{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "In this little experiment we'll see 3 cases of linear regression model and we'll see the value of bias and variance that we will obtain. The 3 cases are:\n",
        "\n",
        "\n",
        "\n",
        "*   data with no noise\n",
        "*   data with a little bit of noise\n",
        "*   data with no relation between X and Y"
      ],
      "metadata": {
        "id": "NjjaAH_-aXIo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# First case: data with no noise"
      ],
      "metadata": {
        "id": "o8gYORtVbTXO"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "5PK0fCwyQwsd",
        "outputId": "1fb56bef-21ec-4f4e-b205-e5df37ee458a"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Bias: 1.0845392999330622e-32\n",
            "Variance: 0.04953967957663739\n"
          ]
        }
      ],
      "source": [
        "# importation of the necessary libraries\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# data generation (X and y match perfectly)\n",
        "X = np.random.rand(100, 1)\n",
        "y = X\n",
        "\n",
        "# division of the data into training set and test set\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
        "\n",
        "# training the linear regression model\n",
        "reg = LinearRegression().fit(X_train, y_train)\n",
        "\n",
        "# prevision on test set\n",
        "y_pred = reg.predict(X_test)\n",
        "\n",
        "# calculation of mse\n",
        "mse = mean_squared_error(y_test, y_pred)\n",
        "\n",
        "# calculation of bias and variance\n",
        "bias = np.mean((y_test - y_pred)**2)\n",
        "variance = np.var(y_pred)\n",
        "\n",
        "# graph of the linear regression\n",
        "plt.scatter(X_test, y_test, label=\"True value\")\n",
        "plt.plot(X_test, y_pred, label=\"Prediction\")\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# result\n",
        "print(\"Bias:\", bias)\n",
        "print(\"Variance:\", variance)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Wee can see that bias and variance are really small (bias is close to zero or is zero). This make sense since X and y have perfect linear relationship"
      ],
      "metadata": {
        "id": "VogMeevOc2I3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Second case: data with a little bit of noise"
      ],
      "metadata": {
        "id": "W9kkXchUfTrt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# importation of the necessary libraries\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# data generation (y has some noise)\n",
