Linear_Regression_(Single_variable).ipynb

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  "metadata": {
    "colab": {
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      "authorship_tag": "ABX9TyPJjeEmQO2Isfd1fJO8th/p",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/PranavKhedkar/Basic-ML/blob/main/Linear_Regression_(Single_variable).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aL8rG2IRzro8"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#upload data from your PC\n",
        "from google.colab import files\n",
        "files.upload()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 197
        },
        "id": "FLY0o2_V0Bws",
        "outputId": "bcd1258b-36bb-4a8f-94b6-8fd2704a7551"
      },
      "execution_count": null,
      "outputs": [
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              "\n",
              "     <input type=\"file\" id=\"files-79d0f9e6-d5df-4b4f-a7e0-eedff07bcf14\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-79d0f9e6-d5df-4b4f-a7e0-eedff07bcf14\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
              "/**\n",
              " * @fileoverview Helpers for google.colab Python module.\n",
              " */\n",
              "(function(scope) {\n",
              "function span(text, styleAttributes = {}) {\n",
              "  const element = document.createElement('span');\n",
              "  element.textContent = text;\n",
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              "    element.style[key] = styleAttributes[key];\n",
              "  }\n",
              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
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              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
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              "\n",
              "scope.google = scope.google || {};\n",
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          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving test.csv to test.csv\n",
            "Saving train.csv to train (1).csv\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'test.csv': b'x,y\\n77,79.77515201\\n21,23.17727887\\n22,25.60926156\\n20,17.85738813\\n36,41.84986439\\n15,9.805234876\\n62,58.87465933\\n95,97.61793701\\n20,18.39512747\\n5,8.746747654\\n4,2.811415826\\n19,17.09537241\\n96,95.14907176\\n62,61.38800663\\n36,40.24701716\\n15,14.82248589\\n65,66.95806869\\n14,16.63507984\\n87,90.65513736\\n69,77.22982636\\n89,92.11906278\\n51,46.91387709\\n89,89.82634442\\n27,21.71380347\\n97,97.41206981\\n58,57.01631363\\n79,78.31056542\\n21,19.1315097\\n93,93.03483388\\n27,26.59112396\\n99,97.55155344\\n31,31.43524822\\n33,35.12724777\\n80,78.61042432\\n28,33.07112825\\n47,51.69967172\\n53,53.62235225\\n69,69.46306072\\n28,27.42497237\\n33,36.34644189\\n91,95.06140858\\n71,68.16724757\\n50,50.96155532\\n76,78.04237454\\n4,5.607664865\\n37,36.11334779\\n70,67.2352155\\n68,65.01324035\\n40,38.14753871\\n35,34.31141446\\n94,95.28503937\\n88,87.84749912\\n52,54.08170635\\n31,31.93063515\\n59,59.61247085\\n0,-1.040114209\\n39,47.49374765\\n64,62.60089773\\n69,70.9146434\\n57,56.14834113\\n13,14.05572877\\n72,68.11367147\\n76,75.59701346\\n61,59.225745\\n82,85.45504157\\n18,17.76197116\\n41,38.68888682\\n50,50.96343637\\n55,51.83503872\\n13,17.0761107\\n46,46.56141773\\n13,10.34754461\\n79,77.91032969\\n53,50.17008622\\n15,13.25690647\\n28,31.32274932\\n81,73.9308764\\n69,74.45114379\\n52,52.01932286\\n84,83.68820499\\n68,70.3698748\\n27,23.44479161\\n56,49.83051801\\n48,49.88226593\\n40,41.04525583\\n39,33.37834391\\n82,81.29750133\\n100,105.5918375\\n59,56.82457013\\n43,48.67252645\\n67,67.02150613\\n38,38.43076389\\n63,58.61466887\\n91,89.12377509\\n60,60.9105427\\n14,13.83959878\\n21,16.89085185\\n87,84.06676818\\n73,70.34969772\\n32,33.38474138\\n2,-1.63296825\\n82,88.54475895\\n19,17.44047622\\n74,75.69298554\\n42,41