import pandas as pd # Load example dataset df = pd.read_csv('https://raw.githubusercontent.com/Statology/Python-Guides/main/default.csv') # Check unique values in response variable unique_vals = df['default'].nunique() print("Number of unique values in response:", unique_vals)

import seaborn as sns import matplotlib.pyplot as plt from sklearn.linear_model import LogisticRegression from sklearn.model_selection import train_test_split # Prepare data for the model X = df[['balance', 'income']] y = df['default'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42) # Fit the model model = LogisticRegression().fit(X_train, y_train) # Predicted probabilities y_pred_prob = model.predict_proba(X_train)[:,1] residuals = y_train - y_pred_prob # Suppose "index" is the time or order of measurement plt.figure(figsize=(10, 6)) sns.scatterplot(x=range(len(residuals)), y=residuals) plt.axhline(y=0, color='red', linestyle='--') plt.xlabel("Observation Order") plt.ylabel("Residual") plt.title("Residuals vs. Time/Order") plt.show()

from statsmodels.stats.outliers_influence import variance_inflation_factor from statsmodels.tools.tools import add_constant # Assume "features" is a DataFrame with only predictor variables features = df[['balance', 'income']] X_vif = add_constant(features) vif_data = pd.DataFrame() vif_data['Feature'] = X_vif.columns vif_data['VIF'] = [variance_inflation_factor(X_vif.values, i) for i in range(X_vif.shape[1])] print(vif_data)

plt.figure(figsize=(8, 6)) sns.heatmap(features.corr(), annot=True, cmap="coolwarm", fmt='.2f') plt.title('Predictor Correlation Matrix') plt.show()

import statsmodels.api as sm import numpy as np # Fit a model using statsmodels to get influence diagnostics X_sm = sm.add_constant(X) logit_model = sm.Logit(y, X_sm).fit(disp=0) # Get influence diagnostics influence = logit_model.get_influence() cooks_d, p_value = influence.cooks_distance # Plot Cook's Distance plt.figure(figsize=(10, 6)) plt.stem(np.arange(len(cooks_d)), cooks_d, markerfmt=",") plt.axhline(y=4/len(df), color="red", linestyle="--", label="4/n Threshold") plt.title("Cook's Distance") plt.xlabel("Observation Index") plt.ylabel("Cook's Distance") plt.legend() plt.show() # See which points are influential influential_indices = np.where(cooks_d > 4/len(df))[0] print("Influential points (indices):", influential_indices)

# Create a copy of the dataframe for this test df_bt = df.copy() # Add Box-Tidwell interaction terms for continuous predictors for var in ['balance', 'income']: # Add a small constant to avoid log(0) df_bt[f'{var}_log_{var}'] = df_bt[var] * np.log(df_bt[var] + 1e-9) # Build model including original and interaction terms X_bt = df_bt[['balance', 'income', 'balance_log_balance', 'income_log_income']] X_bt = sm.add_constant(X_bt) y_bt = df_bt['default'] model_bt = sm.Logit(y_bt, X_bt).fit(disp=0) print(model_bt.summary())

# Get predicted probabilities from the original model pred_prob = logit_model.predict(X_sm) # Compute logit log_odds = np.log(pred_prob / (1 - pred_prob)) # Plot for 'balance' plt.figure(figsize=(10, 6)) sns.scatterplot(x=df['balance'], y=log_odds, alpha=0.5) sns.regplot(x=df['balance'], y=log_odds, scatter=False, lowess=True, line_kws={'color': 'red'}) plt.xlabel('Balance') plt.ylabel('Logit (log-odds)') plt.title('Balance vs. Logit') plt.show()

events = df['default'].sum() variables = X.shape[1] # Number of predictor variables events_per_variable = events / variables print(f"Number of events (minority class): {events}") print(f"Number of predictor variables: {variables}") print(f"Events per variable: {events_per_variable:.2f}") if events_per_variable < 10: print("\nWarning: Sample size may be insufficient based on the 10 events per predictor rule.") else: print("\nSample size appears to be sufficient.")

from IPython.display import IFrame, display display(IFrame(src="https://www.slideshare.net/slideshow/embed_code/key/algQmXUrmDTzOt?hostedIn=slideshare&page=upload", width="476", height="400"))