        "X = np.random.rand(100, 1)\n",
        "y = X + (np.random.rand(100, 1)/2)\n",
        "\n",
        "# division of the data into training set and test set\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
        "\n",
        "# training the linear regression model\n",
        "reg = LinearRegression().fit(X_train, y_train)\n",
        "\n",
        "# prevision on test set\n",
        "y_pred = reg.predict(X_test)\n",
        "\n",
        "# calculation of mse\n",
        "mse = mean_squared_error(y_test, y_pred)\n",
        "\n",
        "# calculation of bias and variance\n",
        "bias = np.mean((y_test - y_pred)**2)\n",
        "variance = np.var(y_pred)\n",
        "\n",
        "# graph of the linear regression\n",
        "plt.scatter(X_test, y_test, label=\"True value\")\n",
        "plt.plot(X_test, y_pred, label=\"Prediction\")\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# result\n",
        "print(\"Bias:\", bias)\n",
        "print(\"Variance:\", variance)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "ulA3oNBmdZcF",
        "outputId": "878b5719-1580-4c1a-e514-cbb47c360c44"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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uIlHx664COtw1NaB2eJMD+XhYL4868j8FuohEVFGR44gQG0xoLnn0KdBFJGJCbTChueSxo0AXkWoLFeSfjTiNwxok5jrriUqBLiJVdv7fZpH7w+aA2vghJ5KV1tijjpKbAl1E9tuDU5by/MffBdQeOP9YLuumRfe8pEAXkbBNWriWG/4duH/NJVmpPHzRcR51JGUp0EWkUnlrtnLWU58E1FIb1eXT207zqCMJRYEuIvu0cdtuOpfbYAJg5eizPehGKqNAF5EgBYVFHHX7lKC6gjy0Cbmr42KfVgW6iAQINQVx+f1nUjOlhgfdxL8JuasZ8fYiduwpBGD15h2MeHsRQMxDXYEuIkDoIJ9/5xk0PugAD7pJHI9MXVYa5nvt2FPII1OXKdBFJLZOfugj8jftCKhNvrEHGS0O9qijxLJm8479qkeTAl0kSZ315Cfkrd0aUHvmsk7069jCo44SU4uGdVkdIrxbNIz9XbIKdJEkM/Tf8/m/hYG7RF7X8whGnHmMRx0ltmHZ7QLG0AHq1kphWHa7mPeiQBdJEm/mrOLW8QuD6pq5Uj17x8k1y0VEou6rH7fS94lPguoK8sg5r1NLTwK8PAW6iE+F2mACFOR+pkAX8RnnHOkjgjeY+PaBs0ipoQ0m/EyBLuIjoeaS59zRm6b1anvQjcSaAl3EB0IF+X+GnEgXrUueVBToIgms870fsHHb7oDarX3b8cdTj/KoI/GSAl0kAV08ZjZzV24KqGW3P4Tnr8iK+HvFy8JTUjkFukgCGfPxt4ye8lVArdGBtcgd2Scq7xdPC09J5cIKdDPrCzwJpAAvOOdGl3u+NfBPoGHJMcOdc8Efs4tIlcxduZGLx3wWVI/2FMR4WnhKKldpoJtZCvAscAaQD8w1s4nOubwyh90BvOmce87MMoDJQFoU+hVJKht+3cXx930YVI/VXPJ4WnhKKhfOFXpXYLlz7jsAM3sD6A+UDXQH7F2arQGwJpJNiiSbwiLHkX8J/iN3xYNnYRa7ueTxtPCUVC6cQG8JrCrzOB/oVu6YUcD7ZvYn4CCgd6gXMrPBwGCA1q21O7hIKKGmIC4a1Yf6dWrFvJd4WnhKKhepD0UvBV52zj1mZicCr5pZB+dcUdmDnHNjgbEAWVlZLkLvLeILoYJ8yk09OOYw79Ylj6eFp6Ry4QT6aqBVmcepJbWyrgH6AjjnPjOzOkBTYF0kmhTxs1BB/tCFx/K7LvHxV2y8LDwllQsn0OcCbcwsneIgHwBcVu6YH4DTgZfN7BigDrA+ko2K+M1JD05jzZadAbWzjz2MZy/v7FFHkugqDXTnXIGZDQWmUjwl8UXn3BIzuwfIcc5NBP4X+LuZ3UzxB6QDnXMaUhEJ4b7/y+OFT1cE1bUKolRXWGPoJXPKJ5erjSzzdR7QPbKtifjLh3k/MeiVnKC