# Robust linear model estimation using RANSAC#

In this example, we see how to robustly fit a linear model to faulty data using the RANSAC algorithm.

The ordinary linear regressor is sensitive to outliers, and the fitted line can easily be skewed away from the true underlying relationship of data.

The RANSAC regressor automatically splits the data into inliers and outliers, and the fitted line is determined only by the identified inliers.

```Estimated coefficients (true, linear regression, RANSAC):
82.1903908407869 [54.17236387] [82.08533159]
```

```import numpy as np
from matplotlib import pyplot as plt

from sklearn import datasets, linear_model

n_samples = 1000
n_outliers = 50

X, y, coef = datasets.make_regression(
n_samples=n_samples,
n_features=1,
n_informative=1,
noise=10,
coef=True,
random_state=0,
)

np.random.seed(0)
X[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))
y[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)

# Fit line using all data
lr = linear_model.LinearRegression()
lr.fit(X, y)

# Robustly fit linear model with RANSAC algorithm
ransac = linear_model.RANSACRegressor()
ransac.fit(X, y)

# Predict data of estimated models
line_X = np.arange(X.min(), X.max())[:, np.newaxis]
line_y = lr.predict(line_X)
line_y_ransac = ransac.predict(line_X)

# Compare estimated coefficients
print("Estimated coefficients (true, linear regression, RANSAC):")
print(coef, lr.coef_, ransac.estimator_.coef_)

lw = 2
plt.scatter(
)
plt.scatter(
)
plt.plot(line_X, line_y, color="navy", linewidth=lw, label="Linear regressor")
plt.plot(
line_X,
line_y_ransac,
color="cornflowerblue",
linewidth=lw,
label="RANSAC regressor",
)
plt.legend(loc="lower right")
plt.xlabel("Input")
plt.ylabel("Response")
plt.show()
```

Total running time of the script: (0 minutes 0.112 seconds)

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