136 lines
4.5 KiB
Python
136 lines
4.5 KiB
Python
"""
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分析：访问总次数是否由每次访问平均需求量决定
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使用相关性分析和回归分析
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"""
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import pandas as pd
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import numpy as np
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from scipy import stats
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import matplotlib.pyplot as plt
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# 读取数据
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df = pd.read_excel('prob/MFP Regular Sites 2019.xlsx')
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# 提取关键列
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visits = df['Number of Visits in 2019']
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avg_demand = df['Average Demand per Visit']
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std_demand = df['StDev(Demand per Visit)']
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print("=" * 60)
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print("数据基本统计")
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print("=" * 60)
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print(f"样本数量: {len(visits)}")
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print(f"\n访问总次数:")
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print(f" 均值: {visits.mean():.2f}, 标准差: {visits.std():.2f}")
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print(f"\n每次访问平均需求量:")
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print(f" 均值: {avg_demand.mean():.2f}, 标准差: {avg_demand.std():.2f}")
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# 1. 皮尔逊相关系数分析
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print("\n" + "=" * 60)
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print("1. 皮尔逊相关系数分析")
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print("=" * 60)
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r, p_value = stats.pearsonr(avg_demand, visits)
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print(f"相关系数 r = {r:.4f}")
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print(f"p值 = {p_value:.4e}")
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print(f"决定系数 R² = {r**2:.4f} (可解释{r**2*100:.1f}%的变异)")
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if p_value < 0.05:
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print("结论: p < 0.05, 相关性显著")
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else:
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print("结论: p >= 0.05, 相关性不显著")
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# 2. 线性回归分析
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print("\n" + "=" * 60)
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print("2. 线性回归分析 (访问次数 ~ 平均需求量)")
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print("=" * 60)
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slope, intercept, r_val, p_val, std_err = stats.linregress(avg_demand, visits)
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print(f"回归方程: 访问次数 = {slope:.4f} × 平均需求量 + {intercept:.4f}")
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print(f"斜率标准误: {std_err:.4f}")
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print(f"p值: {p_val:.4e}")
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# 3. 标准差作为辅助分析
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print("\n" + "=" * 60)
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print("3. 标准差辅助分析")
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print("=" * 60)
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# 变异系数 (CV) = 标准差/均值, 衡量相对离散程度
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cv = std_demand / avg_demand
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print(f"变异系数 (CV = 标准差/均值) 统计:")
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print(f" 均值: {cv.mean():.4f}")
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print(f" 范围: {cv.min():.4f} - {cv.max():.4f}")
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# 标准差与访问次数的相关性
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r_std, p_std = stats.pearsonr(std_demand.dropna(), visits[std_demand.notna()])
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print(f"\n标准差与访问次数的相关系数: r = {r_std:.4f}, p = {p_std:.4e}")
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# 4. 多元回归 (平均需求量 + 标准差 -> 访问次数)
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print("\n" + "=" * 60)
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print("4. 多元回归分析 (同时考虑平均需求量和标准差)")
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print("=" * 60)
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from sklearn.linear_model import LinearRegression
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from sklearn.preprocessing import StandardScaler
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# 准备数据 (去除缺失值)
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mask = std_demand.notna()
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X = np.column_stack([avg_demand[mask], std_demand[mask]])
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y = visits[mask]
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model = LinearRegression()
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model.fit(X, y)
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y_pred = model.predict(X)
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ss_res = np.sum((y - y_pred) ** 2)
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ss_tot = np.sum((y - y.mean()) ** 2)
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r2_multi = 1 - ss_res / ss_tot
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print(f"多元 R² = {r2_multi:.4f} (可解释{r2_multi*100:.1f}%的变异)")
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print(f"系数: 平均需求量 = {model.coef_[0]:.4f}, 标准差 = {model.coef_[1]:.4f}")
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print(f"截距: {model.intercept_:.4f}")
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# 5. 总结
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print("\n" + "=" * 60)
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print("综合结论")
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print("=" * 60)
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if abs(r) < 0.3:
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strength = "弱"
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elif abs(r) < 0.7:
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strength = "中等"
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else:
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strength = "强"
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direction = "正" if r > 0 else "负"
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print(f"• 平均需求量与访问次数呈{strength}{direction}相关 (r={r:.3f})")
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print(f"• 平均需求量仅能解释访问次数{r**2*100:.1f}%的变异")
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print(f"• 加入标准差后可解释{r2_multi*100:.1f}%的变异")
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if r**2 < 0.25:
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print("• 结论: 访问总次数主要不由每次访问平均需求量决定")
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else:
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print("• 结论: 每次访问平均需求量对访问总次数有较大影响")
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# 绘图
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fig, axes = plt.subplots(1, 2, figsize=(12, 5))
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# 散点图 + 回归线
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ax1 = axes[0]
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ax1.scatter(avg_demand, visits, alpha=0.6, edgecolors='black', linewidth=0.5)
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x_line = np.linspace(avg_demand.min(), avg_demand.max(), 100)
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y_line = slope * x_line + intercept
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ax1.plot(x_line, y_line, 'r-', linewidth=2, label=f'回归线 (R²={r**2:.3f})')
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ax1.set_xlabel('Average Demand per Visit (每次访问平均需求量)')
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ax1.set_ylabel('Number of Visits (访问总次数)')
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ax1.set_title('访问次数 vs 平均需求量')
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ax1.legend()
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ax1.grid(True, alpha=0.3)
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# 残差图
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ax2 = axes[1]
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residuals = visits - (slope * avg_demand + intercept)
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ax2.scatter(avg_demand, residuals, alpha=0.6, edgecolors='black', linewidth=0.5)
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ax2.axhline(y=0, color='r', linestyle='--', linewidth=2)
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ax2.set_xlabel('Average Demand per Visit (每次访问平均需求量)')
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ax2.set_ylabel('Residuals (残差)')
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ax2.set_title('残差分析')
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ax2.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig('analysis_result.png', dpi=150, bbox_inches='tight')
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print("\n图表已保存至 analysis_result.png")
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