JEE_ADV__MarkvRank.ipynb

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        "import pandas as pd\n",
        "import numpy as np\n",
        "import math\n",
        "import copy\n",
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "from scipy import stats\n",
        "import matplotlib.pyplot as plt\n",
        "import csv\n",
        "import statsmodels.formula.api as smf"
      ]
    },
    {
      "cell_type": "code",
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        "id": "oWS2MMbDzo-w"
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        "#datasets\n",
        "real_possible_ranks = np.array([1, 101, 201, 301, 401, 501, 601, 701, 801, 901, 1001, 1101, 1201, 1301, 1401, 1501, 1601, 1701, 1801, 1901, 2001, 2101, 2201, 2301, 2401, 2501, 2601, 2701, 2801, 2901, 3001, 3101, 3201, 3301, 3401, 3501, 3601, 3701, 3801, 3901, 4001, 4101, 4201, 4401, 4501, 4701, 4801, 4901, 5101, 5301, 5501, 5601, 5801, 6001, 6101, 6401, 6601, 6801, 6901, 7201, 7401,7601, 7901, 8101, 8301, 8601, 8801, 9101, 9401, 9701, 10001, 10201, 10601, 10901, 11201, 11501, 11901, 12201, 12601, 12901, 13301, 13701, 14101, 14501, 15001, 15401, 15801, 16301, 16801, 17301, 17801, 18301, 18901, 19401, 19901, 20501, 21101, 21601, 22301, 22901, 23601, 24201, 24801, 25501, 26201, 26801, 27501, 28301])\n",
        "real_scores_set = np.array([314,236,221,209,199,192,186,182,177,173,170,167,163,161,159,156,153,151,149,147,148,146,144,143,141,140,138,137,136,134,133,132,131,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55])\n",
        "real_scores_set_2017 = np.array([339,305,295,289,284,])\n",
        "possible_ranks = (max(real_possible_ranks) - real_possible_ranks)/max(real_possible_ranks)\n",
        "scores_set = (max(real_scores_set) - real_scores_set)/ max(real_scores_set)"
      ]
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      "source": [
        "data = []\n",
        "with open('rank_score.csv', 'w') as f:\n",
        "  for i in range(len(real_possible_ranks)):\n",
        "    data.append([real_possible_ranks[i], real_scores_set[i]])\n",
        "  header = [\"Rank\", \"Mark\"]\n",
        "  rows = data\n",
        "\n",
        "  writer_obj = csv.writer(f)\n",
        "  writer_obj.writerow(header)\n",
        "  writer_obj.writerows(rows)"
      ]
    },
    {
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        "id": "nyPMIKiSz3Si",
        "outputId": "5c7180c9-1880-4eb9-ab33-589b24655711"
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      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "      Rank  Mark\n",
            "0        1   314\n",
            "1      101   236\n",
            "2      201   221\n",
            "3      301   209\n",
            "4      401   199\n",
            "..     ...   ...\n",
            "103  25501    59\n",
            "104  26201    58\n",
            "105  26801    57\n",
            "106  27501    56\n",
            "107  28301    55\n",
            "\n",
            "[108 rows x 2 columns]\n"
          ]
        }
      ],
      "source": [
        "# prompt: a csv file containing the data of ranks and scores in a JEE exam yeaer\n",
        "df = pd.read_csv('rank_score.csv')\n",
        "print(df)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ipap5Vgs5QLn"
      },
      "source": [
        "Since we have two continuous numerical columns/variables, we should use pearson coefficient for hypothesis testing."
