017_04.py

beta_hat_1 = sigma_xy / sigma2_x
beta_hat_0 = y_bar - beta_hat_1*x_bar

Y_hat = beta_hat_0 + beta_hat_1*X

sigma2_y_hat = ((Y_hat - y_bar)**2).sum()/Y.size

R2 = sigma2_y_hat / sigma2_y

r2 = r**2

fig, ax = plt.subplots(facecolor="w")
plt.plot(X, Y, "o", label="observations")
plt.axvline(x_bar, ls="--", label=fr"$\bar{{x}}={x_bar:.2f}$", color="C1")
plt.axhline(y_bar, ls="--", label=fr"$\bar{{y}}={y_bar:.2f}$", color="C2")
X_continuous = np.linspace(min(X), max(X), 100)
sigma_x_1 = (X_continuous>=x_bar-sigma_x)&(X_continuous<=x_bar+sigma_x)
plt.fill_between(
    X_continuous[sigma_x_1],
    min(Y), max(Y),
    color="C1", alpha=.15,
    label=fr"$\sigma_{{x}}={sigma_x:.2f}$"
)
Y_continuous = np.linspace(min(Y), max(Y), 100)
sigma_y_1 = (Y_continuous>=y_bar-sigma_y)&(Y_continuous<=y_bar+sigma_y)
plt.fill_betweenx(
    Y_continuous[sigma_y_1],
    min(X), max(X),
    color="C2", alpha=.15,
    label=fr"$\sigma_{{y}}={sigma_y:.2f}$"
)
plt.plot(X, Y_hat, "k", label="regression line")
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.text(1.05, .4, f"$r={r:.9f}$", ha="left", va="center", transform=ax.transAxes)
plt.text(1.05, .3, fr"$\hat{{\beta}}_0={beta_hat_0:.3f}$", ha="left", va="center", transform=ax.transAxes)
plt.text(1.05, .2, fr"$\hat{{\beta}}_1={beta_hat_1:.3f}$", ha="left", va="center", transform=ax.transAxes)
plt.text(1.05, .1, f"$R^2={R2:.9f}$", ha="left", va="center", transform=ax.transAxes)
plt.text(1.05, .0, f"$r^2={r2:.9f}$", ha="left", va="center", transform=ax.transAxes)
plt.show()