02: Feature_Selection_Categorical_Variables.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "02: Feature_Selection_Categorical_Variables.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oJNS-jOQto9S"
      },
      "source": [
        "Video link of code walkthrough below is here - https://www.youtube.com/watch?v=H9AULpvRxgM"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e9bxlsmdUbGs"
      },
      "source": [
        "import warnings\n",
        "warnings.simplefilter(action='ignore', category=FutureWarning)\n",
        "\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tf-qQhw_UxRY"
      },
      "source": [
        "churn_master_df = pd.read_csv('https://raw.githubusercontent.com/srivatsan88/YouTubeLI/master/dataset/churn_data_st.csv')"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YbGZJ0M3Vit-"
      },
      "source": [
        "churn_df = churn_master_df.copy()"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3kReN7s4U0Mm",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "outputId": "d8042a4c-cf03-4d01-917e-acb5dfa367dc"
      },
      "source": [
        "churn_df.head()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>customerID</th>\n",
              "      <th>gender</th>\n",
              "      <th>SeniorCitizen</th>\n",
              "      <th>tenure</th>\n",
              "      <th>ServiceCount</th>\n",
              "      <th>Contract</th>\n",
              "      <th>PaperlessBilling</th>\n",
              "      <th>MonthlyCharges</th>\n",
              "      <th>TotalCharges</th>\n",
              "      <th>Churn</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>7590-VHVEG</td>\n",
              "      <td>Female</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>Month-to-month</td>\n",
              "      <td>Yes</td>\n",
              "      <td>29.85</td>\n",
              "      <td>29.85</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5575-GNVDE</td>\n",
              "      <td>Male</td>\n",
              "      <td>0</td>\n",
              "      <td>34</td>\n",
              "      <td>4</td>\n",
              "      <td>One year</td>\n",
              "      <td>No</td>\n",
              "      <td>56.95</td>\n",
              "      <td>1889.50</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3668-QPYBK</td>\n",
              "      <td>Male</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>Month-to-month</td>\n",
              "      <td>Yes</td>\n",
              "      <td>53.85</td>\n",
              "      <td>108.15</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>7795-CFOCW</td>\n",
              "      <td>Male</td>\n",
              "      <td>0</td>\n",
              "      <td>45</td>\n",
              "      <td>4</td>\n",
              "      <td>One year</td>\n",
              "      <td>No</td>\n",
              "      <td>42.30</td>\n",
              "      <td>1840.75</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>9237-HQITU</td>\n",
              "      <td>Female</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>Month-to-month</td>\n",
              "      <td>Yes</td>\n",
              "      <td>70.70</td>\n",
              "      <td>151.65</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   customerID  gender  SeniorCitizen  ...  MonthlyCharges  TotalCharges Churn\n",
              "0  7590-VHVEG  Female              0  ...           29.85         29.85    No\n",
              "1  5575-GNVDE    Male              0  ...           56.95       1889.50    No\n",
              "2  3668-QPYBK    Male              0  ...           53.85        108.15   Yes\n",
              "3  7795-CFOCW    Male              0  ...           42.30       1840.75    No\n",
              "4  9237-HQITU  Female              0  ...           70.70        151.65   Yes\n",
              "\n",
              "[5 rows x 10 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TDoaCC55PJxo"
      },
      "source": [
        "customerID - Customer ID\n",
        "\n",
        "Gender - Male or Female\n",
        "\n",
        "SeniorCitizen - Whether the customer is a senior citizen or not (1, 0)\n",
        "\n",
        "tenure - Number of months the customer has stayed with the company\n",
        "\n",
        "ServiceCount - Number of services/product customer has availed\n",
        "\n",
        "Contract - The contract term of the customer (Month-to-month, One year, Two year)\n",
        "\n",
        "PaperlessBilling - Whether the customer has paperless billing or not (Yes, No)\n",
        "\n",
        "MonthlyCharges - The amount charged to the customer monthly\n",
        "\n",
        "TotalCharges - The total amount charged to the customer\n",
        "\n",
        "Churn - Whether the customer churned or not (Yes or No)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q6Y8VC-FU2in",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "56811318-b1e6-42ff-bc21-6d5940cb9134"
      },
      "source": [
        "churn_df.info()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 7043 entries, 0 to 7042\n",
            "Data columns (total 10 columns):\n",
            " #   Column            Non-Null Count  Dtype  \n",
            "---  ------            --------------  -----  \n",
            " 0   customerID        7043 non-null   object \n",
            " 1   gender            7043 non-null   object \n",
            " 2   SeniorCitizen     7043 non-null   int64  \n",
            " 3   tenure            7043 non-null   int64  \n",
            " 4   ServiceCount      7043 non-null   int64  \n",
            " 5   Contract          7043 non-null   object \n",
