Belief in Divine Intervention vs Psychological Resilience

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

# Step 1: Simulate data
np.random.seed(42)
n_samples = 120
belief_in_divine = np.random.uniform(1, 10, n_samples)
psychological_resilience = belief_in_divine + np.random.normal(0, 1, n_samples) # Adding noise

# Create DataFrame
experiment_df = pd.DataFrame({'Belief_in_Divine': belief_in_divine,
'Psychological_Resilience': psychological_resilience})

# Step 2: Visualize the relationship with a scatter plot
plt.figure(figsize=(8, 6))
sns.scatterplot(x='Belief_in_Divine', y='Psychological_Resilience', data=experiment_df)
plt.title('Belief in Divine Intervention vs. Psychological Resilience')
plt.xlabel('Belief in Divine Intervention')
plt.ylabel('Psychological Resilience')

# Step 3: Add regression line equation to the plot
plt.text(3, 15, r'$Y = MX + C$', fontsize=12)

# Step 4: Generate individual plots for each regression line
for i in range(5):
# Create a new figure for each line
plt.figure(figsize=(8, 6))

# Randomly select slope and intercept values
slope = np.random.uniform(0.5, 1.5)
intercept = np.random.uniform(-1, 2)

# Plot regression line
x_values = np.linspace(min(belief_in_divine), max(belief_in_divine), 100)
y_values = slope * x_values + intercept
plt.plot(x_values, y_values, label=f'Line {i+1}: Y = {slope:.2f}X + {intercept:.2f}')

# Add scatter plot on top
sns.scatterplot(x='Belief_in_Divine', y='Psychological_Resilience', data=experiment_df)

plt.title(f'Regression Line {i+1}: Belief in Divine Intervention vs. Psychological Resilience')
plt.xlabel('Belief in Divine Intervention')
plt.ylabel('Psychological Resilience')
plt.legend()
plt.grid(True)
plt.show()

# Step 5: Correlation Analysis
correlation_coefficient = np.corrcoef(experiment_df['Belief_in_Divine'], experiment_df['Psychological_Resilience'])[0, 1]
print("Correlation Coefficient:", correlation_coefficient)

# Step 6: Perform Linear Regression
X = experiment_df['Belief_in_Divine'].values.reshape(-1, 1)
y = experiment_df['Psychological_Resilience'].values

# Calculate coefficients
X = np.column_stack((np.ones_like(X), X)) # Add intercept term
coefficients = np.linalg.lstsq(X, y, rcond=None)[0]
slope = coefficients[1]
intercept = coefficients[0]
print("Slope (m):", slope)
print("Intercept (c):", intercept)

# Step 7: Plot regression line
plt.figure(figsize=(8, 6))
plt.scatter(experiment_df['Belief_in_Divine'], experiment_df['Psychological_Resilience'])
x_values = experiment_df['Belief_in_Divine'].values # Convert to numpy array
plt.plot(x_values, slope * x_values + intercept, color='red', label='Regression Line')
plt.title('Regression Analysis: Belief in Divine Intervention vs. Psychological Resilience')
plt.xlabel('Belief in Divine Intervention')
plt.ylabel('Psychological Resilience')
plt.legend()
plt.grid(True)
plt.show()