(4) Logistic Regression.ipynb

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  "metadata": {
    "colab": {
      "name": "(4) Logistic Regression.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IDH1OhdTacNU"
      },
      "source": [
        "BY: **RIYA JOSHI**\n",
        "\n",
        "EMAIL: riya.joshi@somaiya.edu"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q0_w7ibtamAB"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "### **Basic idea behind Logistic regression algorithm**:\n",
        "\n",
        "*   Logistic regression, contrary to the name, is a classification algorithm.\n",
        "* It is mainly used for binary classification but with some modification we can use it for multi-class classification too.\n",
        "* It transforms the output into a probability value (i.e. a number between 0 and 1) using what is known as the logistic sigmoid function. \n",
        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)\n",
        "* The function is called the sigmoid function because it is s-shaped. Here is what the sigmoid function looks like in mathematical notation:\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "       h(z) is the predicted probability of a given instance (i.e. example) being in the positive class…that is the class represented as 1 in a data set. \n",
        "\n",
        "       1- h(z) is the probability of an instance being in the negative class, the class represented as 0 \n",
        "\n",
        "       z is the input (e.g. a weighted sum of the attributes of a given instance)\n",
        "\n",
        "\n",
        "* z is commonly expressed as the dot product, w · x, where w is a 1-dimensional vector containing the weights for each attribute, and x is a vector containing the values of each attribute for a specific instance of the data set\n",
        "* Often the dot product, w · x, is written as matrix multiplication. In that case, z = wTx where T means transpose of the single dimensional weight vector w. The symbol Ɵ is often used in place of w.\n",
        "\n",
        "So substituting w · x into the sigmoid equation, we get the following equation:\n",
        "\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "      w is a 1-dimensional vector containing the weights for each attribute.\n",
        "\n",
        "      The subscript w on hw means the attributes x are weighted by the weight vector w.\n",
        "\n",
        "      hw(x) is the probability (a value between 0 and 1) that an instance is a member of the positive class.\n",
        "\n",
        "      x is a vector containing the values of each attribute for a specific instance of the data set.\n",
        "\n",
        "      w · x = w1x1 + w2x2 + …. + wdxd + b  \n",
        "      (b: bias)\n",
        "\n",
        "      d is the number of attributes in the data set\n",
        "\n",
        "      \n",
        "\n",
        "\n",
        "### **Applications of Logistic regression**:\n",
        "* Binary Classification  (mostly)\n",
        "* In various fields, including machine learning, most medical fields, social sciences and gaming.\n",
        "*  Conditional random fields, an extension of logistic regression to sequential data, are used in natural language processing.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CjP1gbbiaW6d"
      },
      "source": [
        "# Importing required libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import style\n",
        "\n",
        "from sklearn.metrics import accuracy_score,confusion_matrix\n",
        "from sklearn.preprocessing import LabelEncoder\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ],
      "execution_count": 205,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 502
        },
        "id": "pONNuqe5a6Qz",
        "outputId": "4e919586-a7bb-4ca7-d599-6f2f60203716"
      },
      "source": [
        "df = pd.read_csv('players_20.csv') #importing dataset\n",
        "df.head() # displaying first five records"
      ],
      "execution_count": 206,
      "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>sofifa_id</th>\n",
              "      <th>player_url</th>\n",
              "      <th>short_name</th>\n",
              "      <th>long_name</th>\n",
              "      <th>age</th>\n",
              "      <th>dob</th>\n",
              "      <th>height_cm</th>\n",
              "      <th>weight_kg</th>\n",
              "      <th>nationality</th>\n",
              "      <th>club</th>\n",
              "      <th>overall</th>\n",
              "      <th>potential</th>\n",
              "      <th>value_eur</th>\n",
              "      <th>wage_eur</th>\n",
              "      <th>player_positions</th>\n",
              "      <th>preferred_foot</th>\n",
              "      <th>international_reputation</th>\n",
              "      <th>weak_foot</th>\n",
              "      <th>skill_moves</th>\n",
              "      <th>work_rate</th>\n",
              "      <th>body_type</th>\n",
              "      <th>real_face</th>\n",
              "      <th>release_clause_eur</th>\n",
              "      <th>player_tags</th>\n",
              "      <th>team_position</th>\n",
              "      <th>team_jersey_number</th>\n",
              "      <th>loaned_from</th>\n",
              "      <th>joined</th>\n",
              "      <th>contract_valid_until</th>\n",
              "      <th>nation_position</th>\n",
              "      <th>nation_jersey_number</th>\n",
              "      <th>pace</th>\n",
              "      <th>shooting</th>\n",
              "      <th>passing</th>\n",
              "      <th>dribbling</th>\n",
              "      <th>defending</th>\n",
              "      <th>physic</th>\n",
              "      <th>player_traits</th>\n",
              "      <th>attacking_crossing</th>\n",
              "      <th>attacking_finishing</th>\n",
              "      <th>attacking_heading_accuracy</th>\n",
              "      <th>attacking_short_passing</th>\n",
              "      <th>attacking_volleys</th>\n",
              "      <th>skill_dribbling</th>\n",
              "      <th>skill_curve</th>\n",
              "      <th>skill_fk_accuracy</th>\n",
              "      <th>skill_long_passing</th>\n",
              "      <th>skill_ball_control</th>\n",
              "      <th>movement_acceleration</th>\n",
              "      <th>movement_sprint_speed</th>\n",
              "      <th>movement_agility</th>\n",
              "      <th>movement_reactions</th>\n",
              "      <th>movement_balance</th>\n",
              "      <th>power_shot_power</th>\n",
              "      <th>power_jumping</th>\n",
              "      <th>power_stamina</th>\n",
              "      <th>power_strength</th>\n",
              "      <th>power_long_shots</th>\n",
              "      <th>mentality_aggression</th>\n",
              "      <th>mentality_interceptions</th>\n",
              "      <th>mentality_positioning</th>\n",
              "      <th>mentality_vision</th>\n",
              "      <th>mentality_penalties</th>\n",
              "      <th>mentality_composure</th>\n",
              "      <th>defending_marking</th>\n",
              "      <th>defending_standing_tackle</th>\n",
              "      <th>defending_sliding_tackle</th>\n",
              "      <th>goalkeeping_diving</th>\n",
              "      <th>goalkeeping_handling</th>\n",
              "      <th>goalkeeping_kicking</th>\n",
              "      <th>goalkeeping_positioning</th>\n",
              "      <th>goalkeeping_reflexes</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>158023</td>\n",
              "      <td>https://sofifa.com/player/158023/lionel-messi/...</td>\n",
              "      <td>L. Messi</td>\n",
              "      <td>Lionel Andrés Messi Cuccittini</td>\n",
              "      <td>32</td>\n",
