A6_LogisticRegression.ipynb

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        "\n",
        "```\n",
        "Lakshay Singla\n",
        "102003371\n",
        "3CO15\n",
        "\n",
        "Submission of ASSIGNMENT 6\n",
        "```\n",
        "\n"
      ],
      "metadata": {
        "id": "rznRNAPWrWpR"
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    {
      "cell_type": "markdown",
      "source": [
        "# **ASSIGNMENT_6_LOGISTIC_REGRESSION**"
      ],
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        "id": "FEl3ZKS-iJXX"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FFODdorbJFBu"
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      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as py\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **QUESTION 1**"
      ],
      "metadata": {
        "id": "OQTmbcWAHBoU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import datasets\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "iris = datasets.load_iris() \n",
        "df = pd.DataFrame(iris.data)\n",
        "df['target'] = iris.target"
      ],
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        "id": "4uvF1ipeSTMl"
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      "execution_count": null,
      "outputs": []
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      "source": [
        "df.head()"
      ],
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              "     0    1    2    3  target\n",
              "0  5.1  3.5  1.4  0.2       0\n",
              "1  4.9  3.0  1.4  0.2       0\n",
              "2  4.7  3.2  1.3  0.2       0\n",
              "3  4.6  3.1  1.5  0.2       0\n",
              "4  5.0  3.6  1.4  0.2       0"
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              "      <th>3</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
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              "      <th>3</th>\n",
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              "                                                     [key], {});\n",
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              "            + ' to learn more about interactive tables.';\n",
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        "from sklearn.model_selection import train_test_split\n",
        "x = df.iloc[:,:-1]\n",
        "y = df.iloc[:,-1]\n",
        "x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2,random_state=3)\n",
        "\n",
        "trainer = MinMaxScaler()\n",
        "trainer = trainer.fit_transform(x_train,y_train)\n",
        "\n",
        "tester = MinMaxScaler()\n",
        "tester = tester.fit_transform(x_test,y_test)"
      ],
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        "id": "T3zzbjmuiWG3"
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        "trainer.shape"
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              "(120, 4)"
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          "execution_count": 5
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      "source": [
        "df_train = pd.DataFrame(df)\n",
        "df_train.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid','target']\n",
        "df_train.head()"
      ],
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            "text/plain": [
              "   sepal_len  sepal_wid  petal_len  petal_wid  target\n",
              "0        5.1        3.5        1.4        0.2       0\n",
              "1        4.9        3.0        1.4        0.2       0\n",
              "2        4.7        3.2        1.3        0.2       0\n",
              "3        4.6        3.1        1.5        0.2       0\n",
              "4        5.0        3.6        1.4        0.2       0"
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              "      <th>sepal_len</th>\n",
              "      <th>sepal_wid</th>\n",
              "      <th>petal_len</th>\n",
              "      <th>petal_wid</th>\n",
              "      <th>target</th>\n",
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              "      <td>5.1</td>\n",
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        "df.insert(0, \"ones\", 1, True)\n",
        "n = df.shape[0]\n",
        "alpha = 0.01"
      ],
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        "id": "TFrpRH6aeIc5"
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      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df1 = df.copy()\n",
        "df2 = df.copy()\n",
        "df3 = df.copy()"
      ],
      "metadata": {
        "id": "D5aI-h7cpNuW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def ConvertToBinary(df,ind):\n",
        "  df.is_copy = False\n",
        "  for i in range(0,n):\n",
