Python绘制带最优拟合直线方程、R²及相关系数的散点图

Got it, let's build this visualization step by step. We'll use pandas for data management, matplotlib for plotting, and scipy.stats to compute the linear regression metrics we need. Here's a complete, ready-to-run implementation:

Step 1: Import Required Libraries #

from pandas import DataFrame
import matplotlib.pyplot as plt
from scipy.stats import linregress

Step 2: Load Your Dataset #

data = {'X':[2195,2886,2399,1929,2643,2986,2337,2837,2501,2290,1940,2488,2628,2527,2596,2551,2427,2412,2275,2578,2725,2734,2595,2370,1916,2226,2156,1965], 
        'Y':[10539,20043,12702,8654,19092,16719,8189,18517,12265,7749,5835,7640,8722,12540,16974 ,11614,7458,7896,7929,8820,8925,7993,8178,7258,5702,9240,9877,5338]}
df = DataFrame(data, columns= ['X', 'Y'])

Step 3: Calculate Regression Metrics #

We'll use linregress to get the slope, intercept, correlation coefficient (r), and R-squared value in one go:

# Compute linear regression metrics
slope, intercept, r_value, p_value, std_err = linregress(df['X'], df['Y'])
r_squared = r_value ** 2  # R² is the square of the correlation coefficient

Step 4: Create the Visualization #

# Set up plot dimensions
plt.figure(figsize=(10, 6))

# Plot raw data points
plt.scatter(df['X'], df['Y'], color='steelblue', alpha=0.7, label='Data Points')

# Plot the optimal fitted line
x_fit = df['X']
y_fit = slope * x_fit + intercept
plt.plot(x_fit, y_fit, color='crimson', linewidth=2, label='Optimal Fitted Line')

# Add regression details to the plot (adjust position as needed)
text_content = (f'Fitted Line: y = {slope:.2f}x + {intercept:.0f}\n'
                f'Correlation Coefficient (r): {r_value:.4f}\n'
                f'R²: {r_squared:.4f}')
plt.text(df['X'].min() + 50, df['Y'].max() - 1000, text_content, 
         bbox=dict(facecolor='white', alpha=0.8))

# Add plot labels and styling
plt.xlabel('X Values', fontsize=12)
plt.ylabel('Y Values', fontsize=12)
plt.title('Scatter Plot with Optimal Fitted Line', fontsize=14)
plt.legend()
plt.grid(True, alpha=0.3)

# Display the plot
plt.show()

Key Notes: #

• Correlation Coefficient (r): Ranges from -1 to 1. A value close to 1 means a strong positive linear relationship, close to -1 means strong negative, and 0 means no linear relationship.
• R²: Represents the proportion of variance in Y that's explained by X. A value closer to 1 means the line fits the data better.
• Text Position: The plt.text() coordinates are set to sit in the top-left area of the plot. Tweak the x and y values if you need to move the text box to a different spot.
• Customization: Feel free to adjust colors, line widths, or alpha values to match your preferred visual style.

内容的提问来源于stack exchange，提问作者melik