import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from numpy.polynomial.polynomial import Polynomial

# Read the S&P 500 data
df = pd.read_csv('/path/to/your/csv/file.csv')

# Filter the data to start from March 4, 1957
df_1957 = df[df['Date'] >= '1957-03-04'].reset_index(drop=True)

# Convert the dates to numerical values (number of days since March 4, 1957)
x_data = np.arange(len(df_1957))

# Normalize the S&P 500 data to start from 1
normalized_s_1957 = df_1957['Close'] / df_1957['Close'].iloc[0]

# Fit a first-degree polynomial (a line) to the logarithmic data
p = Polynomial.fit(x_data, np.log(normalized_s_1957), 1)

# Generate y-values based on the fit
y_fit_log = p(x_data)

# Plotting the logarithmic graph and the fitted line
plt.figure(figsize=(15, 6))
plt.semilogy(x_data, normalized_s_1957, label='Normalized Actual S&P 500 (Log scale)', color='b')
plt.semilogy(x_data, np.exp(y_fit_log), label=f'Fitted Line', color='r')
plt.title('Logarithmic Plot of the Normalized Actual S&P 500 and Fitted Line (Starting from March 4, 1957)')
plt.xlabel('Number of Days')
plt.ylabel('Close Price (Log Scale, Normalized)')
plt.legend()
plt.grid(True)
plt.show()

# Show the coefficients of the fitted line
print("Coefficients of the fitted line:", p.convert().coef)