              "      <td>24-06-1987</td>\n",
              "      <td>170</td>\n",
              "      <td>72</td>\n",
              "      <td>Argentina</td>\n",
              "      <td>FC Barcelona</td>\n",
              "      <td>94</td>\n",
              "      <td>94</td>\n",
              "      <td>95500000</td>\n",
              "      <td>565000</td>\n",
              "      <td>RW, CF, ST</td>\n",
              "      <td>Left</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>Medium/Low</td>\n",
              "      <td>Messi</td>\n",
              "      <td>Yes</td>\n",
              "      <td>195800000.0</td>\n",
              "      <td>#Dribbler, #Distance Shooter, #Crosser, #FK Sp...</td>\n",
              "      <td>RW</td>\n",
              "      <td>10.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>01-07-2004</td>\n",
              "      <td>2021.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>87.0</td>\n",
              "      <td>92.0</td>\n",
              "      <td>92.0</td>\n",
              "      <td>96.0</td>\n",
              "      <td>39.0</td>\n",
              "      <td>66.0</td>\n",
              "      <td>Beat Offside Trap, Argues with Officials, Earl...</td>\n",
              "      <td>88</td>\n",
              "      <td>95</td>\n",
              "      <td>70</td>\n",
              "      <td>92</td>\n",
              "      <td>88</td>\n",
              "      <td>97</td>\n",
              "      <td>93</td>\n",
              "      <td>94</td>\n",
              "      <td>92</td>\n",
              "      <td>96</td>\n",
              "      <td>91</td>\n",
              "      <td>84</td>\n",
              "      <td>93</td>\n",
              "      <td>95</td>\n",
              "      <td>95</td>\n",
              "      <td>86</td>\n",
              "      <td>68</td>\n",
              "      <td>75</td>\n",
              "      <td>68</td>\n",
              "      <td>94</td>\n",
              "      <td>48</td>\n",
              "      <td>40</td>\n",
              "      <td>94</td>\n",
              "      <td>94</td>\n",
              "      <td>75</td>\n",
              "      <td>96</td>\n",
              "      <td>33</td>\n",
              "      <td>37</td>\n",
              "      <td>26</td>\n",
              "      <td>6</td>\n",
              "      <td>11</td>\n",
              "      <td>15</td>\n",
              "      <td>14</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>20801</td>\n",
              "      <td>https://sofifa.com/player/20801/c-ronaldo-dos-...</td>\n",
              "      <td>Cristiano Ronaldo</td>\n",
              "      <td>Cristiano Ronaldo dos Santos Aveiro</td>\n",
              "      <td>34</td>\n",
              "      <td>05-02-1985</td>\n",
              "      <td>187</td>\n",
              "      <td>83</td>\n",
              "      <td>Portugal</td>\n",
              "      <td>Juventus</td>\n",
              "      <td>93</td>\n",
              "      <td>93</td>\n",
              "      <td>58500000</td>\n",
              "      <td>405000</td>\n",
              "      <td>ST, LW</td>\n",
              "      <td>Right</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>High/Low</td>\n",
              "      <td>C. Ronaldo</td>\n",
              "      <td>Yes</td>\n",
              "      <td>96500000.0</td>\n",
              "      <td>#Speedster, #Dribbler, #Distance Shooter, #Acr...</td>\n",
              "      <td>LW</td>\n",
              "      <td>7.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>10-07-2018</td>\n",
              "      <td>2022.0</td>\n",
              "      <td>LS</td>\n",
              "      <td>7.0</td>\n",
              "      <td>90.0</td>\n",
              "      <td>93.0</td>\n",
              "      <td>82.0</td>\n",
              "      <td>89.0</td>\n",
              "      <td>35.0</td>\n",
              "      <td>78.0</td>\n",
              "      <td>Long Throw-in, Selfish, Argues with Officials,...</td>\n",
              "      <td>84</td>\n",
              "      <td>94</td>\n",
              "      <td>89</td>\n",
              "      <td>83</td>\n",
              "      <td>87</td>\n",
              "      <td>89</td>\n",
              "      <td>81</td>\n",
              "      <td>76</td>\n",
              "      <td>77</td>\n",
              "      <td>92</td>\n",
              "      <td>89</td>\n",
              "      <td>91</td>\n",
              "      <td>87</td>\n",
              "      <td>96</td>\n",
              "      <td>71</td>\n",
              "      <td>95</td>\n",
              "      <td>95</td>\n",
              "      <td>85</td>\n",
              "      <td>78</td>\n",
              "      <td>93</td>\n",
              "      <td>63</td>\n",
              "      <td>29</td>\n",
              "      <td>95</td>\n",
              "      <td>82</td>\n",
              "      <td>85</td>\n",
              "      <td>95</td>\n",
              "      <td>28</td>\n",
              "      <td>32</td>\n",
              "      <td>24</td>\n",
              "      <td>7</td>\n",
              "      <td>11</td>\n",
              "      <td>15</td>\n",
              "      <td>14</td>\n",
              "      <td>11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>190871</td>\n",
              "      <td>https://sofifa.com/player/190871/neymar-da-sil...</td>\n",
              "      <td>Neymar Jr</td>\n",
              "      <td>Neymar da Silva Santos Junior</td>\n",
              "      <td>27</td>\n",
              "      <td>05-02-1992</td>\n",
              "      <td>175</td>\n",
              "      <td>68</td>\n",
              "      <td>Brazil</td>\n",
              "      <td>Paris Saint-Germain</td>\n",
              "      <td>92</td>\n",
              "      <td>92</td>\n",
              "      <td>105500000</td>\n",
              "      <td>290000</td>\n",
              "      <td>LW, CAM</td>\n",
              "      <td>Right</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>High/Medium</td>\n",
              "      <td>Neymar</td>\n",
              "      <td>Yes</td>\n",
              "      <td>195200000.0</td>\n",
              "      <td>#Speedster, #Dribbler, #Playmaker  , #Crosser,...</td>\n",
              "      <td>CAM</td>\n",
              "      <td>10.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>03-08-2017</td>\n",
              "      <td>2022.0</td>\n",
              "      <td>LW</td>\n",
              "      <td>10.0</td>\n",
              "      <td>91.0</td>\n",
              "      <td>85.0</td>\n",
              "      <td>87.0</td>\n",
              "      <td>95.0</td>\n",
              "      <td>32.0</td>\n",
              "      <td>58.0</td>\n",
              "      <td>Power Free-Kick, Injury Free, Selfish, Early C...</td>\n",
              "      <td>87</td>\n",
              "      <td>87</td>\n",
              "      <td>62</td>\n",
              "      <td>87</td>\n",
              "      <td>87</td>\n",
              "      <td>96</td>\n",
              "      <td>88</td>\n",
              "      <td>87</td>\n",
              "      <td>81</td>\n",
              "      <td>95</td>\n",
              "      <td>94</td>\n",
              "      <td>89</td>\n",
              "      <td>96</td>\n",
              "      <td>92</td>\n",
              "      <td>84</td>\n",
              "      <td>80</td>\n",
              "      <td>61</td>\n",
              "      <td>81</td>\n",
              "      <td>49</td>\n",
              "      <td>84</td>\n",
              "      <td>51</td>\n",
              "      <td>36</td>\n",
              "      <td>87</td>\n",
              "      <td>90</td>\n",
              "      <td>90</td>\n",
              "      <td>94</td>\n",
              "      <td>27</td>\n",
