data_exploration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**A data science experiment using data from the KDD 2010 Educational Data Mining Challenge**\n",
    "\n",
    "The aim of this IPython Notebook is to give you a sense of the dataset.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the data: Algebra 2005-2006\n",
    "#train_filepath = 'algebra_2005_2006_train.txt'\n",
    "#traindata = pd.read_table(train_filepath)\n",
    "traindata = pd.read_csv('train.csv',sep = '\\t')\n",
    "testdata = pd.read_csv('test.csv',sep = '\\t')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some more information the data format can be found on the [challenge website](https://pslcdatashop.web.cmu.edu/KDDCup/rules_data_format.jsp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Row', 'Anon Student Id', 'Problem Hierarchy', 'Problem Name',\n",
       "       'Problem View', 'Step Name', 'Step Start Time',\n",
       "       'First Transaction Time', 'Correct Transaction Time', 'Step End Time',\n",
       "       'Step Duration (sec)', 'Correct Step Duration (sec)',\n",
       "       'Error Step Duration (sec)', 'Correct First Attempt', 'Incorrects',\n",
       "       'Hints', 'Corrects', 'KC(Default)', 'Opportunity(Default)'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traindata.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Row</th>\n",
       "      <th>Anon Student Id</th>\n",
       "      <th>Problem Hierarchy</th>\n",
       "      <th>Problem Name</th>\n",
       "      <th>Problem View</th>\n",
       "      <th>Step Name</th>\n",
       "      <th>Step Start Time</th>\n",
       "      <th>First Transaction Time</th>\n",
       "      <th>Correct Transaction Time</th>\n",
       "      <th>Step End Time</th>\n",
       "      <th>Step Duration (sec)</th>\n",
       "      <th>Correct Step Duration (sec)</th>\n",
       "      <th>Error Step Duration (sec)</th>\n",
       "      <th>Correct First Attempt</th>\n",
       "      <th>Incorrects</th>\n",
       "      <th>Hints</th>\n",
       "      <th>Corrects</th>\n",
       "      <th>KC(Default)</th>\n",
       "      <th>Opportunity(Default)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9938</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C1</td>\n",
       "      <td>2005-09-09 12:23:34.0</td>\n",
       "      <td>2005-09-09 12:24:07.0</td>\n",
       "      <td>2005-09-09 12:24:07.0</td>\n",
       "      <td>2005-09-09 12:24:07.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9939</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C2</td>\n",
       "      <td>2005-09-09 12:24:07.0</td>\n",
       "      <td>2005-09-09 12:24:22.0</td>\n",
       "      <td>2005-09-09 12:24:22.0</td>\n",
       "      <td>2005-09-09 12:24:22.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9940</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C1</td>\n",
       "      <td>2005-09-09 12:24:22.0</td>\n",
       "      <td>2005-09-09 12:25:16.0</td>\n",
       "      <td>2005-09-09 12:25:40.0</td>\n",
       "      <td>2005-09-09 12:25:40.0</td>\n",
       "      <td>78.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>78.0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Define Variable</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9941</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C2</td>\n",
       "      <td>2005-09-09 12:25:40.0</td>\n",
       "      <td>2005-09-09 12:25:51.0</td>\n",
       "      <td>2005-09-09 12:27:24.0</td>\n",
       "      <td>2005-09-09 12:27:24.0</td>\n",
       "      <td>104.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>104.0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Write expression, positiv...</td>\n",
       "      <td>1~~1~~1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9942</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R4C1</td>\n",
       "      <td>2005-09-09 12:27:24.0</td>\n",
       "      <td>2005-09-09 12:27:30.0</td>\n",
       "      <td>2005-09-09 12:27:30.0</td>\n",
       "      <td>2005-09-09 12:27:30.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>9943</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R5C1</td>\n",
       "      <td>2005-09-09 12:27:30.0</td>\n",
       "      <td>2005-09-09 12:27:41.0</td>\n",
       "      <td>2005-09-09 12:27:41.0</td>\n",
       "      <td>2005-09-09 12:27:41.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9944</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R6C1</td>\n",
       "      <td>2005-09-09 12:27:41.0</td>\n",
       "      <td>2005-09-09 12:28:41.0</td>\n",
       "      <td>2005-09-09 12:28:41.0</td>\n",
       "      <td>2005-09-09 12:28:41.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>9945</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R7C2</td>\n",
       "      <td>2005-09-09 12:28:50.0</td>\n",
       "      <td>2005-09-09 12:28:58.0</td>\n",