        "    if df.iloc[i,5] == ind:\n",
        "      df.iloc[i,5]  = 1 \n",
        "    elif df.iloc[i,5] != ind:\n",
        "      df.iloc[i,5]  = 0\n",
        "  print(df)\n",
        "  return df"
      ],
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        "id": "6uwmMi62oQIF"
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      "execution_count": null,
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    },
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      "cell_type": "code",
      "source": [
        "df1=ConvertToBinary(df1,0)\n",
        "df2=ConvertToBinary(df2,1)\n",
        "df3=ConvertToBinary(df3,2)"
      ],
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        "id": "CnfptgDgmpnW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6d328b35-82c2-4463-ba5d-1503a2d831d5"
      },
      "execution_count": null,
      "outputs": [
        {
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          "text": [
            "     ones  sepal_len  sepal_wid  petal_len  petal_wid  target\n",
            "0       1        5.1        3.5        1.4        0.2       1\n",
            "1       1        4.9        3.0        1.4        0.2       1\n",
            "2       1        4.7        3.2        1.3        0.2       1\n",
            "3       1        4.6        3.1        1.5        0.2       1\n",
            "4       1        5.0        3.6        1.4        0.2       1\n",
            "..    ...        ...        ...        ...        ...     ...\n",
            "145     1        6.7        3.0        5.2        2.3       0\n",
            "146     1        6.3        2.5        5.0        1.9       0\n",
            "147     1        6.5        3.0        5.2        2.0       0\n",
            "148     1        6.2        3.4        5.4        2.3       0\n",
            "149     1        5.9        3.0        5.1        1.8       0\n",
            "\n",
            "[150 rows x 6 columns]\n",
            "     ones  sepal_len  sepal_wid  petal_len  petal_wid  target\n",
            "0       1        5.1        3.5        1.4        0.2       0\n",
            "1       1        4.9        3.0        1.4        0.2       0\n",
            "2       1        4.7        3.2        1.3        0.2       0\n",
            "3       1        4.6        3.1        1.5        0.2       0\n",
            "4       1        5.0        3.6        1.4        0.2       0\n",
            "..    ...        ...        ...        ...        ...     ...\n",
            "145     1        6.7        3.0        5.2        2.3       0\n",
            "146     1        6.3        2.5        5.0        1.9       0\n",
            "147     1        6.5        3.0        5.2        2.0       0\n",
            "148     1        6.2        3.4        5.4        2.3       0\n",
            "149     1        5.9        3.0        5.1        1.8       0\n",
            "\n",
            "[150 rows x 6 columns]\n",
            "     ones  sepal_len  sepal_wid  petal_len  petal_wid  target\n",
            "0       1        5.1        3.5        1.4        0.2       0\n",
            "1       1        4.9        3.0        1.4        0.2       0\n",
            "2       1        4.7        3.2        1.3        0.2       0\n",
            "3       1        4.6        3.1        1.5        0.2       0\n",
            "4       1        5.0        3.6        1.4        0.2       0\n",
            "..    ...        ...        ...        ...        ...     ...\n",
            "145     1        6.7        3.0        5.2        2.3       1\n",
            "146     1        6.3        2.5        5.0        1.9       1\n",
            "147     1        6.5        3.0        5.2        2.0       1\n",
            "148     1        6.2        3.4        5.4        2.3       1\n",
            "149     1        5.9        3.0        5.1        1.8       1\n",
            "\n",
            "[150 rows x 6 columns]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**REAL CODE STARTS HERE**"
      ],
      "metadata": {
        "id": "zV_5QoObGS-1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "beta_count = df.shape[1]-1\n",
        "beta1 = np.zeros(beta_count)\n",
        "beta2 = np.zeros(beta_count)\n",
        "beta3 = np.zeros(beta_count)"
      ],
      "metadata": {
        "id": "AA_1ZT7fKCQw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def findBetas(df,beta):\n",
        "  x = df.iloc[:,:-1]\n",
        "  y = df.iloc[:,-1]\n",
        "  for iteration in range(5000):\n",
        "    print(iteration)\n",
        "    z = np.dot(x,beta)\n",
        "    for j in range(beta_count):\n",
        "      t_dJ=0\n",
        "      for i in range(n):\n",
        "        hypo = 1/(1+np.exp(-z[i]))\n",