              "      <td>26</td>\n",
              "      <td>29</td>\n",
              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "      <td>15</td>\n",
              "      <td>15</td>\n",
              "      <td>11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>200389</td>\n",
              "      <td>https://sofifa.com/player/200389/jan-oblak/20/...</td>\n",
              "      <td>J. Oblak</td>\n",
              "      <td>Jan Oblak</td>\n",
              "      <td>26</td>\n",
              "      <td>07-01-1993</td>\n",
              "      <td>188</td>\n",
              "      <td>87</td>\n",
              "      <td>Slovenia</td>\n",
              "      <td>Atlético Madrid</td>\n",
              "      <td>91</td>\n",
              "      <td>93</td>\n",
              "      <td>77500000</td>\n",
              "      <td>125000</td>\n",
              "      <td>GK</td>\n",
              "      <td>Right</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>Medium/Medium</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Yes</td>\n",
              "      <td>164700000.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>GK</td>\n",
              "      <td>13.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>16-07-2014</td>\n",
              "      <td>2023.0</td>\n",
              "      <td>GK</td>\n",
              "      <td>1.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Flair, Acrobatic Clearance</td>\n",
              "      <td>13</td>\n",
              "      <td>11</td>\n",
              "      <td>15</td>\n",
              "      <td>43</td>\n",
              "      <td>13</td>\n",
              "      <td>12</td>\n",
              "      <td>13</td>\n",
              "      <td>14</td>\n",
              "      <td>40</td>\n",
              "      <td>30</td>\n",
              "      <td>43</td>\n",
              "      <td>60</td>\n",
              "      <td>67</td>\n",
              "      <td>88</td>\n",
              "      <td>49</td>\n",
              "      <td>59</td>\n",
              "      <td>78</td>\n",
              "      <td>41</td>\n",
              "      <td>78</td>\n",
              "      <td>12</td>\n",
              "      <td>34</td>\n",
              "      <td>19</td>\n",
              "      <td>11</td>\n",
              "      <td>65</td>\n",
              "      <td>11</td>\n",
              "      <td>68</td>\n",
              "      <td>27</td>\n",
              "      <td>12</td>\n",
              "      <td>18</td>\n",
              "      <td>87</td>\n",
              "      <td>92</td>\n",
              "      <td>78</td>\n",
              "      <td>90</td>\n",
              "      <td>89</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>183277</td>\n",
              "      <td>https://sofifa.com/player/183277/eden-hazard/2...</td>\n",
              "      <td>E. Hazard</td>\n",
              "      <td>Eden Hazard</td>\n",
              "      <td>28</td>\n",
              "      <td>07-01-1991</td>\n",
              "      <td>175</td>\n",
              "      <td>74</td>\n",
              "      <td>Belgium</td>\n",
              "      <td>Real Madrid</td>\n",
              "      <td>91</td>\n",
              "      <td>91</td>\n",
              "      <td>90000000</td>\n",
              "      <td>470000</td>\n",
              "      <td>LW, CF</td>\n",
              "      <td>Right</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>High/Medium</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Yes</td>\n",
              "      <td>184500000.0</td>\n",
              "      <td>#Speedster, #Dribbler, #Acrobat</td>\n",
              "      <td>LW</td>\n",
              "      <td>7.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>01-07-2019</td>\n",
              "      <td>2024.0</td>\n",
              "      <td>LF</td>\n",
              "      <td>10.0</td>\n",
              "      <td>91.0</td>\n",
              "      <td>83.0</td>\n",
              "      <td>86.0</td>\n",
              "      <td>94.0</td>\n",
              "      <td>35.0</td>\n",
              "      <td>66.0</td>\n",
              "      <td>Beat Offside Trap, Selfish, Finesse Shot, Spee...</td>\n",
              "      <td>81</td>\n",
              "      <td>84</td>\n",
              "      <td>61</td>\n",
              "      <td>89</td>\n",
              "      <td>83</td>\n",
              "      <td>95</td>\n",
              "      <td>83</td>\n",
              "      <td>79</td>\n",
              "      <td>83</td>\n",
              "      <td>94</td>\n",
              "      <td>94</td>\n",
              "      <td>88</td>\n",
              "      <td>95</td>\n",
              "      <td>90</td>\n",
              "      <td>94</td>\n",
              "      <td>82</td>\n",
              "      <td>56</td>\n",
              "      <td>84</td>\n",
              "      <td>63</td>\n",
              "      <td>80</td>\n",
              "      <td>54</td>\n",
              "      <td>41</td>\n",
              "      <td>87</td>\n",
              "      <td>89</td>\n",
              "      <td>88</td>\n",
              "      <td>91</td>\n",
              "      <td>34</td>\n",
              "      <td>27</td>\n",
              "      <td>22</td>\n",
              "      <td>11</td>\n",
              "      <td>12</td>\n",
              "      <td>6</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   sofifa_id  ... goalkeeping_reflexes\n",
              "0     158023  ...                    8\n",
              "1      20801  ...                   11\n",
              "2     190871  ...                   11\n",
              "3     200389  ...                   89\n",
              "4     183277  ...                    8\n",
              "\n",
              "[5 rows x 72 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 206
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tAkdZXWAbDVU"
      },
      "source": [
        "# replacing null values with 0\n",
        "df = df.fillna(value= 0)"
      ],
      "execution_count": 207,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "53N_uDhUq0Py",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 205
        },
        "outputId": "ca666ee7-193e-47a8-9693-d44b4386a401"
      },
      "source": [
        "# nationality , club , body_type , work_rate , team_position\n",
        "# target : preferred_foot\n",
        "new_df=df[['nationality' , 'club' , 'body_type' , 'work_rate' , 'team_position' , 'preferred_foot']]\n",
        "new_df.head()"
      ],
      "execution_count": 208,
      "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>nationality</th>\n",
              "      <th>club</th>\n",
              "      <th>body_type</th>\n",
              "      <th>work_rate</th>\n",
              "      <th>team_position</th>\n",
              "      <th>preferred_foot</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Argentina</td>\n",
              "      <td>FC Barcelona</td>\n",
              "      <td>Messi</td>\n",
              "      <td>Medium/Low</td>\n",
              "      <td>RW</td>\n",
              "      <td>Left</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Portugal</td>\n",
              "      <td>Juventus</td>\n",
              "      <td>C. Ronaldo</td>\n",
              "      <td>High/Low</td>\n",
              "      <td>LW</td>\n",
              "      <td>Right</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Brazil</td>\n",
              "      <td>Paris Saint-Germain</td>\n",
              "      <td>Neymar</td>\n",
              "      <td>High/Medium</td>\n",
              "      <td>CAM</td>\n",
              "      <td>Right</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Slovenia</td>\n",
              "      <td>Atlético Madrid</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Medium/Medium</td>\n",
