# Listing 18
x3=np.arange(1,51)
y3=np.zeros(50)
y3[25:50]= 1
y3[20:25:2] = 1
y3[25:29:2] = 0

x3 = x3.reshape(-1, 1)
clf = linear_model.LogisticRegression(C=1e5, solver='lbfgs')
clf.fit(x3, y3)

sigmuid_prob = logistic_mispredict_proba(x3).flatten()
prob = logistic_mispredict_proba(x3_test)

plt.scatter(x3, y3, color='black', zorder=10)

plt.plot(x3_test, prob, color='red', linewidth=5)
plt.xlabel("x" , fontsize=14)
plt.ylabel("p" , fontsize=14)

plt.show()

fpr, tpr, threshold = metrics.roc_curve(y3, sigmuid_prob)
roc_auc = metrics.auc(fpr, tpr)

plt.plot(fpr, tpr, 'b', label = "AUC = %0.2f" % roc_auc)
plt.legend(loc = "upper left")
plt.plot([0,1],[0,1], 'r--')
plt.xlabel("False Positive Rate" , fontsize=12)
plt.ylabel("True Positive Rate" , fontsize=12)

plt.show()