       "      <td>2005-09-09 12:28:58.0</td>\n",
       "      <td>2005-09-09 12:28:58.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9946</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>ValidEquations</td>\n",
       "      <td>2005-09-09 12:31:39.0</td>\n",
       "      <td>2005-09-09 12:31:52.0</td>\n",
       "      <td>2005-09-09 12:31:52.0</td>\n",
       "      <td>2005-09-09 12:31:52.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9947</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>7/10*X = 1400</td>\n",
       "      <td>2005-09-09 12:31:52.0</td>\n",
       "      <td>2005-09-09 12:32:28.0</td>\n",
       "      <td>2005-09-09 12:32:35.0</td>\n",
       "      <td>2005-09-09 12:32:35.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>43.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>9948</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>7X/10 = 1400</td>\n",
       "      <td>2005-09-09 12:32:35.0</td>\n",
       "      <td>2005-09-09 12:32:58.0</td>\n",
       "      <td>2005-09-09 12:32:58.0</td>\n",
       "      <td>2005-09-09 12:32:58.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>9949</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R7C1</td>\n",
       "      <td>2005-09-09 12:28:41.0</td>\n",
       "      <td>2005-09-09 12:28:50.0</td>\n",
       "      <td>2005-09-09 12:33:04.0</td>\n",
       "      <td>2005-09-09 12:33:04.0</td>\n",
       "      <td>176.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>176.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Find X, Simple~~Using dif...</td>\n",
       "      <td>2~~1~~2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>9950</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C1</td>\n",
       "      <td>2005-09-09 12:33:21.0</td>\n",
       "      <td>2005-09-09 12:33:31.0</td>\n",
       "      <td>2005-09-09 12:33:31.0</td>\n",
       "      <td>2005-09-09 12:33:31.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>9951</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C2</td>\n",
       "      <td>2005-09-09 12:33:31.0</td>\n",
       "      <td>2005-09-09 12:33:39.0</td>\n",
       "      <td>2005-09-09 12:33:39.0</td>\n",
       "      <td>2005-09-09 12:33:39.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>9952</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C1</td>\n",
       "      <td>2005-09-09 12:33:39.0</td>\n",
       "      <td>2005-09-09 12:33:47.0</td>\n",
       "      <td>2005-09-09 12:33:47.0</td>\n",
       "      <td>2005-09-09 12:33:47.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Define Variable</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>9953</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C2</td>\n",
       "      <td>2005-09-09 12:33:47.0</td>\n",
       "      <td>2005-09-09 12:35:47.0</td>\n",
       "      <td>2005-09-09 12:35:47.0</td>\n",
       "      <td>2005-09-09 12:35:47.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Write expression, positiv...</td>\n",
       "      <td>3~~2~~3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9954</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R4C2</td>\n",
       "      <td>2005-09-09 12:35:51.0</td>\n",
       "      <td>2005-09-09 12:35:57.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005-09-09 12:35:57.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Find Y, Simple~~Using small numbers~~Using dif...</td>\n",
       "      <td>1~~4~~4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>9955</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R4C1</td>\n",
       "      <td>2005-09-09 12:35:47.0</td>\n",
       "      <td>2005-09-09 12:35:51.0</td>\n",
       "      <td>2005-09-09 12:37:55.0</td>\n",
       "      <td>2005-09-09 12:37:55.0</td>\n",
       "      <td>122.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>122.0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>9956</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R5C1</td>\n",
       "      <td>2005-09-09 12:37:55.0</td>\n",
       "      <td>2005-09-09 12:38:02.0</td>\n",
       "      <td>2005-09-09 12:38:02.0</td>\n",
       "      <td>2005-09-09 12:38:02.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>9957</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R6C1</td>\n",
       "      <td>2005-09-09 12:38:02.0</td>\n",
       "      <td>2005-09-09 12:38:11.0</td>\n",
       "      <td>2005-09-09 12:38:11.0</td>\n",
       "      <td>2005-09-09 12:38:11.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>9958</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R7C2</td>\n",
       "      <td>2005-09-09 12:38:11.0</td>\n",
       "      <td>2005-09-09 12:38:35.0</td>\n",
       "      <td>2005-09-09 12:38:35.0</td>\n",
       "      <td>2005-09-09 12:38:35.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>9959</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>ValidEquations</td>\n",