              "      <td>GK</td>\n",
              "      <td>Right</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Belgium</td>\n",
              "      <td>Real Madrid</td>\n",
              "      <td>Normal</td>\n",
              "      <td>High/Medium</td>\n",
              "      <td>LW</td>\n",
              "      <td>Right</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  nationality                 club  ... team_position preferred_foot\n",
              "0   Argentina         FC Barcelona  ...            RW           Left\n",
              "1    Portugal             Juventus  ...            LW          Right\n",
              "2      Brazil  Paris Saint-Germain  ...           CAM          Right\n",
              "3    Slovenia      Atlético Madrid  ...            GK          Right\n",
              "4     Belgium          Real Madrid  ...            LW          Right\n",
              "\n",
              "[5 rows x 6 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 208
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dVl9XGqJ5du7",
        "outputId": "b717d321-6232-4e30-e027-205b6150c254"
      },
      "source": [
        "# printing datatypes\n",
        "new_df.dtypes"
      ],
      "execution_count": 209,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "nationality       object\n",
              "club              object\n",
              "body_type         object\n",
              "work_rate         object\n",
              "team_position     object\n",
              "preferred_foot    object\n",
              "dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 209
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-bechEfR5gAL"
      },
      "source": [
        "# changing the datatypes of these attributes from object to string as object datatype can't be converted to numeric attributes using LabelEncoder\n",
        "new_df['nationality']=new_df['nationality'].astype(dtype='string',copy=True)\n",
        "new_df['club']=new_df['club'].astype(dtype='string',copy=True)\n",
        "new_df['body_type']=new_df['body_type'].astype(dtype='string',copy=True)\n",
        "new_df['work_rate']=new_df['work_rate'].astype(dtype='string',copy=True)\n",
        "new_df['team_position']=new_df['team_position'].astype(dtype='string',copy=True)\n",
        "new_df['preferred_foot']=new_df['preferred_foot'].astype(dtype='string',copy=True)"
      ],
      "execution_count": 210,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_-YL7ZER5ilU",
        "outputId": "9a21a8d8-2489-4f01-daf0-dbe5ad2ec011"
      },
      "source": [
        "# printing changed datatypes\n",
        "new_df.dtypes"
      ],
      "execution_count": 211,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "nationality       string\n",
              "club              string\n",
              "body_type         string\n",
              "work_rate         string\n",
              "team_position     string\n",
              "preferred_foot    string\n",
              "dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 211
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 205
        },
        "id": "CtmAduUM5mJ1",
        "outputId": "d09eb77d-5e36-4aa7-ae9b-81ced44d527a"
      },
      "source": [
        "# converting catagorical attributes to numeric attributes using Label encoder\n",
        "for i in new_df.columns:\n",
        "  new_df[i] = LabelEncoder().fit_transform(new_df[i])\n",
        "new_df.head()"
      ],
      "execution_count": 212,
      "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>nationality</th>\n",
              "      <th>club</th>\n",
              "      <th>body_type</th>\n",
              "      <th>work_rate</th>\n",
              "      <th>team_position</th>\n",
              "      <th>preferred_foot</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>224</td>\n",
              "      <td>4</td>\n",
              "      <td>7</td>\n",
              "      <td>26</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>121</td>\n",
              "      <td>350</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>15</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>18</td>\n",
              "      <td>462</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>133</td>\n",
              "      <td>63</td>\n",
              "      <td>6</td>\n",
              "      <td>8</td>\n",
              "      <td>6</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>12</td>\n",
              "      <td>505</td>\n",
              "      <td>6</td>\n",
              "      <td>2</td>\n",
              "      <td>15</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   nationality  club  body_type  work_rate  team_position  preferred_foot\n",
              "0            5   224          4          7             26               0\n",
              "1          121   350          1          1             15               1\n",
              "2           18   462          5          2              1               1\n",
              "3          133    63          6          8              6               1\n",
              "4           12   505          6          2             15               1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 212
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8te2e-xyq0yf"
      },
      "source": [
        "# splitting dataset into 70:30 ratio\n",
        "\n",
        "# Defining train size\n",
        "train_size = int(0.7 * len(new_df))\n",
        "\n",
        "# Splitting dataset\n",
        "train_set = new_df[:train_size]\n",
        "test_set = new_df[train_size:]"
      ],
      "execution_count": 213,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HD4MB96U6AjW"
      },
      "source": [
        "# separating train_set into X and Y\n",
        "X=train_set.drop('preferred_foot', axis=1)\n",
        "y=train_set['preferred_foot']\n",
        "\n",
        "# separating test_set into X and Y\n",
        "X_test=test_set.drop('preferred_foot', axis=1)\n",
        "y_test=test_set['preferred_foot']"
      ],
      "execution_count": 214,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 205
        },
        "id": "4e4lgG9NxeWp",
        "outputId": "04dcd5bb-325b-4e9e-aa7f-9a51a8cdaab9"
      },
      "source": [
        "X.head()"
      ],
      "execution_count": 215,
      "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>nationality</th>\n",
              "      <th>club</th>\n",
              "      <th>body_type</th>\n",
              "      <th>work_rate</th>\n",
              "      <th>team_position</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>224</td>\n",
              "      <td>4</td>\n",
              "      <td>7</td>\n",
              "      <td>26</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>121</td>\n",
              "      <td>350</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>18</td>\n",
              "      <td>462</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>133</td>\n",
              "      <td>63</td>\n",
              "      <td>6</td>\n",
              "      <td>8</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>12</td>\n",
              "      <td>505</td>\n",
              "      <td>6</td>\n",
              "      <td>2</td>\n",
              "      <td>15</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   nationality  club  body_type  work_rate  team_position\n",
              "0            5   224          4          7             26\n",
              "1          121   350          1          1             15\n",
              "2           18   462          5          2              1\n",
              "3          133    63          6          8              6\n",
              "4           12   505          6          2             15"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 215