        "        dJ = (hypo - y[i])*x.iloc[i,j]\n",
        "        t_dJ+=dJ\n",
        "      beta[j]-=(alpha/n)*t_dJ \n",
        "  return beta"
      ],
      "metadata": {
        "id": "Z93-xN_VG3M0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "beta1 =findBetas(df1,beta1)\n",
        "beta2 =findBetas(df2,beta2)\n",
        "beta3 =findBetas(df3,beta3)"
      ],
      "metadata": {
        "id": "QGz48u_L3y_3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(beta1)\n",
        "print(beta2)\n",
        "print(beta3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dJK4NHF7srCs",
        "outputId": "8cad3f73-844e-4d0b-f6f1-ba450ecb82d1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 0.28693488  0.45010713  1.53318488 -2.40404209 -1.08580724]\n",
            "[ 0.4074006   0.40638772 -1.34346969  0.42800077 -0.94167673]\n",
            "[-0.80469168 -1.57367763 -1.4148281   2.33322675  2.01157281]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def findProb(df,beta):\n",
        "  x = df.iloc[:,:-1]\n",
        "  z = np.dot(x,beta)\n",
        "  fx = 1/(1+np.exp(-z))\n",
        "  for i in range(n):\n",
        "    if fx[i]<0.5:\n",
        "      fx[i]=0\n",
        "  return fx"
      ],
      "metadata": {
        "id": "BHVSAi0ds2Wk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p1=findProb(df1,beta1)\n",
        "p2=findProb(df2,beta2)\n",
        "p3=findProb(df3,beta3)"
      ],
      "metadata": {
        "id": "_g4im1VwcmnS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p2[0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bMxjPBeHze0m",
        "outputId": "0a9ac441-d85c-4455-f14d-98e092406ac3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "p1[3]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7GPqlPrszZOd",
        "outputId": "7c331df5-92f5-4ead-c750-990e49ee8224"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9639827781628152"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_predict = np.zeros(n)\n",
        "for i in range(n):\n",
        "  if p1[i]>=p2[i] and p1[i]>=p3[i]:\n",
        "    y_predict[i] = 0\n",
        "  elif (p2[i]>=p3[i] and p2[i]>=p1[i]):\n",
        "    y_predict[i] = 1\n",
        "  else:\n",
        "    y_predict[i] = 2"
      ],
      "metadata": {
        "id": "VfYIgzk7y8BU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def findAccuracy(x,y):\n",
        "  count = 0\n",
        "  for i in range(n):\n",
        "    if(x[i]==y[i]):\n",
        "      count+=1\n",
        "  accuracy = (count/n)*100\n",
        "  print(accuracy)"
      ],
      "metadata": {
        "id": "k3mbMf1leG1_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "findAccuracy(y,y_predict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AWT863rgePey",
        "outputId": "2922162a-d9fa-4660-9da0-1646b6400db0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "76.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Question 2**"
      ],
      "metadata": {
        "id": "tA_EplOpqRxL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### ***`Question`*** 2(i)\n"
      ],
      "metadata": {
        "id": "V3Ms8V5XJ_B7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "exam = pd.read_csv('exam6.txt',header = None)\n",
        "exam.head(2)"
      ],
      "metadata": {
        "id": "LknAfzk0egmc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "outputId": "20006785-5ed5-4307-c6b0-b5bd041445b2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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        "exam.head(2)"
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          "height": 112
        },
        "id": "yggDpX7C7YgR",
        "outputId": "1f869caf-37f2-4719-87bb-77addce55522"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-a82033b1-b8b6-45c1-9905-c0f8e1d73894 button.colab-df-convert');\n",
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              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-a82033b1-b8b6-45c1-9905-c0f8e1d73894');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
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      "source": [
        "exam.drop(['x1_2'],axis=1,inplace = True)\n",
        "exam"
      ],
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          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "CApebWlresRU",
        "outputId": "21700480-d2a8-4d1c-cbe2-fd40d5e492df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "            0         1  2\n",
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              "116 -0.006336  0.999270  0\n",
              "117  0.632650 -0.030612  0\n",
              "\n",
              "[118 rows x 3 columns]"
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              "      <td>0.465640</td>\n",