       "      <td>2005-09-09 12:39:32.0</td>\n",
       "      <td>2005-09-09 12:39:52.0</td>\n",
       "      <td>2005-09-09 12:39:52.0</td>\n",
       "      <td>2005-09-09 12:39:52.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>9960</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>3/5*X = 1200000</td>\n",
       "      <td>2005-09-09 12:39:52.0</td>\n",
       "      <td>2005-09-09 12:39:57.0</td>\n",
       "      <td>2005-09-09 12:39:57.0</td>\n",
       "      <td>2005-09-09 12:39:57.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>9961</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>3X/5 = 1200000</td>\n",
       "      <td>2005-09-09 12:39:57.0</td>\n",
       "      <td>2005-09-09 12:40:59.0</td>\n",
       "      <td>2005-09-09 12:41:13.0</td>\n",
       "      <td>2005-09-09 12:41:13.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>76.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9962</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP07</td>\n",
       "      <td>1</td>\n",
       "      <td>R7C1</td>\n",
       "      <td>2005-09-09 12:38:35.0</td>\n",
       "      <td>2005-09-09 12:39:24.0</td>\n",
       "      <td>2005-09-09 12:41:24.0</td>\n",
       "      <td>2005-09-09 12:41:24.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>68.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Find X, Simple~~Using dif...</td>\n",
       "      <td>5~~2~~5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9963</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP08</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C1</td>\n",
       "      <td>2005-09-09 12:41:28.0</td>\n",
       "      <td>2005-09-09 12:41:41.0</td>\n",
       "      <td>2005-09-09 12:41:41.0</td>\n",
       "      <td>2005-09-09 12:41:41.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>9964</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP08</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C2</td>\n",
       "      <td>2005-09-09 12:41:41.0</td>\n",
       "      <td>2005-09-09 12:41:51.0</td>\n",
       "      <td>2005-09-09 12:41:51.0</td>\n",
       "      <td>2005-09-09 12:41:51.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>9965</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP08</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C1</td>\n",
       "      <td>2005-09-09 12:41:51.0</td>\n",
       "      <td>2005-09-09 12:41:54.0</td>\n",
       "      <td>2005-09-09 12:41:54.0</td>\n",
       "      <td>2005-09-09 12:41:54.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Define Variable</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>9966</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP08</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C2</td>\n",
       "      <td>2005-09-09 12:41:54.0</td>\n",
       "      <td>2005-09-09 12:42:06.0</td>\n",
       "      <td>2005-09-09 12:42:06.0</td>\n",
       "      <td>2005-09-09 12:42:06.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Write expression, positiv...</td>\n",
       "      <td>6~~3~~6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>9967</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP08</td>\n",
       "      <td>1</td>\n",
       "      <td>R4C1</td>\n",
       "      <td>2005-09-09 12:42:06.0</td>\n",
       "      <td>2005-09-09 12:42:13.0</td>\n",
       "      <td>2005-09-09 12:42:13.0</td>\n",
       "      <td>2005-09-09 12:42:13.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>10013</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP12</td>\n",
       "      <td>1</td>\n",
       "      <td>6X/500 = 600</td>\n",
       "      <td>2005-09-14 12:35:49.0</td>\n",
       "      <td>2005-09-14 12:35:58.0</td>\n",
       "      <td>2005-09-14 12:35:58.0</td>\n",
       "      <td>2005-09-14 12:35:58.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>[SkillRule: Eliminate Parens; {CLT nested; CLT...</td>\n",
       "      <td>1~~4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>10014</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP12</td>\n",
       "      <td>1</td>\n",
       "      <td>6X = 300000</td>\n",
       "      <td>2005-09-14 12:35:58.0</td>\n",
       "      <td>2005-09-14 12:36:06.0</td>\n",
       "      <td>2005-09-14 12:36:06.0</td>\n",
       "      <td>2005-09-14 12:36:06.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>[SkillRule: Remove positive coefficient; {ax/b...</td>\n",
       "      <td>4~~5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>10015</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP12</td>\n",
       "      <td>1</td>\n",
       "      <td>R4C1</td>\n",
       "      <td>2005-09-14 12:28:29.0</td>\n",
       "      <td>2005-09-14 12:28:37.0</td>\n",
       "      <td>2005-09-14 12:36:12.0</td>\n",
       "      <td>2005-09-14 12:36:12.0</td>\n",