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R6X1nktgFxkp"
      },
      "source": [
        "### Pre-processing\n",
        "\n",
        "( this is really an inportant step , because if the values of different attributes vary in ranges by much different it can affect the model heavily resulting in NaN loss ;/ )"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-nR-_FfjDhJv",
        "outputId": "cc42bdca-daa2-4efb-d602-5331572769b8"
      },
      "source": [
        "# Using StandardScaler function of sklearn.preprocessing we are standardizing \n",
        "# and transforming the data in such a way that the mean of the transformed data is 0 and the Variance is 1.\n",
        "sc_x = StandardScaler()\n",
        "X = sc_x.fit_transform(X)\n",
        "X_test = sc_x.fit_transform(X_test)\n",
        "X[0:2]"
      ],
      "execution_count": 216,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.44865589, -0.62322224, -0.7110833 ,  0.51821518,  0.58377733],\n",
              "       [ 0.96986745,  0.00748178, -2.47304581, -1.51929096, -0.62068117]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 216
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XXItfauwxjYO",
        "outputId": "acbb2fb3-b29f-429a-9179-c825197595aa"
      },
      "source": [
        "y.head()"
      ],
      "execution_count": 217,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    0\n",
              "1    1\n",
              "2    1\n",
              "3    1\n",
              "4    1\n",
              "Name: preferred_foot, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 217
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZVcxIf30bGOo"
      },
      "source": [
        "##**LOGISTIC REGRESSION**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1r00yO-xRC_X"
      },
      "source": [
        "Formulae's"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MLFOxYMxM7KD"
      },
      "source": [
        "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATcAAABkCAYAAADjT3ffAAAgAElEQVR4Ae2dCYxlRfWHWWSTRWCMgigKRAlRWWURFcOOgiyJxAVEwhIWFRBMQAVFEREBFRxRURajBGQLjgIDEUE2h3VkRBQYEHBBUUQQF1Ao89V/vvs/c3k93W96e7c5lbyuulWnTp3zq6rfrap7+71FSoZEIBFIBKYgAotMQZ/SpUQgEUgESpJbDoJEIBGYkggkuU3Jbk2nEoFEIMktx0AikAhMSQSS3KZkt6ZTiUAikOSWYyARSASmJAJJblOyW9OpRCARSHLLMZAIJAJTEoEktynZrelUIpAIJLnlGEgEEoEpiUCS25Ts1nQqEUgEktxyDCQCicCURCDJbUp2azqVCCQCSW45BhKBRGBKIpDkNiW7NZ1KBBKBMSG3p59+ukHyn//8Z5Mm8e9//7te/+tf/6rxf/7zn/LMM8/UTxR87rnnmsv//ve/RZ3IGsg3xLR5zz77bFGP9SmLNj322GNVHDv4EP7+97/XmPoG27Ud/UDGMmTVrRztIqNuZCjz2rrkxfaop834oJz2/OUvfzHZYKqvbVkEo71cI0tebNO0tiOHnU8++WRtyz6jrm3pBwL/+Mc/qhx5UYd4Ukgb+uW1ttXK8/6oA/nYRpSxPfJMaxc2W88Ym/SbOtGOqNd8/LXuU089VUW85oK0slyLX5SxnHYjJsprr3LoUA9l7XLl/vrXvz7PnljPdBVq/XF8MFbVr3/GVMEPfXEMkB9lbMc+3HbbbcsiiyxSzj///Nqq5bRpWy1zJuxy1OSmk9FiBsnjjz8es2paWWMANA0oduTzKs7LcLAAWpS1rSeeeKIhBTvUQYFNtoW6WD/mk7YdO1hd2sUgwV47Hfk4uZBDZtasWbXj2wSoHur/7W9/m28CUoZubSBtfdL6KvE4GKmH/wQnvtf4pHwVmEd26HMQgqn+KkMsNpSjb8kllyxXX311k6+dyEZSA19t0562jOWxPdK0hV7ss5+wg2sC9WI/KUOZ+eiIIdrGZPzpT39a26Cd2L/oUtYbIbioDxsilvqADrGyvu3bZ73GJzJxbKJPe2zH+urTX+XMb8faHOXQj8/Y6vi49NJLyxJLLFEeffTRtop6rY/Epu0LdIDnb37zm0ZW/+PY6Kl4nDNHTW4CyAAW9LbNOttr8iDr5LWeoACgIFImsMrFetahzHaMlXeSOQFiHWQcnMobawODPbZpeRsD2kH3z372szpoKGcQQGQE7bC+sYOnjSP56KAesfYg5wSgveiPExPd5lM3TlQHvTqQRTek++c//1mz5hv0L3rRi8qNN95Yy5B1giiMTv2jXXQhxyf2n1j/8Y9/bHQ5TsiwnHoGbFc3eWJBjHy0Jcrpp3qWXXbZcvvtt9dLsaa+OKDPQJqPcmJJuf5YZh1i2oz5sZ7jMvYFdRwfUY+24Jt+REy8wVqHdqyjHHZaFz+jLcjeeuutlaDQQR+IHWNdHZSBj3WNZ8+eXd761rc2tvfqQ22b6HjU5KaTAho79Jvf/GYFbeWVV67xcsstV9Zbb72GIAAuDhCA4Rpdgmo5sXmxDdpnwnH3oB7XsbPo/He96121nHyDOuxIyGCTTTYpr3jFK8p9991X/vSnP5VddtmlrLXWWrWKbXOBTgYJdWlPHeo2/vGPf1wWW2yxZmBpH4M6kiRtO/i0/e1vf3v1l3ZPO+206oN68ZWPQV3Iihfb2A022KC87GUvK3PmzKk2b7PNNtUffW/X51pdpONAtYx2WZHGcjBApz5cd9111b7tttuuyvHna1/7Wtl6663rNf4vuuiiPX1QLzqZ0JtvvnldLc6dO7fizDbo5S9/efUTmXaI/UEfRV+5JuADKzfw4kMddeE/dfCd/rIO9fSPPImQfOT5kNdeZaF3QeOT/mKcIXPttddW+9DDB9tsn/Q999xTmEOMU8Itt9xSXvva15Zjjz22/Pa3v615/HFcmoHdjgvz8E1ypd3FF1/cogYLMiJ+UQf56Pj6179ePvnJT9ZtKT688Y1vLHfddVeJxyiN4glO/P8MGWXDOEpgcNChxF/60pfKeeedVwcFhLHVVluVuKKg4xwwJ598cllhhRUqyBACA3DppZeu16Qp++IXv9h0Nm3ROYRTTz21ToB6UUo599xzy4tf/OLa+eRdccUV5TWveU0tdvJCUNjMBxu+8Y1vlF//+td14HzrW98qhx9+eL27U06n2sm97q4MPP2PK54bbrih+uEAVQeGIA9O7QGDzO6771522mkn3Skf/OAHy6qrrloHO5knnnhiOeyww2q5kzLqYWKA5yOPPFI23njjgj8f/vCHy/3339/oRN7Bre0U4gsfAvnoIog1kws8bVdZZJA1f7fddisQkXnvfve768CXMD/zmc+UQw89tOpGRv2OBwq+8IUvVLJ4wxveUE4//fRyxBFH1BtPrTRv4oGtuLqK0YZov/1OXcbSZZddVtV4Y0KP/RTrI4Qe5MAs4hx91yZi7FEH18ONz6uuuqpstNFGtZ6+RH2OuWOOOabiwXy4/PLLKx7chO2jWIc0NusT1xHbSMI33XRTHaf2DbLihR/4H/02D7ldd921fOQjH2nGxGqrrVY++9nPUjTpYczIzdVM9IiO4u4LMNtvv3258sorm4njQBQ0AKMTY+cCqsHBz3VMI8/gYNL97ne/q+IvfelLK5ndeeedtXMvuOCCMnPmzFoWO1vd6HAwfuxjHysrrrhi+clPflIHR5SJg8MBpR/Y+sMf/rCu/Bh83AmJsYvYuzcrEXymPT4OqOg3E3mdddapTf/qV7+qaXQQqHPQQQeVn//855pWBx9ni+CCf+JGfOSRRxZWzhdddFEz0D2HbBTMSziJ8FP/uNHw4awNG7jhcK0/+CkG6qP+V77ylbLhhhvWLEiWm4s+MCE//vGPl1/84heN/9bF/ogFaXSxWuNGSWBiOm641m7SEA5+az95tGt/kGbVyNaUNB98kqic1GB09tlnl1VWWaX88pe/RE1hC7388svX1YpyEC7kG7fEjiXqYP+CxicyZ555ZjnjjDNqG/7Rfu1yJQS2b3rTm2qbt91223yEBXb0RcRGfcTqZGy/6lWvqr4vs8wyDQ745op65513bvRgg/OGtDZhy7Rp0+oiBsy53myzzcopp5xSm3VsRxsmMj1qcvPOFzsUB8zHQVYhN998c+MXHS7QZAKKgY5xciKjXvUhJ7h2IgOLQUpns2o7+uijC9u6a665pt6BPvCBDxQGKwPygQceqHcaVj/optNsA72cJ3Fn985mG1x/7nOfK+giUEe7qaecfpHn9gx5fTKtfFUWzpiwB5LkgBecWHFxl2YyPvTQQ+Xuu+8uJ5xwQh3Ef/jDH8r+++9fJy6DlTM+AvXQjw0SLvlOENIQKKtBcNtyyy1rvV5/tFsCQf7666+fzx/q0R7tggl1LrzwwkqClB144IH1GlwJ2EkfgSEPJ9hmoZeb0sUXX1xlXOGjd8aMGWWppZaq+WJO/p577ln7igm6ww471HJ8pIyAPfQ59tjH5NOWZ25cR3muvXlyHADuDz74INk15hqSpZ+o9+lPf7qsueaatZw/kgB2OhYWND4h/n333bexIRKCaYmT/kQ/21BW8xIs7dpPGoJsLCffmxCy3uCwk+0tmIiDOoyRtwxMDWC4xhprNGXkr7322uU73/lO47uykxGPmtwwWocBQUAZTBACg45zJMFpO6k8E9a7hqsCtpamWTmcdNJJ84GGTtumc5hQm266ab2LMmG//e1vF5bynK8QuAOzXeOMgy0ugUFAwFYGEQONlQkkaOC8h8n45S9/ua5AbZPyXoMI38GCSYz9XOs/+YSoQ+Ign8HGjQB/WNmwtSNwzbYS28GMQf75z3++cK5JYAUBoRtoB4JglQd2nNcQ0E/b66+/fvUZsoQYuRHgi3YiKyF4Y6EMfzwbog0+TmJ9wz5WnNjMBPDsjWtWnGy7Jdrjjjuu8YGzm3e+853NTQMf6RfIkbqeKzlmWM1RzlM+ylkhGSQErsVX4oGgOA/VfmRI45/jQV+M8RHsCNpeL8If6kf8KLKfsa/X+DzqqKMKOwyC5ENactce8tANfqyqXvnKV9Y62Ec/Rbn2NYLaoR506Q/9Sb/GMtLoRL8YkCeG4MH8et/73tfUA1NWwYw1x0wtnKQ/Y0JuOgII3vU4e9prr73qIMI3HGZCIePgjKAtrP8OJiYoy3WIDHs4B6A9SMw7oG2waoMYCHYwd7IPfehD5Y477qhLa4iUsxJWSwQ6kxULE1MfnfzagD+mGUysShjUhGgD9ZxwDCD1GEOm1GOie07GHZJzGVaWcaBW5aXUiaNP+M+kxx+eZoEDpD59+vRKOtZxoLIFhgycIMS2oQx16Dfs4oyGoK/IOBGIyX/44YerLMQmsa6++ur15uPNRjvoA14l2GOPPSqxOz4grUMOOaSugCFuznDxQ5KjXTD/wQ9+UG9K6hNHYseYvmEbPnAD0X7rjUdsG0ONT8YigfEF0WMbK/4dd9yxpnlNg0CfguN73/veihVyPNhxBfzd7363Hqdwvsp5LCRDGX6jW0yqsvAH+7yZaqtYgR31GAv2iVXJxxbsJLDVpU1WlYMSxoTcBEOnmFjHH3987Ry2V6zIWD1sscUWiowps0MU3M2YCC63mQis4gyQC51Eh/HkjknC5KBDf/SjH1VbITYCA4TBw0MGgkTEoPNJFXocDMbISgqUs/JCj2RIeRwkEocEG+Wo973vfa+2D76sRBn8DrhaME8fZ0H77bdfHcTo4rCcMyZWBLTH2RH6OLsiONDRy8uXbF0N2sS1fuGTqwr0QPIGZbj2Jkf697//fbWBYwID564f/ehHG12sTqhPX6EXMgczwjnnnFNWWmml5myRVTMyZ511VnOjAAvykOPhA77jk3iiBxlXQVzTHvJs9ScqLGh8ijfbU2xipQ5hcA1JeRbHA6511123IRqOR9iO23ecqYIBT/dZ3bF1PuCAAxoXwUF8msx5CdoFk9iXYEadGOhfZZjjnB+zeKAPmN9s4xlbkCl+EU9mGDW5OZAYVHSinSUwcTJHR51gMW9h0gJIuxILHUBHkBcJA/3Yy6qMQ8+hbGAit8vwj7sTT4cos5PRGWW1h3yI1rJohxhFfxnMhkgS5tE+gbKYRhdbT1ZKBsnYa22A4Em7ZeNBCyQCbrEOOm3DuujCZ/sbP7VTP5Hl4yrV/tAObzxeG9sGd31e2yFEvMSUsWT7TD7StMGZ2Otf//qGdO2b+FIqfao9xurVjvGIbQNMbTeOT9qkDF+YM76KRD3IgxsX5faPRE2ewb56//vfXx8csbLlfJgbFxg4F8WFemKufdpG7I1M/fSF8rRl/2Jz7FNlrDfZ8ajJLYKsM4DpwCcPsAAWYABTEATUegsbO+DRT9ttm2zHwc45AWdUBiYN9jnAzHfQSNAcwr/5zW+uxfhgO3HQ0Jb1EEQOLNoDhjL0Yq94gA069cdB5MC2HeqQx92Trb9nQDyBFGdsUD6+nkK7lLEqvOSSS6pdbEu420cbsYl2CNiFTeJHnjaS1v4qPK9MDLCB+vYBMpCrBMuZLCsH/OaGw7t4QwV0ijlnedxowJDtGiuWeLarL/YtOklHu4dqZ6zzbRP72+NT7MAJP3xwAmm8+tWvrlvP6Bdyzi3GB/rAFoxZfXGGSnjLW95SH7CxyhZr+5Ny5NsBO8GIQDumoxz5sS8ti/nowTb9Vmai41GTGwbTae1JTT4DEUCdpDrnwPN6NLGTSB12IG0CeASYbRpLaD5s21jWO7iojzwBnd6RLPfBhnV9kRV5ZGyX2DRlMQ0e2BVtduDRtm1Rr91+1EM54eCDD66Twdcc4rY/6kKWa9pmUHP3FwdizkrYyrbr/F8r808EiZYybIq+