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              "      <td>-0.593890</td>\n",
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              "      <th>115</th>\n",
              "      <td>-0.484450</td>\n",
              "      <td>0.999270</td>\n",
              "      <td>0</td>\n",
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              "    <tr>\n",
              "      <th>116</th>\n",
              "      <td>-0.006336</td>\n",
              "      <td>0.999270</td>\n",
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              "      <th>117</th>\n",
              "      <td>0.632650</td>\n",
              "      <td>-0.030612</td>\n",
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              "  </tbody>\n",
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              "<p>118 rows × 3 columns</p>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
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              "    .colab-df-container {\n",
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              "\n",
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              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
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              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-464fb085-16c5-4a9e-ab38-403020858060');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# exam.drop(['x1_3','x11_3','x111_3'],axis = 1,inplace = True)\n",
        "exam"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "T3AjsRcfhbli",
        "outputId": "6f29fd67-2d69-41d5-b531-06a067985eb0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     ones         0         1      x1_2      x2_2      x2_3  2\n",
              "0       1  0.051267  0.699560  0.002628  0.489384  0.342354  1\n",
              "1       1 -0.092742  0.684940  0.008601  0.469143  0.321335  1\n",
              "2       1 -0.213710  0.692250  0.045672  0.479210  0.331733  1\n",
              "3       1 -0.375000  0.502190  0.140625  0.252195  0.126650  1\n",
              "4       1 -0.513250  0.465640  0.263426  0.216821  0.100960  1\n",
              "..    ...       ...       ...       ...       ...       ... ..\n",
              "113     1 -0.720620  0.538740  0.519293  0.290241  0.156364  0\n",
              "114     1 -0.593890  0.494880  0.352705  0.244906  0.121199  0\n",
              "115     1 -0.484450  0.999270  0.234692  0.998541  0.997812  0\n",
              "116     1 -0.006336  0.999270  0.000040  0.998541  0.997812  0\n",
              "117     1  0.632650 -0.030612  0.400246  0.000937 -0.000029  0\n",
              "\n",
              "[118 rows x 7 columns]"
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              "      <td>0.263426</td>\n",
              "      <td>0.216821</td>\n",
              "      <td>0.100960</td>\n",
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              "      <td>0.156364</td>\n",
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              "    <tr>\n",
              "      <th>114</th>\n",
              "      <td>1</td>\n",
              "      <td>-0.593890</td>\n",
              "      <td>0.494880</td>\n",
              "      <td>0.352705</td>\n",
              "      <td>0.244906</td>\n",
              "      <td>0.121199</td>\n",
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              "      <th>115</th>\n",
              "      <td>1</td>\n",
              "      <td>-0.484450</td>\n",
              "      <td>0.999270</td>\n",
              "      <td>0.234692</td>\n",
              "      <td>0.998541</td>\n",
              "      <td>0.997812</td>\n",
              "      <td>0</td>\n",
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              "    <tr>\n",
              "      <th>116</th>\n",
              "      <td>1</td>\n",
              "      <td>-0.006336</td>\n",
              "      <td>0.999270</td>\n",
              "      <td>0.000040</td>\n",
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              "      <th>117</th>\n",
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              "      <td>0.400246</td>\n",
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              "      <td>-0.000029</td>\n",
              "      <td>0</td>\n",
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              "  </tbody>\n",
              "</table>\n",
              "<p>118 rows × 7 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-bc83e7d8-a5ec-442a-a075-5bc12627953d')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
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              "      display:flex;\n",
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              "      gap: 12px;\n",