      ]
    },
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            "text/plain": [
              "          Rank      Mark\n",
              "Rank  1.000000 -0.822911\n",
              "Mark -0.822911  1.000000"
            ],
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "sns.pairplot(df)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "vjXM1OEG0zgm",
        "outputId": "5dfb2251-f73b-4a55-ff7e-98b6882df4ab"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Mark', ylabel='Rank'>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "sns.regplot(x=\"Mark\", y = \"Rank\", data=df)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "s_kN2BqZz95n",
        "outputId": "9f5a41d0-b881-4aa1-9bd9-dd8a1f9c914e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7b86dc3ee470>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.scatter(df['Rank'], df['Mark'])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xaqre987z4cs",
        "outputId": "e97842cb-ea4b-47f3-b593-8c9d1a71268d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The Pearson Correlation Coefficient is -0.8229106714924899  with a P-value of P = 8.826240230637984e-28\n"
          ]
        }
      ],
      "source": [
        "#H0 -> There is no correlation between JEE_ADV Mark vs Rank\n",
        "\n",
        "#H1 -> There is a correlation between JEE_ADV Mark vs Rank\n",
        "\n",
        "\n",
        "#finding pearson Coefficient\n",
        "pearson_coef, p_value = stats.pearsonr(df['Rank'], df['Mark'])\n",
        "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IaTe_otQ59c8"
      },
      "source": [
        "<b><h5>Since the p-value <= 0.05, we can approve alternate hypothesis to be true</h5></b>\n",
        "\n",
        "We can now start with our regression model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vL2MoERH027P",
        "outputId": "dae1362b-4060-4f96-8c93-c6df261204ec"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration    0: Cost 10897689.72   \n",
            "Iteration 1000: Cost 272574.32   \n",
            "Iteration 2000: Cost 272574.06   \n",
            "Iteration 3000: Cost 272573.80   \n",
            "Iteration 4000: Cost 272573.53   \n",
            "Iteration 5000: Cost 272573.27   \n",
            "Iteration 6000: Cost 272573.01   \n",
            "Iteration 7000: Cost 272572.74   \n",
            "Iteration 8000: Cost 272572.48   \n",
            "Iteration 9000: Cost 272572.22   \n",
            "[[-1065.0943845183476, 5.200033573425672, -0.0080861995317073], 70999.99996126402]\n"
          ]
        }
      ],
      "source": [
        "#model\n",
        "b_0 = 71000\n",
        "w_0 = [-1100,5.2,-0.009]\n",
        "def compute_cost(x, y, w, b):\n",
        "\n",
        "    m = x.shape[0]\n",
        "    cost = 0\n",
        "\n",
        "    for i in range(m):\n",
        "        f_wb = w[0]* (x[i]) + w[1]*(x[i])**2 + w[2]*(x[i])**3 + b\n",
        "        cost = cost + (f_wb - y[i])**2\n",
        "    total_cost = 1 / (2 * m) * cost\n",
        "\n",
        "    return total_cost\n",
        "cost = compute_cost(df['Mark'], df['Rank'],w_0,b_0)\n",
        "\n",
        "def compute_gradient(x,y,w,b):\n",
        "  m = x.shape[0]\n",
        "  dj_dw_1 = 0\n",
        "  dj_dw_2 = 0\n",
        "  dj_dw_3 = 0\n",
        "  dj_db = 0\n",
        "\n",
        "  for i in range(m):\n",
        "      f_wb = w[0]* (x[i]) + w[1]*(x[i])**2 + w[2]*(x[i])**3 + b\n",
        "      dj_dw_1_i = (f_wb - y[i]) * x[i]\n",
        "      dj_dw_2_i =(f_wb - y[i]) * x[i]**2\n",
        "      dj_dw_3_i = (f_wb - y[i]) * x[i]**3\n",
        "      dj_db_i = f_wb - y[i]\n",
        "      dj_db += dj_db_i\n",
        "      dj_dw_1 += dj_dw_1_i\n",
        "      dj_dw_2 += dj_dw_2_i\n",
        "      dj_dw_3 += dj_dw_3_i\n",
        "  dj_dw_1 = dj_dw_1/m\n",
        "  dj_dw_2 = dj_dw_2/m\n",
        "  dj_dw_3 = dj_dw_3/m\n",
        "  dj_db = dj_db/ m\n",
        "\n",
        "  return dj_dw_1,dj_dw_2, dj_dw_3, dj_db\n",
        "\n",
        "def gradient_descent(x,y,w_in,b_in,cost_function,gradient_function,alpha, num_iters):\n",
        "   # An array to store cost J and w's at each iteration primarily for graphing later\n",
        "    J_history = []\n",