8CqOGFIeJwH90O4PZCBYzgQ5usB+zhtdnUDehNgm17xKwhkd56rYz2qHLXscV+iwfeI4DrBbkqwNjOOfiA/N2I+Oz0gybLl9is9Knq0exw0GfUBHu6/uvffe5siEscNKljNaz2zRQVv2mdiQ7zyN7VjO+LQtVnDRH/sl4k4fRxl1TkY8anIDsNhBOCww0SEcpiwCEetF2X7S6uAuEwcsNtiR3unQq210mPLmUe67cr1ssC07Ow62dofStoMQv+PSHt3xrmhdsEFOveYjz2S1jpMe+01rL20SYl2utZm0K70q2HrYQfuGWIdBC6kQwIsy2zC2HnhrF/X4iB0yyOMjH/RQRh4f+8KJow3ISHraoK/oN02ZOKHPm4Tjzusor93jEev3UOOTNsELe9pEoj3ghI8xgBO6qSdmYhjl9JNYXChHNpaRJzZtrKI+bKE9ZewfZLBRW4xj3YlOj5rchjIY4IaaKNSJoAylYyT5bT10IMDSCe3gYCDfcgjCgdPuECaoxEhn2qFRvwMEnQwYQ6+BRhntUabdTmLKXMWp07a1i3raYDvE+kKML9rBtas15GhTX7VD3W292oAO9aFDedtHJ7iCO7rVb3v6yTUy6It55LfzbIN8gqRKGlvExWtidDresD0SIeUxOMnVH8vGOt32dajxGcdhGw/8sX8oi/5LnuASxxLyylHWtgOd4CwGYtL233zsawf08kGH44Vrgzc4ryc6HjW5CQ7ORQDNxyHTDlpBF5DROG27EXwBJo6TLaY9P1I2Dh7sib5E+/BBP5CJcjGtXnVpn4ORfO0BH3WSpq6DSj2xnrLUN61+5KOstisnXtoVbbafxMK6xNZXhjxtM1ZOW/RBPyFag2XWMR+C0qY4Psjz2jjiRn2uLVOf9mqTBMh1tFv5sY6xB9ttH/22axzLKNdm6pkmP2KGXnGlLOrwywgsF091Mz7ECRusG7FRlpigDPZQx/qOC9oiDxuJzZ9XfVKiUZPbpFidjSYCiUAiMAwCSW7DAJTFiUAi0E0Ekty62W9pdSKQCAyDQJLbMABlcSKQCHQTgSS3bvZbWp0IJALDIJDkNgxAWZwIJALdRCDJrZv9llYnAonAMAgkuQ0DUBYnAolANxFIcutmv00Zq31J1ZdCdSy+iIxMu9yXSZXPOBFoI5Dk1kYkryccAYmMN+slMfOiMbxp71v9ysXyTCcCEYEkt4hGpiccAf81yH/9iQZAcPFftlit+S9FUS7TiUAvBJLceqGSeROKgP/L6mqN/z3mGyr4Snd+c1VCkwg1znyvM04EIgJJbhGNTE8qAn6hAj+s4/ft8e3H/tO2W1KNHIR/ztaWjAcPgSS3weuTF5xFbEldvfGbAPwWAAGCiz8m48OH9gruBQdYOjwiBJLcRgRTCo03An6Xne1AZHzLrr+0Rb7k5kpO2YwTgV4IJLn1QiXzJgwBt6I2CHH5JBRy4xfHCGxJ3ZYmuYlWxgtCIMltQegMQJmrFSY82zEnvlszrzEVoojXA2D+iEzAFwmLczQfLLAt5XdaCfglucUnqCNqIIVekAgkuXWs2534fvV2JAZckQS6QgCSGrZD5JGcWbnxK+au2mIZ8rFux7oxzZ0ABJLcJgDk0TQhmTHx24Tl5I5fPz2atiajbiQsn37qK7/+xM8OGnj1g4+r2S77rU8Zjx8CSW7jh+2YaG6/y+WPgAz14xtOfBqXGMfEkHFU4u+quu2E8CA6fk6RHxa2XBOij+ZlnAi0EUhyayMyoNdxlcJW1DM38iUFTCctIcZV0YC61dga7eNX51m1sS1dbLHF6o8vR5LDP1atrlxj3UwnAiKQ5CYSAxq7VcM8VmKSWpu4eJgwVNmAujafWdjvk9P4Wgg+SdZW0E+vM04EeiGQ5NYLlQHL8wVXzOIHldmSbrbZZmXatGll9uzZ1VrIzpUMqzdIMa72Bsylxpw2SVPQthu/8KeXbKMoE4lAC4EktxYgg3bpyo1VGx9WN+uuu275/ve/Xy699NKyzjrrNC+6xu3poPkxlD3a7Dma11E+rtTiKi6mo3ymEwEQSHIb8HHQXq3svffe5aGHHmreebv33nvLnnvuOd/WzYcNkRSGcrOtX5IxllzbRMJqsl13qDYmM7/9UKVts1tg/MPnXuQ6mfZn2wuPQJLbwmM3ITWZjBAJE++2224rq666annd615X26bs1FNPrQfvn/rUp+Z7VcTzq+GMZDKjxy2t8pEYIUvJDVtiGfUH+aM/xPiJ7cReE0uA+kg5/++qXBXOP51DIMltwLssEsknPvGJ8sgjj1Qyg+gMSy+9dLn11lu9rDFfGQQh8sRxQZ9FF120ynvOxaR21UaBE1wSJG+kxFkVD8AffABHfdAnTBNfY3w3PQCmpwmjQCDJbRTgTURVJiKTUvIh3mSTTcpxxx1XD9n59tott9yymsIWy23kSG1zwiMvqcUVDGnIkXfOlltuuZqGTBdEmINaxr9z4Yf2cU36JS95SY157YRrQnyIM1IsU26wEEhyG6z+6GkNL+5KOAgccMAB5dBDD62yfD3QXXfd1axMyIwrk54KQ+Zw5IYohAnxdW3FFtycL+kqzkyxNTa/3xuF9TIeDASS3AajH4a0ok0oENeJJ55Ydtppp/pgga0qk5VXRAiQFUGCc5UyVDzctpQJrk63a+hu/ytYbXQA/2g7Mb7wERvMxafHHnussdyHMWzrM3QbgSS3jvQfKycn3i233FK3T4cffnhhWzpUkIyGKiefSc9kH+qBguTglhVyiHqpO8if6Lu+mBd9jqs25YyVz7hbCCS5daC/nISuOJiIrLiuuOKKZlXFWZyk42rP6wW5qE5lJDFj8j1/ol3I7eKLLy7bbrutVQY6jgQVV22s1u64446y7777Ni9C40hcsbWxGWhH07jnIZDk9jxIBi/DhwlYxmTl5d1jjz32eaut8bI8Et0+++xTDjvssNpUJA7Igq3yrFmzapkrIQjWlR0FEnW0VTKOq0Jfz0DOLTc4RFts37aQNU9Cpm3y2Jb7QISHCnx9Oe2ie/311y/XXHNNQ+LowZYM3UYgyW3A+689ma+++upy8MEHT5jVTnLiq666qhIYNnnmBnFADKusskpZfvnlCz/oYpCUITjk/LiilJTQ5ypJMtJv2/fbUKjz6KOPzkc+5PGkc4kllqgkBpEtu+yyzZNP/kVtl112qcR4yCGHlNNOO00Tax4vRa+00kp11aZNCESCbSpkojMIJLl1oKuYcHxpI5P2iCOOqKsNiWMizIeUIBlWOBdeeGHTJCR15ZVXlpNPPrnmYd/tt99e05KRJEWmX7BJ2vJIarVieCWFa1ZXtE/wzFE56roSbMfWkawgsHe84x1l5syZldB4bQYZiXaPPfZo/KDM/1ywrYy7h0CS24D3GasHJ6imOpGdwOaPV0w7999/fyVXzqR8uihxGUNukHAM2B6JGEJSPsqZL9lQpt/I4zNnZO95z3vKMsssUz8XXHBBVSFRRn3o8YeeL7/88npGePfdd5c777yz8N8ckVRpB118GYGY0qbpqDfT3UEgya0jfeW5FGQXCWC8zZcE2JKuttpqDVFJsLF9zrT4zVFXPZHEIAo++IFOVoL4wacXOemv+vmPDLaO06dPr/WPOuqossMOOzRfZKkOiIp2JVSuefiy1FJLNS/rnnnmmVVt9OGyyy6r22rrIZDbUtHvZpzkNuD9BhEwySaa1NqwnHDCCeVtb3tbzYYwJD0JAJJi5QYJWqYOCAPCufbaa8vqq69e5Tif42CfszJWYp6R7brrrs2KjcN+6kJCO++8c/nqV79ay2iD/8o4+uijbaISJ+1iG8GzOtKSLLZqm09FKcN2ttPYT6A9H0jUjPzTSQSS3DrUbUxYVj9MyPbKZrzccGt25JFHlq222qo2E1c3ZGCL5MbWkaCt9WLeH2QgFYnHWH34ZZ6ERFVIidUX5MNDg2222aacddZZjWpXbWa4HcUu7JfwXKnZBvK2w1niCiusoIqab70mMxOdQiDJrQPdxQR1hdRrYo6nC6x0+PCKB8QSA2QhOZDPSqx95hYJy1WTOiJBS6KU4SOy5s2YMaNZVVEGSRIsVx9lEpgEp/3ItOtJXmyjeaLKKrL90ELdGXcPgSS37vXZhFoseT344IOVvPhWEggDYoAsLPfbSs4999xqXyTh0RhMW7TNqm3OnDlVFUTrlwWMRDd2SmRDyZ9zzjll4403nm87qm9D1cn8wUYgyW2w+2dgrIMcOC+76KKLqk2eWXGx9dZb14cNEBDftLHFFlvUbwpur6wWxhl1nH766fXAn9UVTzXjT/4tSC/1IcgYuCYfn1wl7rXXXuXss8+uYm6TY51Mdw+BJLfu9dmEWsyqxy0x3xm35pprNiu3uLJxZSQZYWSbVBbGcNvopWskh/6xHrrUF21hW8pDDVafEJt1RqI/6sn0YCGQ5DZY/THQ1jDx+aol3vInQHwSAOQmsXHeBSH2IpJ+HfQ/IagXf7/Us7Xh9GGjAXskYfKwfe7cufXlZJ7k+mACPz2zs27G3UMgya17fTbhFrOSiQftbBF5chqJA6MgorE6a4tOSjQSE8QJAY2E4IaSgcjuueeewjer+F8VblFpmzZcwUVbMt0dBJLcutNXk2IpJCKJMfm5NjD5Y5krN8r5/0+3s8ovTNxe/cWzvn7IJ9qKHRAluvRHEoRIXY36MvLC2J11Jh+BJLfJ74OBt0ACgCAgMD6QQ1zpSEKRECS+sXAQ/ZIObWNLP+SGLdjr6i/aJLHRRpsEo1ymu4VAklu3+mtSrGXCSwoSimSmQRIP12xhx4rYIKQYaN+8kbQRV5Pqwfa2/fGdO/T2qmf9jLuBQJJbN/oprUwEEoE+EUhy6xOwFE8EEoFuIJDk1o1+SisTgUSgTwSS3PoELMUTgUSgGwgkuXWjn9LKRCAR6BOBJLc+AUvxRCAR6AYCSW7d6Ke0MhFIBPpEIMmtT8BSPBFIBLqBQJJbN/oprUwEEoE+EUhy6xOwFE8EEoFuIJDk1o1+SisTgUSgTwSS3PoELMUTgUSgGwgkuXWjn9LKRCAR6BOBJLc+AUvxRCAR6AYCSW7d6CCB2/cAAABMSURBVKe0MhFIBPpEIMmtT8BSPBFIBLqBQJJbN/oprUwEEoE+EUhy6xOwFE8EEoFuIJDk1o1+SisTgUSgTwSS3PoELMUTgUSgGwj8D7uIC+dJeBlKAAAAAElFTkSuQmCC)\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        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)\n",
        "\n",
        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dthhh541GTKgg6OPPjrvkHp+E96M5Nw+4Yn+tqP+UQft9FLXYwcbFbPiTEmi8ZNG78QIR2+lAdqI0hIvj36KcqpDPnvnNl3bcEl3VDM/cTEsj1i229WkaaDSDfIZ1a2LNMijTPC37qRj5I7YXJM/pptPWe1E5A09unAkYwrK9MxjbMqNTGyd89pAAEQ7vOpVr0qcGMHZDgICoDH1PPvssy1q2j4jO+W++MUvzu+boSzkjvX91Kc+ld9HQ7nIDDBZ88YznehMvbT1OW0hJ8hg7GCzoZQXA2ELFwUzD+fVB/gYPjtR3kdDYUwPuFGtUb3yla/M+RgdcRi+BiF/fZTPlIL0aOjIE3tswwKPRt5nn32yHEx3aVDO3z384Q/P28xMdbhhzrVyWGY/H77KaFlOg6AnTF356QCDtOaN0yONinoZJi/hWA/iqI/AtSMCjIahEXyEAa6nTbhuO/ORR75tmqlcy9f62GboxbB8LZd45BCYsR7Qyst8pf2xg80K0sA4Ft4M/4xo9GCcTnDRzekHdsEwNJR83HHHZXDR05KfHo1dOZStwuGJsmksG0xwWraNYbqGbeNooNB/+tOfzjthPLPGQt1n1ziuxDm8Qw45JLNlGz9uQlhWP59Gp074GoAgivQCzDjlVl51CJ2ySwM/w5YRjTTmgX9Mgxf5o0zwslx1LX/1qJzT8ZXV+lCWeqAc0ymjn0yWHemM69ofO9hsIJTIE9iMaIDHhsWgeY0d7gtf+EJOd1q0/PLL51GFXTcAwcmIz372s03PO4pGt5GUh2sMkbUkaxcN7gUveEHacMMNG0PgaNHnPve5bAzk1VhiA5s3xtXwgquBsYMt9qAcA2Iko+fSEB/3uMcl5uQ4pi+AkVPtzM/ZeuatVuyCkebJBWjt/abbdIAL0CqPvTivYQDYlEMcx6C490PnweKcazYYoiMN+n7Ai3Q1vGBqYOxgQ60a7Cte8Yp8M5U4QMgbtgAXW/8YO3S8mJUT30zbmGaus846+RgPwHNBjFE7Io2i2ZyeKSv3vpBLx0l6ru04kJsTGIAUGR0VoUc2gWv+6s8ODfy/xYypvgCIH+4d73hHvrdDmF0oNhre+9739ki21FJL5XsnjCIAipuxnFCXLm4URCPvYTLFC58B4/QF60pAg5yc2WOtyDU/DtMy4nL0itHNaW+7WOvdjq/XC6YGxg421crogXGy9mGUYAT74Ac/2Gx2OFJxwpxNCXYNARPb0hq6IxC0jjLyn44feRFmI4TTHTrWbnQUOteWnHFkeutIxqgWOwDrZL7qL9gaGDvYNGTXQlHdGqlxGOogA4UWYx61Qz7WWPBXnggY4tyIIRx3LttrM65j3lHLWvnNbA2MHWxuw0djFoBxJHDUcioHDYYrSOXDNdOzEsADLMpBszplFYSW6bRxfrKYb2abSJVuVBoYO9ioiEZKOBogoInXAqs9OjiykD+OJtJPV1mUx89RFaDbIUT5KVuaYWXCK9Z5GG1NW3A0MCPAtuCos9akamCwBirYBuumplQNjFQDFWwjVWdlVjUwWAMVbIN1U1OqBkaqgQq2kaqzMqsaGKyBCrbBuqkpVQMj1UAF20jVWZlVDQzWQAXbYN3UlKqBkWqggm2k6izDzNMxcOcGvjfOveHvDfZ4Ez/e6OewdHQxLcbXcFkNVLCV1e+0uXtahkd1cF5HxoBtENCk48xmPLdZnzhQM935FWzd6XpKJQmiNsgYreLRNJlHEDEicu15Umnw+8XF9BoevQYq2Eav05FzBGh85omnw3HxXKWHoYkXaAC0H5gEqHnqdHLkTTWUYQXbUPWMPzGCBpABPF4Lscgii+Tn/nj2zy/+8Lq39gjoUwoVWONvywq28bfBfCXgnf28wo93NzqqxdfJOVL5uWDe5QII+cIMD7YS5n0pG2+8cX43yjvf+c4MSkfC+QpQCUaigQq2kaixLBM2R7bYYov8nkx2Ih2tfOemAGRUA3CAjNcy8EJVvhC677775pen8u4UPqrxoQ99KAvcb81Xtiazm3sF2wxvf4HEW8ZwAIRX9zFa8YJafH58VIMvl3pbgHdt8poJrhnRmHri3vCGN/R9JXdOrH9FNVAcbO6mWQvvDXFtWBoNizQfxNR4uLYn9r6R1/Iu5SODcrj26XIKxtu7eHktn3jiTWPKEOurfMRBx/cRoCMeMOp4rz+fEvZzUcZXv7wG/r8VypeV1xtMdQCVBizgvAdEvCCKi30NzLS4ZikturLZKShzF4CjLD7o9+hHPzq/6MiykYXpJLpUJ+gBvfBlUD73i2O9t9FGGzUdG5spL3/5y/MLk6xPaf1V/v/TQGdgA0QaSlQ+xhJPSJCmEQC2aEgYN3xw+pFXibCyRN7I0ZY5po8yrM7YlTTst9ZiOaQpk50Z6VF+Oy9ugnfRUUT5ajil4mDDCGh8DaWtdL5iycf8eHUd0x3fne/IxWLedYnvhoQfzg2CNs8S17xKnE0H69MV2KPerLdAETyMcISVSb1EOjotZgdurjhTKKGryrO