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              "\n",
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              "      background-color: #E8F0FE;\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-bc83e7d8-a5ec-442a-a075-5bc12627953d button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-bc83e7d8-a5ec-442a-a075-5bc12627953d');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "exam.insert(exam.shape[1]-1,\"x1_2\",exam[0]**2)\n",
        "exam.insert(exam.shape[1]-1,\"x2_2\",exam[1]**2)\n",
        "exam.insert(exam.shape[1]-1,\"x2_3\",exam[1]**3)\n",
        "exam.insert(exam.shape[1]-1,\"x1_3\",exam[0]**3)\n",
        "exam.insert(exam.shape[1]-1,\"x1_4\",exam[0]**4)\n",
        "exam.insert(exam.shape[1]-1,\"x2_4\",exam[1]**4)\n",
        "exam.insert(0,\"ones\",1,True)\n",
        "exam"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "mMBj2vv07C9I",
        "outputId": "770d5e2c-7c76-4590-83a5-fee19721c3b8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     ones         0         1      x1_2      x2_2      x2_3          x1_3  \\\n",
              "0       1  0.051267  0.699560  0.002628  0.489384  0.342354  1.347453e-04   \n",
              "1       1 -0.092742  0.684940  0.008601  0.469143  0.321335 -7.976812e-04   \n",
              "2       1 -0.213710  0.692250  0.045672  0.479210  0.331733 -9.760555e-03   \n",
              "3       1 -0.375000  0.502190  0.140625  0.252195  0.126650 -5.273438e-02   \n",
              "4       1 -0.513250  0.465640  0.263426  0.216821  0.100960 -1.352032e-01   \n",
              "..    ...       ...       ...       ...       ...       ...           ...   \n",
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              "\n",
              "             x1_4          x2_4  2  \n",
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              "..            ...           ... ..  \n",
              "113  2.696654e-01  8.423971e-02  0  \n",
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              "115  5.508024e-02  9.970832e-01  0  \n",
              "116  1.612020e-09  9.970832e-01  0  \n",
              "117  1.601969e-01  8.781462e-07  0  \n",
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            ]
          },
          "metadata": {},
          "execution_count": 116
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n = exam.shape[0]\n",
        "alpha = 10\n",
        "beta_count = exam.shape[1]\n",
        "beta = np.zeros(beta_count-1)"
      ],
      "metadata": {
        "id": "bVhdMRVM6I3o"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def findBetas(df,beta):\n",
        "  x = df.iloc[:,:-1]\n",
        "  y = df.iloc[:,-1]\n",
        "  for iteration in range(1000):\n",
        "    print(iteration)\n",
        "    z = np.dot(x,beta)\n",
        "    for j in range(beta_count-1):\n",
        "      t_dJ=0\n",
        "      for i in range(n):\n",
        "        hypo = 1/(1+np.exp(-z[i]))\n",
        "        dJ = (hypo - y[i])*x.iloc[i,j]\n",
        "        t_dJ+=dJ\n",
        "      beta[j]-=(alpha/n)*t_dJ \n",
        "  return beta"
      ],
      "metadata": {
        "id": "9JpUWw8l5a2Q"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "beta = findBetas(exam,beta)"
      ],
      "metadata": {
        "id": "HT4CGDs75xIu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "beta"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oKA0ZrHH54bi",
        "outputId": "0b7520bc-636b-4558-d19b-a4ee0cc45b54"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 3.12240582,  0.50691247,  3.08012648, -3.43596764, -5.58370252,\n",
              "       -2.4152913 ,  2.72967317, -9.11691845, -1.16760715])"
            ]
          },
          "metadata": {},
          "execution_count": 120
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def findProb(df,beta):\n",
        "  x = df.iloc[:,:-1]\n",
        "  z = np.dot(x,beta)\n",
        "  fx = 1/(1+np.exp(-z))\n",
        "  for i in range(n):\n",
        "    if fx[i]<0.5:\n",
        "      fx[i]=0\n",
        "    else: fx[i]=1\n",
        "  return fx"
      ],
      "metadata": {
        "id": "S7zwudT06ZFh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p = findProb(exam,beta)\n",
        "p"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1_5io7kD6fKV",
        "outputId": "f7d94828-2d28-4a36-99c5-981b76920ce2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 1., 0., 1., 1., 1.,\n",
              "       1., 1., 1., 0., 0., 0., 1., 1., 0., 0., 0., 1., 0., 0., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 0., 0., 1., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0., 1., 0.,\n",
              "       0., 0., 0., 1., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 1., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.])"
