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      "cell_type": "code",
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        "%matplotlib inline"
      ]
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      "source": [
        "\n# Robust linear model estimation using RANSAC\n\nIn this example we see how to robustly fit a linear model to faulty data using\nthe RANSAC algorithm.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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      "source": [
        "import numpy as np\nfrom matplotlib import pyplot as plt\n\nfrom sklearn import linear_model, datasets\n\n\nn_samples = 1000\nn_outliers = 50\n\n\nX, y, coef = datasets.make_regression(\n    n_samples=n_samples,\n    n_features=1,\n    n_informative=1,\n    noise=10,\n    coef=True,\n    random_state=0,\n)\n\n# Add outlier data\nnp.random.seed(0)\nX[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))\ny[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)\n\n# Fit line using all data\nlr = linear_model.LinearRegression()\nlr.fit(X, y)\n\n# Robustly fit linear model with RANSAC algorithm\nransac = linear_model.RANSACRegressor()\nransac.fit(X, y)\ninlier_mask = ransac.inlier_mask_\noutlier_mask = np.logical_not(inlier_mask)\n\n# Predict data of estimated models\nline_X = np.arange(X.min(), X.max())[:, np.newaxis]\nline_y = lr.predict(line_X)\nline_y_ransac = ransac.predict(line_X)\n\n# Compare estimated coefficients\nprint(\"Estimated coefficients (true, linear regression, RANSAC):\")\nprint(coef, lr.coef_, ransac.estimator_.coef_)\n\nlw = 2\nplt.scatter(\n    X[inlier_mask], y[inlier_mask], color=\"yellowgreen\", marker=\".\", label=\"Inliers\"\n)\nplt.scatter(\n    X[outlier_mask], y[outlier_mask], color=\"gold\", marker=\".\", label=\"Outliers\"\n)\nplt.plot(line_X, line_y, color=\"navy\", linewidth=lw, label=\"Linear regressor\")\nplt.plot(\n    line_X,\n    line_y_ransac,\n    color=\"cornflowerblue\",\n    linewidth=lw,\n    label=\"RANSAC regressor\",\n)\nplt.legend(loc=\"lower right\")\nplt.xlabel(\"Input\")\nplt.ylabel(\"Response\")\nplt.show()"
      ]
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