       "      <td>232.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>232.0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Find X, Simple~~Using dif...</td>\n",
       "      <td>18~~7~~18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>10016</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP12</td>\n",
       "      <td>1</td>\n",
       "      <td>R5C1</td>\n",
       "      <td>2005-09-14 12:36:12.0</td>\n",
       "      <td>2005-09-14 12:36:57.0</td>\n",
       "      <td>2005-09-14 12:36:57.0</td>\n",
       "      <td>2005-09-14 12:36:57.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>10017</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP12</td>\n",
       "      <td>1</td>\n",
       "      <td>R6C1</td>\n",
       "      <td>2005-09-14 12:36:57.0</td>\n",
       "      <td>2005-09-14 12:37:02.0</td>\n",
       "      <td>2005-09-14 12:37:02.0</td>\n",
       "      <td>2005-09-14 12:37:02.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>10018</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C1</td>\n",
       "      <td>2005-09-14 12:38:09.0</td>\n",
       "      <td>2005-09-14 12:38:21.0</td>\n",
       "      <td>2005-09-14 12:38:21.0</td>\n",
       "      <td>2005-09-14 12:38:21.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>10019</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C2</td>\n",
       "      <td>2005-09-14 12:38:21.0</td>\n",
       "      <td>2005-09-14 12:38:26.0</td>\n",
       "      <td>2005-09-14 12:38:26.0</td>\n",
       "      <td>2005-09-14 12:38:26.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>10020</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C1</td>\n",
       "      <td>2005-09-14 12:38:26.0</td>\n",
       "      <td>2005-09-14 12:38:29.0</td>\n",
       "      <td>2005-09-14 12:38:29.0</td>\n",
       "      <td>2005-09-14 12:38:29.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Define Variable</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>10021</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C2</td>\n",
       "      <td>2005-09-14 12:38:29.0</td>\n",
       "      <td>2005-09-14 12:38:40.0</td>\n",
       "      <td>2005-09-14 12:38:40.0</td>\n",
       "      <td>2005-09-14 12:38:40.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Write expression, positiv...</td>\n",
       "      <td>19~~7~~19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>10022</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R4C1</td>\n",
       "      <td>2005-09-14 12:38:40.0</td>\n",
       "      <td>2005-09-14 12:38:47.0</td>\n",
       "      <td>2005-09-14 12:38:47.0</td>\n",
       "      <td>2005-09-14 12:38:47.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>10023</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R5C2</td>\n",
       "      <td>2005-09-14 12:38:50.0</td>\n",
       "      <td>2005-09-14 12:38:55.0</td>\n",
       "      <td>2005-09-14 12:38:55.0</td>\n",
       "      <td>2005-09-14 12:38:55.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>10024</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R6C1</td>\n",
       "      <td>2005-09-14 12:38:55.0</td>\n",
       "      <td>2005-09-14 12:39:02.0</td>\n",
       "      <td>2005-09-14 12:39:02.0</td>\n",
       "      <td>2005-09-14 12:39:02.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>10025</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R7C1</td>\n",
       "      <td>2005-09-14 12:39:02.0</td>\n",
       "      <td>2005-09-14 12:39:08.0</td>\n",
       "      <td>2005-09-14 12:39:08.0</td>\n",
       "      <td>2005-09-14 12:39:08.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>10026</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>ValidEquations</td>\n",
       "      <td>2005-09-14 12:39:08.0</td>\n",
       "      <td>2005-09-14 12:40:03.0</td>\n",
       "      <td>2005-09-14 12:40:03.0</td>\n",
       "      <td>2005-09-14 12:40:03.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>10027</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>1/5*X = 40</td>\n",
       "      <td>2005-09-14 12:40:03.0</td>\n",
       "      <td>2005-09-14 12:40:06.0</td>\n",
       "      <td>2005-09-14 12:40:06.0</td>\n",
       "      <td>2005-09-14 12:40:06.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>10028</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>X/5 = 40</td>\n",
       "      <td>2005-09-14 12:40:06.0</td>\n",
       "      <td>2005-09-14 12:40:11.0</td>\n",
       "      <td>2005-09-14 12:40:11.0</td>\n",
       "      <td>2005-09-14 12:40:11.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>[SkillRule: Remove positive coefficient; {ax/b...</td>\n",
       "      <td>5~~6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>10029</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP02</td>\n",
       "      <td>1</td>\n",
       "      <td>R5C1</td>\n",
       "      <td>2005-09-14 12:38:47.0</td>\n",
       "      <td>2005-09-14 12:38:50.0</td>\n",