            ]
          },
          "metadata": {},
          "execution_count": 122
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "exam.iloc[:,-1]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k1ZPovcoeihF",
        "outputId": "3ba0c39c-5e92-42af-990a-4c4225d84121"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0      1\n",
              "1      1\n",
              "2      1\n",
              "3      1\n",
              "4      1\n",
              "      ..\n",
              "113    0\n",
              "114    0\n",
              "115    0\n",
              "116    0\n",
              "117    0\n",
              "Name: 2, Length: 118, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def findAccuracy(x,y):\n",
        "  count = 0\n",
        "  for i in range(n):\n",
        "    if(x[i]==y[i]):\n",
        "      count+=1\n",
        "  accuracy = (count/n)*100\n",
        "  print(accuracy)"
      ],
      "metadata": {
        "id": "EDCsTyG46it8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "findAccuracy(exam.iloc[:,-1],p)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_Y9uYu2T6jeW",
        "outputId": "2e3789ce-809c-4e93-875d-21c34ee7e080"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "80.50847457627118\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# x1_2 = 56%\n",
        "# & x2_2 = 80.5%\n",
        "# x11_3 =x2_3  = 78%\n",
        "# x1_3 = 78%\n"
      ],
      "metadata": {
        "id": "dxNO2BZE63ie"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### ***`QUESTION 2(ii)`***"
      ],
      "metadata": {
        "id": "zKGfdTF5mPKU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "exam"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "OuBn1aYeoQUS",
        "outputId": "30a62c32-6671-41d7-9f1f-58de74e30083"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     ones         0         1      x1_2      x2_2      x2_3          x1_3  \\\n",
              "0       1  0.051267  0.699560  0.002628  0.489384  0.342354  1.347453e-04   \n",
              "1       1 -0.092742  0.684940  0.008601  0.469143  0.321335 -7.976812e-04   \n",
              "2       1 -0.213710  0.692250  0.045672  0.479210  0.331733 -9.760555e-03   \n",
              "3       1 -0.375000  0.502190  0.140625  0.252195  0.126650 -5.273438e-02   \n",
              "4       1 -0.513250  0.465640  0.263426  0.216821  0.100960 -1.352032e-01   \n",
              "..    ...       ...       ...       ...       ...       ...           ...   \n",
              "113     1 -0.720620  0.538740  0.519293  0.290241  0.156364 -3.742131e-01   \n",
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            ]
          },
          "metadata": {},
          "execution_count": 130
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n = exam.shape[0]\n",
        "lam = 0.2\n",
        "alpha = 10\n",
        "beta_count = exam.shape[1]\n",
        "beta = np.zeros(beta_count-1)"
      ],
      "metadata": {
        "id": "W9a4FPwIn7Bz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def findBetas(df,beta):\n",
        "  x = df.iloc[:,:-1]\n",
        "  y = df.iloc[:,-1]\n",
        "  for iteration in range(1000):\n",
        "    print(iteration)\n",
        "    z = np.dot(x,beta)\n",
        "    for j in range(beta_count-1):\n",
        "      t_dJ=0\n",
        "      for i in range(n):\n",
        "        hypo = 1/(1+np.exp(-z[i]))\n",
        "        dJ = (hypo - y[i])*x.iloc[i,j]+(lam/n)*beta[j]\n",
        "        t_dJ+=dJ\n",
        "      beta[j]-=(alpha/n)*t_dJ \n",
        "  return beta"
      ],
      "metadata": {
        "id": "BzUHyAgKgo9d"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "beta = findBetas(exam,beta)\n",
        "beta"
      ],
      "metadata": {
        "id": "UTVi6azUoFhq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "beta"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eSDUhF35pOZI",
        "outputId": "787452af-d955-4721-be61-3463c55dde9d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2.98680855,  0.83247894,  2.15600326, -3.93892338, -2.83407251,\n",
              "       -0.89673653,  0.34134519, -3.35978371, -2.69929316])"
            ]
          },
          "metadata": {},
          "execution_count": 134
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "p = findProb(exam,beta)\n",
        "findAccuracy(exam.iloc[:,-1],p)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HyWrUXU0oebf",
        "outputId": "753b3dff-11bb-408a-dc50-047efbaed986"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "77.11864406779661\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "AjMwobsGoqSJ"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}