/BoqDjWKjwRB2xCKMAfNJWnplFvR81/qyyy5rpMWA1lhjjfy96HgGMI54DXGBAHLtvPPO+YMe3MfSUYdYL+NH7VO+IIO3YBlWDmBTP21QCUDyR77D+NW00WigE7ApKgagERgXfba4+WDFMccck9ce0j7xiU/M7/YHeBpIF4aObHzRkq10vjfAl2ksn7Q4RYv1GHWYegsadUIZAMdrfDaOonzEkdcREBCSLi/SqutOA8XBFhvURrd69NJnnXVW4osvfHuNtyGzi8Z3n3XcJyKNT0hpWGxYaDDSlfb5lgAbCzqnuV6X9Llp7Ufa+WSW02q2+9ni95pZgd/VJo6pOTfDyYMO8dlswbXboqT8lff/NFAcbHEEig1ML8wnY/naCyMZdL6228/EAqhTTjklrbjiio1xADR77wjkUg2KzMjBVzW5j8VoJui7KB+9UA4vfn3Sk56UgUWHhA6IjzpVB3ZEdGbkZ8bAhyIB3pe//OUc52aKeapfXgPFwdY2SAxVY+Ad/bvssktTy9tuuy33wN/5zndyHGs00vlkK07Dcis+rj8aJoUCdADrr79+AzSKEXSFimzYWk86JzeS6KBwpqln17WxQyLMN+8Y7a6++uqcTzouSIePeYiDX+woibO+ApVry81M5/4Z184faboKazOUp90Q7moJEOtZHGwWRqVj49BgfAqXb6tZ+ZNPPjl/uYYpmg3F6Qc2UHTutAlY40v5Ntahhx6aRwfLicZqXAnfeqITwscff3xacsklM3DiRpLnI6ExjzpELgxtrbXWSuedd948YkaQcdwrGiU81EHMSBnyVxfwkVfkEfPNhLBAs/PoSqbiYLOXi0Cjcn7T7K677sqNRjrfZ9trr72a3vqee+7JRnXrrbc2vSrTSj4ThbORSypL+flkL5s3TM36GV9JGaLhYuDPfvaz0xJLLJE8DWLZdkReKzvfFscJSMJM402HpyOkAIr0AEhwxbprrObl2rgu2iZXaj5/yK1MfoNhXLIVB5sVjY2Ifm688ca09NJL5w8e0liMXkxz7rjjjqw+D9RycsLekk0S8nz1q1/NNNEI56PzKSdjkPzoBJ7ylKf08GnXqSdxxBcYOeWhT0DFdJJNjx122CGX1E8XgikaFzz4meYoCH97fBjG+FgV8lIW6fCwfQUctAJSP+YfR5j6qwNtCfuKMnchV3GwWQkqScPQWDh8RimmkoBs8803zx8ONB3lrLvuujmNTRR31/BxKi9fFPxjasuW/2KLLZZlYLOGEc5t9IJFZ9aCIt5fo+7XXntt3l1k95Hv2OHQnfSuq+zNlTMCQBrTBA7XGqVp5IsyGE8eQUoe8yGjbSntuHzlRp5Yx67l6QxsVkxj4Dr2LIKHdAyZBiSOxqOh4xSIa+nlW9JnvRSnaP1GkVLlx7Latxt8bo0O6IYbbugRoW1U6Nq4CDgyxXbgug0UTvlEd8YZZ+QOJ7YJ6fCl3SLoY75xhK0rH6Y85JBDsgh0MrE9u5KrONgAS7uHi4ATTFTYtUWsvD2leVQeRmg40o863Aa1Bt+lQbF2xcWR6N57781xnGphdsCNf0dbQYXhG4Y4rl+81ugYKTkqt/jii+cRnFkFu5+xTPJwr5Hn43S2D/I8+clPTjwKxKeNu2gbZZiIT3tdfPHF+Vvs0DtNnkjeUdEUB5uC2ihex8aIYNS4AZPxsQfFgNo9sTxL+MjdT4444pQoN/KMugI8sWwOJfNuEu6hccYUh7zRmAaFLQOd8kQ3IyWOadcqq6yS16iCFZ1fcMEFeUcW/spAmPXP2muvnZ8w4IlwvoXO+toO0nLG5VMH5OTHbSQfnqXeXbriYMNYBZo+FaTik3ECLBoejQmfyBeeKJc4GzuWBR/jLd/eHTrSyKuRSTPMj/yVBV8ZDjrooHTmmWdmWS2bhubZNM6Gxka3s6G8yHdY+ZwK8UHSSy+9NOcj70Tyq09GMMOM3kceeWQe4ShX+bgves4558wjym677Za+9a1vNfG33HJL2nHHHTMgra+Jtg3X6sq0Qb6jK/Uhv22DT5xlaCPwiTSRL+dvmQnQgUsT00uGi4NN4VUYDadB4aOoYT/yO3XzoVHiNAwVTRw9svFckxYVSjg2sDKZFz866IfJRlqsi0YZ+cKPKRrTMwCHw0Do+blfdvbZZ+c45SaNX5QzEwz4o3zo99xzzzy6cXzr9ttv77uZMYBFo9+YfuCBB6YVVlgh65N6couG3U93i6FF38cdd1x61KMe1TO1pANhHcmZUmTDxdGVa3U1P/1Kp09edHP66afnMvbff//Mnzim1JR74YUX5jh1Sho/wEib0mmce+65mabLv07ARqVRKhWerLOxzAcfFKYiibchuAHO+UAUHn8xDsMXvOSVH8bg1Ih4wu2ylWGYTx3hGeWDnlMxrGcAF09JMxIBPmWPxkh+fhN1jszrrbderjfrLZwdwfz4KKv+nXfemR7zmMdkgzTuoosuym/xgpd6oVM5+uij8412dIwjjoMKCy20UFOsnaTLAeoc69sQDghEXRCmbXhpEWswy6FNL7nkknzOFjZMbdtOPptssknivmnXrjjYaBiNOE7hAAPrjAiKQWEP19KzSoOiYoPFLW6NQeXiG+6nYA0KoBCmDF4VFw/9Wm7btw7wpQynMoIVfnYyAB2+3JA+9dRTG1GQl19bRnk1hH0CdhwAiykSIEHGK6+8sg/1vFECVWDykOqaa645z3Tx8MMPzwfF5UCHh0NGzl5y34+zrbjzzz8/ccuENPnnhNAxck192/rsdw2tbUSbWzavd4Cee7a4q666Kh188ME5zB961y7ULaMxt244fjcR/TbMRhAoDjZkRDlWFqXZmwvCidYjNpy9pHlVKteTAZvGSiPYiPCgrInIJw110iCoq7wIK4/TyWWWWSaxfa6bDtjgoQyEeVcJO4bq2zKG+RgwhgcfbpJzpKs9MrTB1ubPpgijNvG8CYwdVOVil/L666/PIqBvaEizExomm2n9nk4njSNoxx57bCbbbLPN0t13392M6CuttFKeUpOoLLQzOuJsqe1lGaX94mBz9HH72kZqg2VYRW1483qLQN6CdyrTSMsFrPJnGjUZZ13Mb12VD168Ro7TLxgkR9V4F8hpp53WdDyRFj7ymp8cjogYEa+pYx1o+eppGI/YKey6667psMMOawwTADItpAymkWws4Ow8MFY7wFe/+tV5VOGgM/XSuKFnGmkbWR7xExlZ2nqAFyDlR37WacjMBg2HJHSUT5n8kBd65d50000XzGlkVLoGRQOqdBQw7IfyyCd9bCDCsTEwuNhbkWY++BCOvSlyQG8efRuM/MNks/HgCy9lNT91h4b7VYCAF/EoM+c92TSZ7gaJ9WdHsj19jHVVpn4+ow2bCuwg4pCZOm299dZ5E4QwIwvTajZfrLf6oqP66Ec/mjbYYIPmRUMYOXyRaZ999smjjbK6hnNzB36DfsgDXbvjEOQ858dZUWTV0RYsObbbbjujsm8Zg3ZVe3Z+SXwAAAoBSURBVIgLXBQf2ZBZxRAWcBOtiw1Kg9tYkQcKbBsVtMRJD41OY/caX37yAbRTcfIhb6zzEUcckZ8jI976IMdNN900kq1/dgqXX375xAOu1rVtnMPqQx7OfbpeYrPDI3Lkcz3H6yl42LefA+yLLrpoHsFjOkfJfD4R/arjqKtI3w5bH32n/dDRvrw9jPOzrN+4tu2ZJh511FGNDWgL7AIzQsf2aZdZ6roTsKEolIBD2Roc1zzDtvvuu+fNEhp47733bhREupsifFgCA8XpRz45YQp/8qAntqeFjfLKUjquqUM7XboSfiwb/hiqRss1ayTWLhokccgXrwWMafgTcRip+uam9jrrrJOzxQ4JWbiX6JZ71A1rwGuuuaYpyik3Eeh8fs66I4dTQvMQd8ABB2TAUablkocHfenMop7Ih615lrSdJt9SfnGw2aNQgTilRHFUlgPITAVQEOsadh59xo04TiRwEBinMgk7bcsJ0/izI4i8Zae80WijkY1KBsvr51M2OsSPhqqhnHjiifkECUekcNYjyiwtsssL2tg2/cqOcdZ1p512Sttuu21Ogi9AZPOEUQTHtZtVlEdnySgCUHUAP4Lf+EF+/LiI+bAfToK4OWJey+bgOA/MsoZkNKQt2SFdeeWVMym2FXVk/pJ+cbDFCsWhW0NuV457ILyCQKPmPs4ee+yRjQgFayA2fjv/VK4ZKTRS8tOgcZqDAbXLU46plDfZPNRbp16Qid1NplBO7UzTJw9yqmtBJy94TMRhmDjbj91Kdv4YVbiNwcuQKBOdSau+llpqqbyW4/YAthBlkN8wGaS3DtSHEyvLLbdcMz0lP3UhTXtjPYwtOZ3mvhydAg45Y8c1rPxRphUHG8JGQ47XKIanjXkIknk0N2VZF7DG0fFu+ssvvzxxaps1wYYbbtjTYNJN1Vc2Gh6Q0bg333xzPhuILDQgZwa5j7TNNtvkRt1vv/3y+obrrlwEhoaCvrbffvssgvXAKDU4R4HoA4LIa37yy1c6wUQ5pPGLHZN0Aimm2Qk4+kg7zDc/vsCDPtZBQBEfASdf0wfJKl1pvxOwRSVRYXspjsywKP/kJz+Z68kJAKaR7GzhoAOEPBrBfRp29UjHp7fXqKajJA1GHjQi60bKYArE/J4TH6xHkJW1CWf/2ApHlq5cBAxl0lPzAiB29hxFiLfDIIx+ou6VdVC86W1fgBEvYGKc9HEExujRra5NT9pU2g8+tFG/esWy4N0uk3Rtrw1e85b0i4NNhaocKklD4HiBDlMCHL0P6w5OWDDPxoCYc2PwTJd0GDxfcRmls/fUOGgQ1o9sdXO+DwfYKZuDvsjPaLvsssuOUoyBvCI4MDROh6AnAK/M1EHjir2+xgVzRkSvqUOkG1h42K2FBlkAHGVZNte0lwAT/LQ5P29IO9pFUA4rlzTyUzfLivTIENPiiGk9obGe3nIY1mFE/qMOFwebAtMQAo44GgDjBVgaO/ecmK7p2DjhsRF7Kd8h6e6WxiX9VP3YkMrI/H611VZrWPLCH475UA8cz35xE7i0Uzbryjb/4x//+Hwjl7IZyaTh2ikTYfVKGACw9j3hhBMmtAtInuiodzRm02LZxmnolq9OSY/06tJ8E/XhaxnkETyCSj7SEO/MINJL15XfCdg0FJVL5a+77roMNnsbejte0srWrPRbbbVVz24TGyccdcLFRpuOsiwL2WJj8XwX70WxIXnvIoDTrb766umKK67wsqjvSEEhnNRgLakhE4cuoj4cQZxVmMbxJTY1dNbd636+eWOa/AURekN/8R6Y+dQfhm+cvMzvdT8/tonlSEf91IM6gqdh6y89NqYMpE2kfPOOwi8ONiunsPYwbOdyYpuP9NEQHDViB4nDtDgUxnm7k046KSuFLV6mlHzggoZt85X/VHx4tfkhC2XpmLYJLoyKrWVeeMpzX9bJxosGYv7p+PJjbcsalhuzOsvkOobjdjn64uAzR8R4JEZ+8qh+NxooDjaqQS9iL4pB0Pg4gMQxJoyAb4ixC4iDlqnia17zmrz7yHRz1VVX7TF+6NoAyZkn+afhUaZh1kJMZ1njEM9Ul6ehmcbae7M5wT0b0nDUSWOXzyRF6UvuyEA56MHXjaMzrn3qIIY5AQIoiaODwvcX17+2Sd+Ca+TINdAJ2DDCCAwNyNqwftNAY48cjYHpAnyMk14e0/E9uAsP5/mEnYYwyjpdadMoj6Mb6bGuXE/XMf3Zcsst80OagoZZAWFO3QAsj1eZjg+NP+53EcexKhz3varrVgPFwRZHMqtGnDtShHUCDSN39JPOebi07WvjJ+sLKPJ5/0qwUIZykK4sAi8arGnQyXMUHULkETuCWA6jrSMu8To6AjsDdUsa9Ys6lr76ZTVQHGw2Ln4Emdf4jHRtY9VISI9OQydOcMT0yYYBUzRo8kej1ojxI60gxI8dikCDT5R1snJJL/C5Rk7u8fEaAjeWouzKHUdqXhvA6MaGDrcvpJF/9bvTQCdgi0bXnkJaVWgw3DgdA3D96AFmNDJ5TNW3l4evIEcORrZo7PJHJuKRIabDh3wCTkCabyq+9ZRnnAnwqgXXZNxgZ53JVJGDyYy6nCvleS/qxQYTj5bo5Od19ctroDjYNA6N2EY23m1kqmqvi4FBpyGbB5oIPumnq6bIE17KJl/kiTTtdOmI7yez6dPxGVkZmRZeeOH8lDEjm2Xh86PDivp86Utf2nwXgXtkABGHPkfREUynPrMxb2dgwwg0DhQdw1HxGnLbGNrAisYf8082LJAjuOURp7bG4WvQdiDIjLxR5jhCx7yTDUc9wZ+n0QGdjjh1ZpyjITfh44clBZtyR97mrX45DRQHWznRZwdngBFBzOkRrukceBQJAMXtf6aTPLYE2Hl62bdI8WoJwabmBKXX1S+rgQq2svodGXeOYXEfkvuRHJLmyeRBI5MbR9xwZyrJq8G5Ic4TEzimmxz7qq5bDVSwdavvSZfGKOa0jwPYPGbEkwdOUxmd3NiRzmkloxngZERjRORFQ9E5HY5xNVxOAxVs5XQ7Es6uKQESP4DEr72GpTCARxp5nHpKTzrx7FIOGhFHInBlMlADFWwDVTNzEgBR3BCKYGGEA1j9NnO88S+9I59gFMgzp6YLtiQVbDO8fQUKwOAnuIj3hjtV8F4m8QKTUc1w3A2O+WZ49Rco8SrYZnhzumaLO4cRRIRjGoCMo5xgjeszp6B1ZOu28SvYutX3lEpz/cU0MALJaaHp3OgGfDpHuwhG46SpfncaqGDrTte1pFmugTmuBao/+BXYJXUzy+1vVlW/jmyzqrlrZcepgQq2cWq/lj2rNFCnkUO+oFJy+ijvWWVts7yydWSb5QZQq9+dBirYutN1LWmWa2AOJxLqb3w6mOX2N6uqX8E25s5mVlnbLK9sBVsF2yyHQHfV/z93oJRbfyn17AAAAABJRU5ErkJggg==)\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f03VJHxVbI1V"
      },
      "source": [
        "# sigmoid function\n",
        "def sigmoid(z):\n",
        "    return 1/(1 + np.exp(-z))"
      ],
      "execution_count": 218,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JWjiPQNwXkhL"
      },
      "source": [
        "# predicting y\n",
        "def y_predicted(X,weights,bias):\n",
        "  z=np.dot(X,weights)+bias\n",
        "  y=sigmoid(z)"
      ],
      "execution_count": 219,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HKqYc82rYTl2"
      },
      "source": [
        "# calculating binary cross entropy loss\n",
        "def binary_cross_entropy(y,y_predicted):\n",
        "  m=len(y)\n",
        "  return -(1/m)*np.sum(y*np.log(y_predicted)+(1-y)*np.log(1-y_predicted))"
      ],
      "execution_count": 220,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YrA-4tgNm3dZ"
      },
      "source": [