       "      <td>2005-09-14 12:40:17.0</td>\n",
       "      <td>2005-09-14 12:40:17.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Using small numbers~~Find X, Simple~~Using dif...</td>\n",
       "      <td>20~~8~~20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>10030</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C1</td>\n",
       "      <td>2005-09-14 12:40:21.0</td>\n",
       "      <td>2005-09-14 12:40:35.0</td>\n",
       "      <td>2005-09-14 12:40:35.0</td>\n",
       "      <td>2005-09-14 12:40:35.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>10031</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C2</td>\n",
       "      <td>2005-09-14 12:40:35.0</td>\n",
       "      <td>2005-09-14 12:40:41.0</td>\n",
       "      <td>2005-09-14 12:40:41.0</td>\n",
       "      <td>2005-09-14 12:40:41.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>10032</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C1</td>\n",
       "      <td>2005-09-14 12:40:41.0</td>\n",
       "      <td>2005-09-14 12:40:42.0</td>\n",
       "      <td>2005-09-14 12:40:42.0</td>\n",
       "      <td>2005-09-14 12:40:42.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Define Variable</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>10033</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C2</td>\n",
       "      <td>2005-09-14 12:40:42.0</td>\n",
       "      <td>2005-09-14 12:41:10.0</td>\n",
       "      <td>2005-09-14 12:41:10.0</td>\n",
       "      <td>2005-09-14 12:41:10.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Using difficult numbers~~Using small numbers~~...</td>\n",
       "      <td>21~~21~~8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>10034</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R4C1</td>\n",
       "      <td>2005-09-14 12:41:10.0</td>\n",
       "      <td>2005-09-14 12:41:16.0</td>\n",
       "      <td>2005-09-14 12:41:16.0</td>\n",
       "      <td>2005-09-14 12:41:16.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>10035</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R5C1</td>\n",
       "      <td>2005-09-14 12:41:16.0</td>\n",
       "      <td>2005-09-14 12:41:22.0</td>\n",
       "      <td>2005-09-14 12:41:22.0</td>\n",
       "      <td>2005-09-14 12:41:22.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>10036</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R6C1</td>\n",
       "      <td>2005-09-14 12:41:22.0</td>\n",
       "      <td>2005-09-14 12:41:29.0</td>\n",
       "      <td>2005-09-14 12:41:29.0</td>\n",
       "      <td>2005-09-14 12:41:29.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>10037</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>R7C2</td>\n",
       "      <td>2005-09-14 12:41:29.0</td>\n",
       "      <td>2005-09-14 12:41:36.0</td>\n",
       "      <td>2005-09-14 12:41:36.0</td>\n",
       "      <td>2005-09-14 12:41:36.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Entering a given</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>10038</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>ValidEquations</td>\n",
       "      <td>2005-09-14 12:41:39.0</td>\n",
       "      <td>2005-09-14 12:42:05.0</td>\n",
       "      <td>2005-09-14 12:42:05.0</td>\n",
       "      <td>2005-09-14 12:42:05.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>10100</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_06, Section CTA1_06-1</td>\n",
       "      <td>LDEMO_4QGRPH</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C1</td>\n",
       "      <td>2005-09-16 12:23:33.0</td>\n",
       "      <td>2005-09-16 12:23:43.0</td>\n",
       "      <td>2005-09-16 12:23:43.0</td>\n",
       "      <td>2005-09-16 12:23:43.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>10101</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_06, Section CTA1_06-1</td>\n",
       "      <td>LDEMO_4QGRPH</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C2</td>\n",
       "      <td>2005-09-16 12:23:43.0</td>\n",
       "      <td>2005-09-16 12:23:50.0</td>\n",
       "      <td>2005-09-16 12:23:50.0</td>\n",
       "      <td>2005-09-16 12:23:50.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>10102</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_06, Section CTA1_06-1</td>\n",
       "      <td>LDEMO_4QGRPH</td>\n",
       "      <td>1</td>\n",
       "      <td>R2C2</td>\n",
       "      <td>2005-09-16 12:23:50.0</td>\n",
       "      <td>2005-09-16 12:23:54.0</td>\n",
       "      <td>2005-09-16 12:23:54.0</td>\n",
       "      <td>2005-09-16 12:23:54.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Identifying units</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104</th>\n",
       "      <td>10103</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_06, Section CTA1_06-1</td>\n",
       "      <td>LDEMO_4QGRPH</td>\n",
       "      <td>1</td>\n",