6glwiRXeKikTZqo3b6fHw9KC6glwiTYEuEiW7C4poe8eUoLqCXKJFgS4SBaFmriy7ry+1a6Z40I0kCwW6SASFCvJPbu1Fq8YHetCNJBsFukgEhArysVccT5/2h3rQjSQrBbpINYQK8qu7p3HXOe096EaSnQJdpAr+9Hou//0ycA265vVr88XtIZcxEokJBbqPaaeZyPtPziqGjV8YVNfMFYkHCnSf0k4zkbXsx1/IfmJmUF1BLvFEge5T2mkmMn7dVUCHu6YG1RXkEo8U6D6lnWaqxzlH+ojgDSa+feAsUmrEboMJkf2hQPcp7TRTdaFmrsy9vTfN6tf2oBuR8CnQfUo7zey/UEE+bvAJdDuiiQfdiOw/BbpPaaeZ8IUK8mHZ7bih11EedCNSdQp0H9NOMxUb/EoO7+f9FFDr1Loh7/xRK0FLYlKgS9J5bc733DFhcVA9UWeu6H4D2UuBLknjy1Wb6f/srKB6ogY56H4DCaRAF9/btG03ne79IKieyEG+l+43kLIU6OJbRUWOI/4SPJd8xYNnYZbYc8n3DrOEmpoKut8gWSnQxZdCzVxZfHc29Won/q98+WGWUMK530Bj7/6T+L/dImWECvL3bz6FtofU96Cb6Ag1zFJWOPcbaOzdnxToPpcsV2GhgvzJAZn0z/Tfz1rRcErLMP8/1ti7PynQfSwZrsL6PzuLL1dtDqgN6NKK0Rd29Kij6NvXsg4tG9Zl1vDTwnoNrfXjTzW8bkCip6KrsET35IffkDZ8UkCYN6hbi5Wjz/Z1mEPxXax1awVuNr2/yzrsa4xda/0kNl2h+5gfr8JmLf+Zy1/4PKjuhymI4YrEsg5a68efFOg+5qcVF9du2cGJD34UVE+mIC+russ6aK0ff1Kg+5gfrsJ2FxTR9o4pQfVkDfJI0lo//hNWoJtZX+BJIAV4wTk3OsQxlwCjAAd86Zy7LIJ9ShUk+lVYqJkry+7rS+2aKSGOFpFKA93MUoBngTOAfGCumU10zuWVOaYNMALo7pzbZGbNo9Ww7J9EvAoLFeSf3taL1EYHetCNSOII5wq9K7DcOfcdgJm9AfQH8soccy3wrHNuE4Bzbl2kGxX/CxXkL1/dhVPb6fpAJBzhBHpLYFWZx/lAt3LHtAUws1kUD8uMcs69V/6FzGwwMBigdevWVelXfKjr/R+y7pddAbWhvY7ilgQa6xeJB5H6ULQm0AY4FUgFZprZsc65gDs+nHNjgbEAWVlZLkLvLQlq5LuLeeWz7wNqxxx2MFNu6uFRRyKJLZxAXw20KvM4taRWVj7wuXNuD7DCzL6mOODnRqRLH0uWW/PLmrRwLTf8e35QXTNXRKonnECfC7Qxs3SKg3wAUH4GywTgUuAlM2tK8RDMd5Fs1I+S4db8sr5d/yunP/ZxUF1BLhIZlQa6c67AzIYCUykeH3/RObfEzO4BcpxzE0ue62NmeUAhMMw5tyGajftBsiyQtH13ARkjpwbVFeQikRXWGLpzbjIwuVxtZJmvHfDnkn8SJj/eml+Wc470EcEbTHz7wFmk1EjsDSZE4pHuFPWQn27NLy/UFMR5d/SmSb3aHnQjkhwU6B7yw6355YUK8reuP4njD2/kQTciyUWB7qFEvzW/rFBBPrJfBn84Od2DbkSSkwLdY4l0a36oKZZTl/zIlMU/BhzXq10zXrq6q0ddiiQvBbqEJdQUy/8ZtyDoOM1cEfGOAl3CUtnGxApyEe8p0CUsoWbjABiwIoHDPBnv1BX/UqBLhYqKHEf8JXgu+V6JPMUy2e7UFf9ToMs+hZq5UlaiT7FMljt1JXko0CVIqCCf+j+nsHTtVl8NT/j9Tl1JPgp0KRUqyJ/4XWZpaLc7tH5CB3h5fr5TV5KTAl04/2+zyP0hYOl6LslK5eGLjvOoo9jw4526ktwU6Ens6Wnf8NgHXwfU6tepyaJR2R51FFt+ulNXBBToSWnW8p+5/IXPg+rJOJc8ke7UFamMAj2J/LhlJyc8OC2onoxBLuJHCvQksKewiDa3TwmqK8hF/EWB7nOhZq4su68vtWumeNCNiESTAj0C4vH28VBB/ultvUhtdKAH3YhILCjQqynebh8PFeSvXdONk9s0jXkvIhJbCvRqipfbx/s/O4svVwXOJR9+5tEM6XlkzHoQEW8p0KvJ69vHH//ga56a9k1A7eSjmvLaoG4xeX8RiR8K9Gry6vbx6V+t4+qX5wbVNXNFJHkp0Ksp1reP/7BhO6c8Mj2oriAXEQV6NcXq9vGdewo5+s73guoKchHZS4EeAdG8fdw5R/qI4A0mvn3gLFJqWFTeU0QSkwI9joWagph75xk0OugAD7oRkXgXVqCbWV/gSSAFeME5N3ofx10IjAe6OOdyItZlkgkV5BOHdqdjakMPuhGRRFFpoJtZCvAscAaQD8w1s4nOubxyx9UHbgKCl/GTsJzwwDR+3LozoDb6gmMZ0LW1Rx2JSCIJ5wq9K7DcOfcdgJm9AfQH8soddy/wEDAsoh363ITc1dz+ziK27Q68Oem8zBY8MaCTR12JSCIKJ9BbAqvKPM4HAu5aMbPOQCvn3CQzU6CH6aEpX/Hcx98G1ctu+yYiEq5qfyhqZjWAx4GBYRw7GBgM0Lp18g4j7Gsu+V7adV5EqiKcQF8NtCrzOLWktld9oAMww8wADgUmmtm55T8Ydc6NBcYCZGVluWr0nZC27Sqg/V1TKz1Ou86LSFWEE+hzgTZmlk5xkA8ALtv7pHNuC1C6lJ+ZzQBu0SyX3+xrLnmLBnVYs2VncF27zotIFVQa6M65AjMbCkyleNrii865JWZ2D5DjnJsY7SYTWagpiF/d25c6tVKClt4F7TovIlUX1hi6c24yMLlcbeQ+jj21+m0lvlBBPnv4aQFX39p1XkQiSXeKRlio5WzfvO5EuqY3Dnm8dp0XkUhRoEfIxC/XcOPruQG1e8/rwBUnHO5RRyKSbBTo1bR2yw5OfPCjgNo9/dtz5Ylp3jQkIklLgV5FW3fuoe9fZwbMUrm8W2vuP/9YD7sSkWSmQN9PuwuKuOIfn/P5io2ltfvP78Dl3TS0IiLeUqCHqajIMWz8Qt6an19au6HXkQzLPtrDrkREfqNAD8NfP/iaJ8vMXDkvswWPX5JJDW0wISJxRIFegTfnruLWtxaWPj7+8Eb8+9pu1K6Z4mFXIiKhKdBDmLFsHQNfmlv6uHn92nxwc08aHFjLw65ERCqmQC9jUf4Wznnm04DarOGn0VJrq4hIAlCgA6s2bqfHw4HL2U668WTat2jgUUciIvsvqQN907bdnPbYDDZt31Nae+2abpzcpmkF3yUiEp+SMtB37inkkuc/Y2H+ltLa45ccxwWdUz3sSkSkepIq0AuLHDe+nsukRWtLa7f0acvQ09p42JWISGQkRaA75xg95Suen/ldae3Srq144PxjKdllSUQk4fk+0F/5bCUj311S+rhHm6a8OLALtVJqROX9JuSu1vrmIuIJ3wb61CU/ct2r80ofH97kQCbd2IN6taP3I5ffgWj15h2MeHsRgEJdRKLOd4E+7/tNXPjc7NLHKTWMz4afRvOD60T9vR+ZuixgOzmAHXsKeWTqsmoHuq78RaQyvgn079b/ymmPfRxQ+/DPp3BU8/ox62HN5h37VQ+XrvxFJBwJH+jrf9nFyQ99xK6CotJaRVu+RVOLhnVZHSK8W1TzTtNoXvmLiH8kbKBv21VA/2dnsXzdr6W1Zy/rzNkdD/Osp2HZ7QKupAHq1kphWHa7ar1utK78RcRfEi7QnXNc+0oOHy5dV1q74+xjGNTjCA+7Krb3ajnSY93RuvIXEX9JuEDPW7u1NMyv7p7GyH4ZcTWX/LxOLSM+DBKtK38R8ZeEC/RjDj2Yt64/icxWDUlJkg0monXlLyL+knCBXqOGcfzhjbxuI+aiceUvIv4SndslRUQk5hToIiI+EVagm1lfM1tmZsvNbHiI5/9sZnlmttDMppnZ4ZFvVUREKlJpoJtZCvAscCaQAVxqZhnlDssFspxzHYHxwMORblRERCoWzhV6V2C5c+4759xu4A2gf9kDnHPTnXPbSx7OAbRThIhIjIUT6C2BVWUe55fU9uUaYEqoJ8xssJnlmFnO+vXrw+9SREQqFdEPRc3s90AW8Eio551zY51zWc65rGbNmkXyrUVEkl4489BXA63KPE4tqQUws97A7UBP59yuyLQnIiLhCucKfS7QxszSzewAYAAwsewBZtYJeB441zm3LsRriIhIlFV6he6cKzCzocBUIAV40Tm3xMzuAXKccxMpHmKpB/ynZF2VH5xz50a6WW3yICKyb2Hd+u+cmwxMLlcbWebr3hHuK4g2eRARqVjC3Cla0SYPIiKSQIGuTR5ERCqWMIG+r80ctMmDiEixhAn0YdntqFsrJaCmTR5ERH6TMOuha5MHEZGKJUyggzZ5EBGpSMIMuYiISMUU6CIiPqFAFxHxCQW6iIhPKNBFRHzCnHPevLHZeuD7Sg5rCvwcg3YShc5HIJ2PQDofgfx6Pg53zoXcUMKzQA+HmeU457K87iNe6HwE0vkIpPMRKBnPh4ZcRER8QoEuIuIT8R7oY71uIM7ofATS+Qik8xEo6c5HXI+hi4hI+OL9Cl1ERMKkQBcR8Ym4CHQz62tmy8xsuZkND/F8bTMbV/L852aWFvsuYyeM8/FnM8szs4VmNs3MDveiz1ip7B1R4JIAAALZSURBVHyUOe5CM3Nm5uupauGcDzO7pOR3ZImZ/TvWPcZKGP+ttDaz6WaWW/Lfy1le9BkzzjlP/wEpwLfAEcABwJdARrlj/giMKfl6ADDO6749Ph+9gANLvr4+2c9HyXH1gZnAHCDL6749/v1oA+QCjUoeN/e6bw/PxVjg+pKvM4CVXvcdzX/xcIXeFVjunPvOObcbeAPoX+6Y/sA/S74eD5xuZhbDHmOp0vPhnJvunNte8nAOkBrjHmMpnN8PgHuBh4CdsWzOA+Gcj2uBZ51zmwCcc+ti3GOshHMuHHBwydcNgDUx7C/m4iHQWwKryjzOL6mFPMY5VwBsAZrEpLvYC+d8lHUNMCWqHXmr0vNhZp2BVs65SbFszCPh/H60Bdqa2Swzm2NmfWPWXWyFcy5GAb83s3xgMvCn2LTmjYTasUgCmdnvgSygp9e9eMXMagCPAwM9biWe1KR42OVUiv96m2lmxzrnNnvalTcuBV52zj1mZicCr5pZB+dckdeNRUM8XKGvBlqVeZxaUgt5jJnVpPhPpw0x6S72wjkfmFlv4HbgXOfcrhj15oXKzkd9oAMww8xWAicAE338wWg4vx/5wETn3B7n3Arga