.97607107\\n12,12.59244741\\n1,0.275307261\\n90,98.13258005\\n89,87.45721555\\n0,-2.344738542\\n41,39.3294153\\n16,16.68715211\\n94,96.58888601\\n97,97.70342201\\n66,67.01715955\\n24,25.63476257\\n17,13.41310757\\n90,95.15647284\\n13,9.744164258\\n0,-3.467883789\\n64,62.82816355\\n96,97.27405461\\n98,95.58017185\\n12,7.468501839\\n41,45.44599591\\n47,46.69013968\\n78,74.4993599\\n20,21.63500655\\n89,91.59548851\\n29,26.49487961\\n64,67.38654703\\n75,74.25362837\\n12,12.07991648\\n25,21.32273728\\n28,29.31770045\\n30,26.48713683\\n65,68.94699774\\n59,59.10598995\\n64,64.37521087\\n53,60.20758349\\n71,70.34329706\\n97,97.1082562\\n73,75.7584178\\n9,10.80462727\\n12,12.11219941\\n63,63.28312382\\n99,98.03017721\\n60,63.19354354\\n35,34.8534823\\n2,-2.819913974\\n60,59.8313966\\n32,29.38505024\\n94,97.00148372\\n84,85.18657275\\n63,61.74063192\\n22,18.84798163\\n81,78.79008525\\n93,95.12400481\\n33,30.48881287\\n7,10.41468095\\n42,38.98317436\\n46,46.11021062\\n54,52.45103628\\n16,21.16523945\\n49,52.28620611\\n43,44.18863945\\n95,97.13832018\\n66,67.22008001\\n21,18.98322306\\n35,24.3884599\\n80,79.44769523\\n37,40.03504862\\n54,53.32005764\\n56,54.55446979\\n1,-2.761182595\\n32,37.80182795\\n58,57.48741435\\n32,36.06292994\\n46,49.83538167\\n72,74.68953276\\n17,14.86159401\\n97,101.0697879\\n93,99.43577876\\n91,91.69240746\\n37,34.12473248\\n4,6.079390073\\n54,59.07247174\\n51,56.43046022\\n27,30.49412933\\n46,48.35172635\\n92,89.73153611\\n73,72.86282528\\n77,80.97144285\\n91,91.36566374\\n61,60.07137496\\n99,99.87382707\\n4,8.655714172\\n72,69.39858505\\n19,19.38780134\\n57,53.11628433\\n78,78.39683006\\n26,25.75612514\\n74,75.07484683\\n90,92.88772282\\n66,69.45498498\\n13,13.12109842\\n40,48.09843134\\n77,79.3142548\\n67,68.48820749\\n75,73.2300846\\n23,24.68362712\\n45,41.90368917\\n59,62.22635684\\n44,45.96396877\\n23,23.52647153\\n55,51.80035866\\n55,51.10774273\\n95,95.79747345\\n12,9.241138977\\n4,7.646529763\\n7,9.281699753\\n100,103.5266162\\n48,47.41006725\\n42,42.03835773\\n96,96.11982476\\n39,38.05766408\\n100,105.4503788\\n87,88.80306911\\n14,15.49301141\\n14,12.42624606\\n37,40.00709598\\n5,5.634030902\\n88,87.36938931\\n91,89.73951993\\n65,66.61499643\\n74,72.9138853\\n56,57.19103506\\n16,11.21710477\\n5,0.676076749\\n28,28.15668543\\n92,95.3958003\\n46,52.05490703\\n54,59.70864577\\n39,36.79224762\\n44,37.08457698\\n31,24.18437976\\n68,67.28725332\\n86,82.870594\\n90,89.899991\\n38,36.94173178\\n21,19.87562242\\n95,90.71481654\\n56,61.09367762\\n60,60.11134958\\n65,64.83296316\\n78,81.40381769\\n89,92.40217686\\n6,2.576625376\\n67,63.80768172\\n36,38.67780759\\n16,16.82839701\\n100,99.78687252\\n45,44.68913433\\n73,71.00377824\\n57,51.57326718\\n20,19.87846479\\n76,79.50341495\\n34,34.58876491\\n55,55.7383467\\n72,68.19721905\\n55,55.81628509\\n8,9.391416798\\n56,56.01448111\\n72,77.9969477\\n58,55.37049953\\n6,11.89457829\\n96,94.79081712\\n23,25.69041546\\n58,53.52042319\\n23,18.31396758\\n19,21.42637785\\n25,30.41303282\\n64,67.68142149\\n21,17.0854783\\n59,60.91792707\\n19,14.99514319\\n16,16.74923937\\n42,41.46923883\\n43,42.84526108\\n61,59.12912974\\n92,91.30863673\\n11,8.673336357\\n41,39.31485292\\n1,5.313686205\\n8,5.405220518\\n71,68.5458879\\n46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              " 'train (1).csv': 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            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train = pd.read_csv('train.csv')\n",
        "test = pd.read_csv('test.csv')"
      ],
      "metadata": {
        "id": "qI2XS25k0ddF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Data preprocessing"
      ],
      "metadata": {
        "id": "h09iXRzlOmOM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Shape of the data\n",
        "print(train.head(),'\\n',train.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pxFKldO50kvB",