       "      <td>R3C1</td>\n",
       "      <td>2005-09-16 12:23:54.0</td>\n",
       "      <td>2005-09-16 12:23:55.0</td>\n",
       "      <td>2005-09-16 12:23:55.0</td>\n",
       "      <td>2005-09-16 12:23:55.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Define Variable</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>105 rows × 19 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Row Anon Student Id                Problem Hierarchy  Problem Name  \\\n",
       "0     9938      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "1     9939      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "2     9940      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "3     9941      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "4     9942      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "5     9943      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "6     9944      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "7     9945      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "8     9946      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "9     9947      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "10    9948      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "11    9949      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP04   \n",
       "12    9950      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "13    9951      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "14    9952      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "15    9953      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "16    9954      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "17    9955      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "18    9956      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "19    9957      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "20    9958      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "21    9959      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "22    9960      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "23    9961      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "24    9962      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP07   \n",
       "25    9963      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP08   \n",
       "26    9964      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP08   \n",
       "27    9965      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP08   \n",
       "28    9966      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP08   \n",
       "29    9967      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP08   \n",
       "..     ...             ...                              ...           ...   \n",
       "75   10013      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP12   \n",
       "76   10014      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP12   \n",
       "77   10015      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP12   \n",
       "78   10016      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP12   \n",
       "79   10017      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP12   \n",
       "80   10018      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "81   10019      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "82   10020      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "83   10021      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "84   10022      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "85   10023      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "86   10024      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "87   10025      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "88   10026      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "89   10027      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "90   10028      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "91   10029      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP02   \n",
       "92   10030      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "93   10031      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "94   10032      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "95   10033      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "96   10034      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "97   10035      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "98   10036      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "99   10037      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "100  10038      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1        PROP01   \n",
       "101  10100      52vEY7f17k  Unit CTA1_06, Section CTA1_06-1  LDEMO_4QGRPH   \n",
       "102  10101      52vEY7f17k  Unit CTA1_06, Section CTA1_06-1  LDEMO_4QGRPH   \n",
