线性回归与配对自助法
统计思维案例研习
Justin Bois
Lecturer, Caltech
细菌生长
1 图片由加州理工学院 Jin Park 与 Michael Elowitz 提供
细菌生长
_ = plt.semilogy(t, bac_area, marker='.', linestyle='none')
_ = plt.xlabel('time (hr)')
_ = plt.ylabel('area (sq. µm)')
plt.show()
使用 np.polyfit() 的线性回归
slope, intercept = np.polyfit(t, bac_area, 1)
t_theor = np.array([0, 14])
bac_area_theor = slope * t_theor + intercept
_ = plt.plot(t, bac_area, marker='.', linestyle='none')
_ = plt.plot(t_theor, bac_area_theor)
_ = plt.xlabel('time (hr)')
_ = plt.ylabel('area (sq. µm)')
plt.show()
细菌生长的回归
np.polyfit() 的半对数线性回归
slope, intercept = np.polyfit(t, np.log(bac_area), 1)
t_theor = np.array([0, 14])
bac_area_theor = np.exp(slope * t_theor + intercept)
_ = plt.semilogy(t, bac_area, marker='.', linestyle='none')
_ = plt.semilogy(t_theor, bac_area_theor)
_ = plt.xlabel('time (hr)')
_ = plt.ylabel('area (sq. µm)')
plt.show()
细菌生长的回归
配对自助法
- 成对重采样数据
- 用重采样数据计算斜率与截距
- 每个斜率和截距都是一次自助法复制
- 由复制的分位数计算置信区间
配对自助法
# Draw 10000 pairs bootstrap reps slope_reps, int_reps = dcst.draw_bs_pairs_linreg( x_data, y_data, size=10000 )# Compute 95% confidence interval of slope slope_conf_int = np.percentile(slope_reps, [2.5, 97.5])
