import numpy as np
import matplotlib.pyplot as plt

# Select the relevant columns from the DataFrame
x = df['population']
y = df['median_house_value']

# Define the desired x-axis range
x_max = 5000

# Create a 2D histogram-like representation
heatmap, xedges, yedges = np.histogram2d(x, y, bins=50, range=[[0, x_max], [min(y), max(y)]])
extent = [0, x_max, yedges[0], yedges[-1]]

# Create the heatmap using imshow
plt.imshow(heatmap.T, origin='lower', extent=extent, aspect='auto', cmap=plt.cm.get_cmap('YlOrRd'))
plt.colorbar(label='Frequency')
plt.xlabel('Population')
plt.ylabel('Median House Value')
plt.title('Heatmap of Median House Value vs Population')
plt.show()