            " 6   PaperlessBilling  7043 non-null   object \n",
            " 7   MonthlyCharges    7043 non-null   float64\n",
            " 8   TotalCharges      7016 non-null   float64\n",
            " 9   Churn             7043 non-null   object \n",
            "dtypes: float64(2), int64(3), object(5)\n",
            "memory usage: 550.4+ KB\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d-PlW4EqU7-8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2e44359-159e-4ae7-d5a7-620e6ac4bdd3"
      },
      "source": [
        "print (\"Rows     : \" ,churn_df.shape[0])\n",
        "print (\"Columns  : \" ,churn_df.shape[1])\n",
        "print (\"\\nFeatures : \\n\" ,churn_df.columns.tolist())\n",
        "print (\"\\nUnique values :  \\n\",churn_df.nunique())"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Rows     :  7043\n",
            "Columns  :  10\n",
            "\n",
            "Features : \n",
            " ['customerID', 'gender', 'SeniorCitizen', 'tenure', 'ServiceCount', 'Contract', 'PaperlessBilling', 'MonthlyCharges', 'TotalCharges', 'Churn']\n",
            "\n",
            "Unique values :  \n",
            " customerID          7043\n",
            "gender                 2\n",
            "SeniorCitizen          2\n",
            "tenure                73\n",
            "ServiceCount           9\n",
            "Contract               3\n",
            "PaperlessBilling       2\n",
            "MonthlyCharges      1585\n",
            "TotalCharges        6514\n",
            "Churn                  2\n",
            "dtype: int64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "APXNL_gUpsXs"
      },
      "source": [
        "## Null Hypothesis - There is no relationship between two categorical values\n",
        "\n",
        "## Alternate Hypothesis - There is a relationship between the two categorical values "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uCDUN6wEMoVo"
      },
      "source": [
        "Questions we are going to answer through statistical test\n",
        "\n",
        "Is there any relationship between user who have Churned to Gender of the user?\n",
        "\n",
        "Is there any relationship between users who have opted for paperless billing to user who have churned? "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xZ9xVZTpdLgS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4621aded-76a6-44e7-e4ad-5e5787b4b535"
      },
      "source": [
        "churn_df['gender'].value_counts()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Male      3555\n",
              "Female    3488\n",
              "Name: gender, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wsfhdDU2SdAu",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 332
        },
        "outputId": "a9b08a80-e2fb-47c5-8cc8-5d2a6b6feeb2"
      },
      "source": [
        "sns.set(style=\"darkgrid\")\n",
        "sns.set_palette(\"hls\", 3)\n",
        "fig, ax = plt.subplots(figsize=(20,5))\n",
        "ax = sns.countplot(x=\"gender\", hue=\"Churn\", data=churn_df)\n",
        "\n",
        "for p in ax.patches:\n",
        "    height = p.get_height()\n",
        "    ax.text(p.get_x()+p.get_width()/2.,\n",
        "            height + 3,\n",
        "            '{:1.2f}'.format(height/churn_df.shape[0]),\n",
        "            ha=\"center\") "
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1440x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sDmmaLRMh7cu"
      },
      "source": [
        "## Note: Statistics alone cannot prove anything. All the tests we do are based on relative likelihood**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0mLjcPRJScu0"
      },
      "source": [
        "gender_churn_ct=pd.crosstab(index=churn_df['gender'],columns=churn_df['Churn'])"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sy81f-69yElz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        },
        "outputId": "35bdf7ed-3bf5-41f6-e66d-8c237b1c6eb3"
      },
      "source": [
        "gender_churn_ct"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>Churn</th>\n",
              "      <th>No</th>\n",
              "      <th>Yes</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>gender</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Female</th>\n",
              "      <td>2549</td>\n",
              "      <td>939</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Male</th>\n",
              "      <td>2625</td>\n",
              "      <td>930</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "Churn     No  Yes\n",
              "gender           \n",
              "Female  2549  939\n",
              "Male    2625  930"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SINtWiVoj75r",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c0cf0f09-d099-4d86-e732-0052b24c3d35"
      },
      "source": [
        "gender_churn_ct.iloc[0].values"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2549,  939])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EB3vDqAiwOMe"
      },
      "source": [
        "*** scipy.stats.chi2_contingency(observed, correction=True, lambda_=None)[source]\n",
        "\n",
        "> Indented block\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8cm3JXvCScpE"
      },
      "source": [
        "from scipy import stats\n",
        "(chi2, p, dof,_) = stats.chi2_contingency([gender_churn_ct.iloc[0].values,gender_churn_ct.iloc[1].values])"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_rCN5lDnwGWQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "75309d41-b63e-45ba-da8e-73f15af43871"
      },
      "source": [