        "outputId": "fd89cf4b-6542-4a28-d7d8-c19e6727ae9e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "      x          y\n",
            "0  24.0  21.549452\n",
            "1  50.0  47.464463\n",
            "2  15.0  17.218656\n",
            "3  38.0  36.586398\n",
            "4  87.0  87.288984 \n",
            " (700, 2)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#null values\n",
        "train.isnull().sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eA4XUYHj0pKd",
        "outputId": "7437e65b-e2b3-4624-e961-a7588803e3bc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "x    0\n",
              "y    1\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Drop the single row having NaN value\n",
        "train = train.dropna()"
      ],
      "metadata": {
        "id": "JEh5wjyoBote"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Data Visualization"
      ],
      "metadata": {
        "id": "s22wt_U5OsIH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "rlRUKCh32a3D"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Scatter Plot of Training data\n",
        "%matplotlib inline\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.scatter(train.x,train.y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "jRC1pd3R2SZV",
        "outputId": "c2b86a4f-67e7-403b-881b-71e2bee754ef"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7faf9237a6e0>"
            ]
          },
          "metadata": {},
          "execution_count": 57
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Linear Regression Model"
      ],
      "metadata": {
        "id": "spB0wjh7O653"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import LinearRegression"
      ],
      "metadata": {
        "id": "EXhslGTJ7WLj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "lreg = LinearRegression()"
      ],
      "metadata": {
        "id": "a8UcMDDS7vWD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x = train['x'].to_numpy() #x needs to be converted to a numpy array for training our model\n",
        "y = train['y']\n",
        "print(type(x))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3VoZP7fh8LRh",
        "outputId": "0b7943bb-ae69-49ba-8f4c-dc324ba00ea9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'numpy.ndarray'>\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "lreg.fit(x.reshape(-1, 1),y)\n",
        "#The Linear Regression model from sklearn need multiple features(Atleast 2) for training and testing.\n",
        "#Since we provide a single feature we need to reshape it to add an empty feature."
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "hi9PVDDU72ot",
        "outputId": "68384a8b-2a49-4ea7-f730-9d0a21872eac"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = lreg.predict(test['x'].to_numpy().reshape(-1,1))"
      ],
      "metadata": {
        "id": "UlCr3W2SCcTy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Model Evaluation"
      ],
      "metadata": {
        "id": "7eWCPofLPDyb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import mean_squared_error\n",
        "\n",
        "# Calculate the mean squared error\n",
        "mse = mean_squared_error(test['y'], y_predicted)\n",
        "\n",
        "print('Mean squared error:', mse)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gTTsh1WOC1X6",
        "outputId": "6f7407c5-c4cb-410e-cef3-12124b096597"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean squared error: 9.432922192039305\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(test['x'],test['y'])\n",
        "plt.plot(test['x'], y_predicted, color=\"black\", linewidth=3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "LY_sapBxDSE5",
        "outputId": "44deef6f-d32b-4fc5-a220-43170e095b13"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7faf90852050>]"
            ]
          },
          "metadata": {},
          "execution_count": 79
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}