lses.Assets    8.371      5.779   1.449   0.1474  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 27.726  on 19  degrees of freedom
## Residual deviance: 13.148  on 17  degrees of freedom
## AIC: 19.148
## 
## Number of Fisher Scoring iterations: 6

# Logit as a function of the predictors
logit_formula <- function(TotExp_Assets, TotLns_Lses_Assets) {
  return(-14.721 + (89.834 * TotExp_Assets) + (8.371 * TotLns_Lses_Assets))
}

# Odds as a function of the predictors
odds_formula <- function(TotExp_Assets, TotLns_Lses_Assets) {
  logit <- logit_formula(TotExp_Assets, TotLns_Lses_Assets)
  return(exp(logit))
}

# Probability as a function of the predictors
probability_formula <- function(TotExp_Assets, TotLns_Lses_Assets) {
  odds <- odds_formula(TotExp_Assets, TotLns_Lses_Assets)
  return(odds / (1 + odds))
}

# Calculate for a new bank with given ratios
new_logit <- logit_formula(0.11, 0.6)
new_odds <- exp(new_logit)
new_prob <- probability_formula(0.11, 0.6)
new_class <- ifelse(new_prob > 0.5, "Weak", "Strong")

# Display the results
cat("Logit:", new_logit, "\n")

## Logit: 0.18334

cat("Odds:", new_odds, "\n")

## Odds: 1.201223

cat("Probability:", new_prob, "\n")

## Probability: 0.545707

cat("Classification:", new_class, "\n")

## Classification: Weak

# Interpretation of the coefficient
# The coefficient for TotLns.Lses.Assets is 8.371.
# This means that for each one-unit increase in the TotLns.Lses.Assets ratio,
# the log-odds of the bank being financially weak increases by 8.371.

# Adjusting the cutoff value
# Since the cost of misclassifying a weak bank as strong is higher,
# the cutoff value should be decreased to reduce the probability threshold,
# making it more likely to classify banks as weak.

# Example: Lowering the cutoff to 0.4
new_cutoff <- 0.4
new_class <- ifelse(new_prob > new_cutoff, "Weak", "Strong")

# Display the new classification
cat("Classification with new cutoff:", new_class, "\n")

## Classification with new cutoff: Weak