        "    w = copy.deepcopy(w_in)  #avoid modifying global w within function\n",
        "    b = b_in\n",
        "\n",
        "    for i in range(num_iters):\n",
        "\n",
        "        # Calculate the gradient and update the parameters\n",
        "        dj_dw_1, dj_dw_2,dj_dw_3, dj_db = gradient_function(x, y, w, b)\n",
        "\n",
        "        # Update Parameters using w, b, alpha and gradient\n",
        "        w[0] = w[0] - alpha * dj_dw_1\n",
        "        w[1] = w[1] - beta * dj_dw_2\n",
        "        w[2] = w[2] - gamma * dj_dw_3\n",
        "        b = b - delta * dj_db\n",
        "\n",
        "        # Save cost J at each iteration\n",
        "        if i<100000:      # prevent resource exhaustion\n",
        "            J_history.append(cost_function(x, y, w, b))\n",
        "\n",
        "        # Print cost every at intervals 10 times or as many iterations if < 10\n",
        "        if i% math.ceil(num_iters / 10) == 0:\n",
        "            print(f\"Iteration {i:4d}: Cost {J_history[-1]:8.2f}   \")\n",
        "\n",
        "    return w, b\n",
        "iterations = 10000\n",
        "alpha = .7e-5\n",
        "beta = 2e-14\n",
        "gamma = 2e-14\n",
        "delta = 2.5e-10\n",
        "final = gradient_descent(df['Mark'],df['Rank'],w_0,b_0,compute_cost,compute_gradient,alpha, iterations)\n",
        "w_f, b_f = final\n",
        "print([w_f, b_f])\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ptg3xtQWn3-1",
        "outputId": "38803c95-8d56-426e-d630-d8ebeaf4d1fd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Enter your marks: 150\n",
            "rank is equal to 945.6742660773598\n"
          ]
        }
      ],
      "source": [
        "data = float(input('Enter your marks: '))\n",
        "f = w_f[2]*data**3 + w_f[1]*data**2 + w_f[0]*data + b_f\n",
        "print(f'rank is equal to {f}')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 864
        },
        "id": "Qd8Wwodd2drB",
        "outputId": "eb468817-8081-472b-ab2d-e3e677d18e16"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-12-63ce1e12df18>:2: UserWarning: \n",
            "\n",
            "`distplot` is a deprecated function and will be removed in seaborn v0.14.0.\n",
            "\n",
            "Please adapt your code to use either `displot` (a figure-level function with\n",
            "similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "\n",
            "For a guide to updating your code to use the new functions, please see\n",
            "https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751\n",
            "\n",
            "  ax1 = sns.distplot(df['Rank'], hist = False, color = 'b', label = \"Actual Value\")\n",
            "<ipython-input-12-63ce1e12df18>:3: UserWarning: \n",
            "\n",
            "`distplot` is a deprecated function and will be removed in seaborn v0.14.0.\n",
            "\n",
            "Please adapt your code to use either `displot` (a figure-level function with\n",
            "similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "\n",
            "For a guide to updating your code to use the new functions, please see\n",
            "https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751\n",
            "\n",
            "  sns.distplot(w_f[2]*df['Mark']**3 + w_f[1]*df['Mark']**2 + w_f[0]*df[\"Mark\"] + b_f, hist = False, color = 'r', label = 'Predicted Value')\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='Mark', ylabel='Density'>"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#model visualization\n",
        "ax1 = sns.distplot(df['Rank'], hist = False, color = 'b', label = \"Actual Value\")\n",
        "sns.distplot(w_f[2]*df['Mark']**3 + w_f[1]*df['Mark']**2 + w_f[0]*df[\"Mark\"] + b_f, hist = False, color = 'r', label = 'Predicted Value')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "RWlxmcABTxZE",
        "outputId": "7f683204-4463-4813-9a65-14aa4b69ce61"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7b86dc344f40>]"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.plot(df['Mark'], df['Rank'])\n",
        "plt.plot(df['Mark'], w_f[2]*df['Mark']**3 + w_f[1]*df['Mark']**2 + w_f[0]*df[\"Mark\"] + b_f)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}