        "print (\"chi2     : \" ,chi2)\n",
        "print (\"p-value  : \" ,p)\n",
        "print (\"Degree for Freedom : \" ,dof)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "chi2     :  0.4840828822091383\n",
            "p-value  :  0.48657873605618596\n",
            "Degree for Freedom :  1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5DWw1tzMFoM3"
      },
      "source": [
        "Df |\t0.5 |\t0.10 |\t0.05 | 0.02 \n",
        "--| -- | -- | -- | --\n",
        "1\t| 0.455 |\t2.706\t| 3.841 |\t5.412\t\n",
        "2\t| 1.386 |\t4.605 |\t5.991\t| 7.824\t\n",
        "3\t| 2.366 |\t6.251\t| 7.815\t| 9.837\t"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "co70UAtIwqde"
      },
      "source": [
        "*** chi-square statistics\n",
        "\n",
        "****** X^2 = sum((Observed – Expected)^2 / Expected)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YiWl6GWeP-DI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 171
        },
        "outputId": "b67fbc38-0e1f-4fef-e98c-c92d6a01d3c6"
      },
      "source": [
        "pd.crosstab(index=churn_df['gender'],columns=churn_df['Churn'], margins=True)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>Churn</th>\n",
              "      <th>No</th>\n",
              "      <th>Yes</th>\n",
              "      <th>All</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>gender</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Female</th>\n",
              "      <td>2549</td>\n",
              "      <td>939</td>\n",
              "      <td>3488</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Male</th>\n",
              "      <td>2625</td>\n",
              "      <td>930</td>\n",
              "      <td>3555</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>All</th>\n",
              "      <td>5174</td>\n",
              "      <td>1869</td>\n",
              "      <td>7043</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "Churn     No   Yes   All\n",
              "gender                  \n",
              "Female  2549   939  3488\n",
              "Male    2625   930  3555\n",
              "All     5174  1869  7043"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZTHBECknvK_b"
      },
      "source": [
        "** Is there any relationship between users who have opted for paperless billing to user who have churned? **"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6UnubQBPisbc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a5f88771-9a9b-436b-9220-22cbd0959669"
      },
      "source": [
        "churn_df['PaperlessBilling'].value_counts()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Yes    4171\n",
              "No     2872\n",
              "Name: PaperlessBilling, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cRkTILtMuCIp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 332
        },
        "outputId": "2dceddca-0f4a-46f6-e6e9-98adb97b32ef"
      },
      "source": [
        "sns.set(style=\"darkgrid\")\n",
        "sns.set_palette(\"hls\", 3)\n",
        "fig, ax = plt.subplots(figsize=(20,5))\n",
        "ax = sns.countplot(x=\"PaperlessBilling\", hue=\"Churn\", data=churn_df)\n",
        "\n",
        "for p in ax.patches:\n",
        "    height = p.get_height()\n",
        "    ax.text(p.get_x()+p.get_width()/2.,\n",
        "            height + 3,\n",
        "            '{:1.2f}'.format(height/churn_df.shape[0]),\n",
        "            ha=\"center\") "
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1440x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vilUt6HhisIu"
      },
      "source": [
        "pb_churn_ct=pd.crosstab(index=churn_df['PaperlessBilling'],columns=churn_df['Churn'])"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PcjZ9coAsMrA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        },
        "outputId": "b6db4309-f70b-46fa-d213-57357a2e66d6"
      },
      "source": [
        "pb_churn_ct"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>Churn</th>\n",
              "      <th>No</th>\n",
              "      <th>Yes</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>PaperlessBilling</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>No</th>\n",
              "      <td>2403</td>\n",
              "      <td>469</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Yes</th>\n",
              "      <td>2771</td>\n",
              "      <td>1400</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "Churn               No   Yes\n",
              "PaperlessBilling            \n",
              "No                2403   469\n",
              "Yes               2771  1400"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NEdXJKpGsOaS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4a689729-0759-4121-dc68-9ec12e694d8a"
      },
      "source": [
        "pb_churn_ct.iloc[0].values"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2403,  469])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CeqZMuNAsds9"
      },
      "source": [
        "(chi2, p, dof,_) = stats.chi2_contingency([pb_churn_ct.iloc[0].values,pb_churn_ct.iloc[1].values])"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "flWIcT7XstK9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0866ed88-30ce-4cd1-fe49-0979a63c7aee"
      },
      "source": [
        "print (\"chi2     : \" ,chi2)\n",
        "print (\"p-value  : \" ,p)\n",
        "print (\"Degree for Freedom : \" ,dof)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "chi2     :  258.27764906707307\n",
            "p-value  :  4.073354668665985e-58\n",
            "Degree for Freedom :  1\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}