t检验

def solve():
    import pandas as pd
    import statsmodels.api as sm
    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import stats
    
    df = pd.read_csv('https://liangdaima.com/static/data/wooldridge/wage1.csv')
    X = sm.add_constant(df[['educ', 'exper', 'tenure']])
    model = sm.OLS(df['wage'], X).fit()
    
    t_stat = model.tvalues['educ']
    p_value = model.pvalues['educ']
    
    plt.figure(figsize=(10,6))
    x = np.linspace(-4, 4, 1000)
    plt.plot(x, stats.t.pdf(x, df=len(df)-4), 'b-', linewidth=2, label='t分布')
    
    plt.axvline(x=t_stat, color='r', linestyle='--', linewidth=2, label=f't统计量={t_stat:.2f}')
    plt.fill_between(x[x > abs(t_stat)], stats.t.pdf(x[x > abs(t_stat)], len(df)-4), 
                     alpha=0.3, color='red')
    
    plt.title(f't检验：educ系数显著性 (p={p_value:.6f})', fontsize=14)
    plt.xlabel('t值', fontsize=12)
    plt.ylabel('密度', fontsize=12)
    plt.legend()
    plt.grid(alpha=0.3)
    plt.tight_layout()
    plt.show()
    
    print(round(model.tvalues['educ'], 4))