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Logistic function#

Shown in the plot is how the logistic regression would, in this synthetic dataset, classify values as either 0 or 1, i.e. class one or two, using the logistic curve.

plot logistic

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
fromscipy.specialimport expit
fromsklearn.linear_modelimport LinearRegression , LogisticRegression
# Generate a toy dataset, it's just a straight line with some Gaussian noise:
xmin, xmax = -5, 5
n_samples = 100
np.random.seed (0)
X = np.random.normal (size=n_samples)
y = (X > 0).astype(float)
X[X > 0] *= 4
X += 0.3 * np.random.normal (size=n_samples)
X = X[:, np.newaxis ]
# Fit the classifier
clf = LogisticRegression (C=1e5)
clf.fit(X, y)
# and plot the result
plt.figure (1, figsize=(4, 3))
plt.clf ()
plt.scatter (X.ravel(), y, label="example data", color="black", zorder=20)
X_test = np.linspace (-5, 10, 300)
loss = expit (X_test * clf.coef_ + clf.intercept_).ravel()
plt.plot (X_test, loss, label="Logistic Regression Model", color="red", linewidth=3)
ols = LinearRegression ()
ols.fit(X, y)
plt.plot (
 X_test,
 ols.coef_ * X_test + ols.intercept_,
 label="Linear Regression Model",
 linewidth=1,
)
plt.axhline (0.5, color=".5")
plt.ylabel ("y")
plt.xlabel ("X")
plt.xticks (range(-5, 10))
plt.yticks ([0, 0.5, 1])
plt.ylim (-0.25, 1.25)
plt.xlim (-4, 10)
plt.legend (
 loc="lower right",
 fontsize="small",
)
plt.tight_layout ()
plt.show ()