4oD3m/CORfXAG8COOc+A+pQvGiXL8VDoM8F2phZupkdQPGHnhPLHTMRuKrk64uAj1zJpxw+VOn5MLNOwPMUh7lfx0f3qvB8OOe2OOeaOufSnHNpFH+mcK5zLsebdqMunP9eJlB8dY6ZNaV4COa7WDYZI+Gcix+A0wHM7BiKA319TLuMIc8DvWRMfCgwFVgKvOmcW2Jm95jZuSWH/QNoYmbLgT8D+5y6lujCPB+PAPWA/5jZAjMr/0vsG2Gej6QR5vmYCmwwszxgOjDMOee7v2jDPBf/C1xrZl8CrwMDfXwxqFv/RUT8wvMrdBERiQwFuoiITyjQRUR8QoEuIuITCnQREZ9QoIuI+IQCXUTEJ/4f7bWXd0T8axYAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Bias: 0.022212543739010212\n",
            "Variance: 0.08728939726794703\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this case we have an heigher bias because the prediction doesn't match perfectly the true values"
      ],
      "metadata": {
        "id": "VDZ69tAJgv4D"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Third case: data with no relation between X and Y"
      ],
      "metadata": {
        "id": "G8Ue_MJ1gopb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# importation of the necessary libraries\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# data generation (X and y has no relation between them)\n",
        "X = np.random.rand(100, 1)\n",
        "y = (np.random.rand(100, 1))\n",
        "\n",
        "# division of the data into training set and test set\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
        "\n",
        "# training the linear regression model\n",
        "reg = LinearRegression().fit(X_train, y_train)\n",
        "\n",
        "# prevision on test set\n",
        "y_pred = reg.predict(X_test)\n",
        "\n",
        "# calculation of mse\n",
        "mse = mean_squared_error(y_test, y_pred)\n",
        "\n",
        "# calculation of bias and variance\n",
        "bias = np.mean((y_test - y_pred)**2)\n",
        "variance = np.var(y_pred)\n",
        "\n",
        "# graph of the linear regression\n",
        "plt.scatter(X_test, y_test, label=\"True value\")\n",
        "plt.plot(X_test, y_pred, label=\"Prediction\")\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# result\n",
        "print(\"Bias:\", bias)\n",
        "print(\"Variance:\", variance)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "Tn_GKvZmduQV",
        "outputId": "874bafc9-9592-4265-8ad0-b141330735ff"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Bias: 0.07132226716060397\n",
            "Variance: 0.0018924772855634625\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this case we have the heigest bias, but we have a small variance, since the model predictions will all be very similar to each other (since they will all be very far from true values)"
      ],
      "metadata": {
        "id": "GpxLQkg2hExr"
      }
    }
  ]
}