        "def Logistic_Regression(X, y, learning_rate, number_of_iterations):\n",
        "\n",
        "  global losses,weights,bias \n",
        "  losses = []\n",
        "\n",
        "  m = X.shape[0] # no: of training examples\n",
        "  n = X.shape[1] # no: of independent/feature variables\n",
        "\n",
        "  # initializing weights and bias\n",
        "  weights=np.zeros(n)\n",
        "  bias=0\n",
        "\n",
        "  for i in range(0,number_of_iterations):\n",
        "\n",
        "    # calculate y_predicted using the line equation and sigmoid function\n",
        "    z = np.dot(X,weights)+bias\n",
        "    y_predicted = sigmoid(z) + np.finfo(float).eps # adding epsilon to avoid 0 in the log function\n",
        "\n",
        "    # calculate the loss\n",
        "    loss = binary_cross_entropy(y,y_predicted)\n",
        "    losses.append(loss)\n",
        "\n",
        "    # calculate partial derivative\n",
        "\n",
        "    dw = (1/m)*(2*np.matmul(X.T,(y_predicted-y)))\n",
        "    db = (1/m)*(np.sum(y_predicted-y))\n",
        "\n",
        "    # update weights and bias\n",
        "    weights -= learning_rate*dw\n",
        "    bias -= learning_rate*db\n",
        "\n",
        "    if i%100==0:\n",
        "      print(\"Loss after iteration \",i,\" iteration is: \",loss)"
      ],
      "execution_count": 221,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vuz2bn50uBDl"
      },
      "source": [
        "# predicting probabilities for the training set\n",
        "def predict_probabilities(X):\n",
        "  z = np.dot(X,weights)+bias\n",
        "  return sigmoid(z)"
      ],
      "execution_count": 222,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YIHBU1Pou2RR"
      },
      "source": [
        "# predicting the final outcome based on the threshold and prediction probabilities\n",
        "\n",
        "def predict_class(X,thetha = 0.5):\n",
        "  # thetha represents the threshold\n",
        "\n",
        "  probabilities = predict_probabilities(X)\n",
        "  predictions = [1 if i>thetha else 0 for i in probabilities]\n",
        "\n",
        "  # print(set(probabilities))\n",
        "  return predictions"
      ],
      "execution_count": 231,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JffXfguKw76J",
        "outputId": "2df94a5d-c37c-4d89-924c-82b4a024e049"
      },
      "source": [
        "Logistic_Regression(X, y, 0.01, 1000)"
      ],
      "execution_count": 232,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Loss after iteration  0  iteration is:  0.693147180559945\n",
            "Loss after iteration  100  iteration is:  0.640836361940794\n",
            "Loss after iteration  200  iteration is:  0.6092673438282016\n",
            "Loss after iteration  300  iteration is:  0.5898481907225694\n",
            "Loss after iteration  400  iteration is:  0.5776750533374495\n",
            "Loss after iteration  500  iteration is:  0.5699149166579361\n",
            "Loss after iteration  600  iteration is:  0.5648962610271326\n",
            "Loss after iteration  700  iteration is:  0.5616109036168895\n",
            "Loss after iteration  800  iteration is:  0.5594381873792835\n",
            "Loss after iteration  900  iteration is:  0.5579890070804306\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9GMMYWsUFPDB",
        "outputId": "7c8607fc-6267-4989-dc9d-d0f64a756c58"
      },
      "source": [
        "print(\"weights: \",weights)\n",
        "print(\"bias: \",bias)"
      ],
      "execution_count": 233,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "weights:  [0.02300137 0.00638824 0.07130289 0.06149242 0.15420906]\n",
            "bias:  0.9774585540548958\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MdnGeYgKx44q",
        "outputId": "378766f5-dbde-4e8d-c5cf-745311290e12"
      },
      "source": [
        "final_classification = predict_class(X,thetha = 0.5)\n",
        "predict_class(X,thetha = 0.5)"
      ],
      "execution_count": 234,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              " ...]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 234
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4UzReikbzsOt"
      },
      "source": [
        "### Visualizing training loss"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "yHWez1GtzLc4",
        "outputId": "0564dc7b-84b5-4777-d936-4413bb432bf5"
      },
      "source": [
        "plt.plot(range(0,len(losses)), losses)\n",
        "plt.xlabel(\"no: of iterations\")\n",
        "plt.ylabel(\"loss\")\n",
        "plt.show()"
      ],
      "execution_count": 235,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v0sLyZV3z2nt"
      },
      "source": [
        "### Evaluation of model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J4NC0nwfJcyF",
        "outputId": "c8db4841-492a-41ef-d812-059cac1c55b8"
      },
      "source": [
        "Logistic_Regression(X_test, y_test, 0.01, 1000)"
      ],
      "execution_count": 236,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Loss after iteration  0  iteration is:  0.693147180559945\n",
            "Loss after iteration  100  iteration is:  0.6261143969027227\n",
            "Loss after iteration  200  iteration is:  0.585473489474409\n",
            "Loss after iteration  300  iteration is:  0.5602937009110805\n",
            "Loss after iteration  400  iteration is:  0.5443457099370156\n",
            "Loss after iteration  500  iteration is:  0.5340412133158399\n",
            "Loss after iteration  600  iteration is:  0.527266757181275\n",
            "Loss after iteration  700  iteration is:  0.5227467439654019\n",
            "Loss after iteration  800  iteration is:  0.5196930155582492\n",
            "Loss after iteration  900  iteration is:  0.5176080914738925\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JspFKWEp1crz",
        "outputId": "f96e5fa8-7527-460c-9606-a4005ac59413"
      },
      "source": [
        "y_pred = predict_class(X_test,thetha = 0.5)\n",
        "accuracy_score(y_test,y_pred)"
      ],
      "execution_count": 237,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7882932166301969"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 237
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TfI_J-991old",
        "outputId": "f3d3cbda-c536-4ba1-ed80-80c2e5c58c35"
      },
      "source": [
        "confusion_matrix(y_test,y_pred)"
      ],
      "execution_count": 238,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[   0, 1161],\n",
              "       [   0, 4323]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 238
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pRWaBvnfKN1C"
      },
      "source": [
        "### Comparing our model with Scikit-learn model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9DkACy6SKNEM"
      },
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "model = LogisticRegression()\n",
        "model.fit(X,y)\n",
        "preds=model.predict(X_test)"
      ],
      "execution_count": 239,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QEEdi-8lKxQY",
        "outputId": "601ac496-533a-4bd1-a1c3-ae2b3a118fd1"
      },
      "source": [
        "accuracy_score(y_test,preds)"
      ],
      "execution_count": 240,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7882932166301969"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 240
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y1oHORUBK4j_",
        "outputId": "27e42546-56fd-4968-d416-1e81c9651841"
      },
      "source": [
        "confusion_matrix(y_test,preds)"
      ],
      "execution_count": 241,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[   0, 1161],\n",
              "       [   0, 4323]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 241
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0IrgSyPKK_6e"
      },
      "source": [
        ":)"
      ]
    }
  ]
}