       "103  10102      52vEY7f17k  Unit CTA1_06, Section CTA1_06-1  LDEMO_4QGRPH   \n",
       "104  10103      52vEY7f17k  Unit CTA1_06, Section CTA1_06-1  LDEMO_4QGRPH   \n",
       "\n",
       "     Problem View        Step Name        Step Start Time  \\\n",
       "0               1             R1C1  2005-09-09 12:23:34.0   \n",
       "1               1             R1C2  2005-09-09 12:24:07.0   \n",
       "2               1             R3C1  2005-09-09 12:24:22.0   \n",
       "3               1             R3C2  2005-09-09 12:25:40.0   \n",
       "4               1             R4C1  2005-09-09 12:27:24.0   \n",
       "5               1             R5C1  2005-09-09 12:27:30.0   \n",
       "6               1             R6C1  2005-09-09 12:27:41.0   \n",
       "7               1             R7C2  2005-09-09 12:28:50.0   \n",
       "8               1   ValidEquations  2005-09-09 12:31:39.0   \n",
       "9               1    7/10*X = 1400  2005-09-09 12:31:52.0   \n",
       "10              1     7X/10 = 1400  2005-09-09 12:32:35.0   \n",
       "11              1             R7C1  2005-09-09 12:28:41.0   \n",
       "12              1             R1C1  2005-09-09 12:33:21.0   \n",
       "13              1             R1C2  2005-09-09 12:33:31.0   \n",
       "14              1             R3C1  2005-09-09 12:33:39.0   \n",
       "15              1             R3C2  2005-09-09 12:33:47.0   \n",
       "16              1             R4C2  2005-09-09 12:35:51.0   \n",
       "17              1             R4C1  2005-09-09 12:35:47.0   \n",
       "18              1             R5C1  2005-09-09 12:37:55.0   \n",
       "19              1             R6C1  2005-09-09 12:38:02.0   \n",
       "20              1             R7C2  2005-09-09 12:38:11.0   \n",
       "21              1   ValidEquations  2005-09-09 12:39:32.0   \n",
       "22              1  3/5*X = 1200000  2005-09-09 12:39:52.0   \n",
       "23              1   3X/5 = 1200000  2005-09-09 12:39:57.0   \n",
       "24              1             R7C1  2005-09-09 12:38:35.0   \n",
       "25              1             R1C1  2005-09-09 12:41:28.0   \n",
       "26              1             R1C2  2005-09-09 12:41:41.0   \n",
       "27              1             R3C1  2005-09-09 12:41:51.0   \n",
       "28              1             R3C2  2005-09-09 12:41:54.0   \n",
       "29              1             R4C1  2005-09-09 12:42:06.0   \n",
       "..            ...              ...                    ...   \n",
       "75              1     6X/500 = 600  2005-09-14 12:35:49.0   \n",
       "76              1      6X = 300000  2005-09-14 12:35:58.0   \n",
       "77              1             R4C1  2005-09-14 12:28:29.0   \n",
       "78              1             R5C1  2005-09-14 12:36:12.0   \n",
       "79              1             R6C1  2005-09-14 12:36:57.0   \n",
       "80              1             R1C1  2005-09-14 12:38:09.0   \n",
       "81              1             R1C2  2005-09-14 12:38:21.0   \n",
       "82              1             R3C1  2005-09-14 12:38:26.0   \n",
       "83              1             R3C2  2005-09-14 12:38:29.0   \n",
       "84              1             R4C1  2005-09-14 12:38:40.0   \n",
       "85              1             R5C2  2005-09-14 12:38:50.0   \n",
       "86              1             R6C1  2005-09-14 12:38:55.0   \n",
       "87              1             R7C1  2005-09-14 12:39:02.0   \n",
       "88              1   ValidEquations  2005-09-14 12:39:08.0   \n",
       "89              1       1/5*X = 40  2005-09-14 12:40:03.0   \n",
       "90              1         X/5 = 40  2005-09-14 12:40:06.0   \n",
       "91              1             R5C1  2005-09-14 12:38:47.0   \n",
       "92              1             R1C1  2005-09-14 12:40:21.0   \n",
       "93              1             R1C2  2005-09-14 12:40:35.0   \n",
       "94              1             R3C1  2005-09-14 12:40:41.0   \n",
       "95              1             R3C2  2005-09-14 12:40:42.0   \n",
       "96              1             R4C1  2005-09-14 12:41:10.0   \n",
       "97              1             R5C1  2005-09-14 12:41:16.0   \n",
       "98              1             R6C1  2005-09-14 12:41:22.0   \n",
       "99              1             R7C2  2005-09-14 12:41:29.0   \n",
       "100             1   ValidEquations  2005-09-14 12:41:39.0   \n",
       "101             1             R1C1  2005-09-16 12:23:33.0   \n",
       "102             1             R1C2  2005-09-16 12:23:43.0   \n",
       "103             1             R2C2  2005-09-16 12:23:50.0   \n",
       "104             1             R3C1  2005-09-16 12:23:54.0   \n",
       "\n",
       "    First Transaction Time Correct Transaction Time          Step End Time  \\\n",
       "0    2005-09-09 12:24:07.0    2005-09-09 12:24:07.0  2005-09-09 12:24:07.0   \n",
       "1    2005-09-09 12:24:22.0    2005-09-09 12:24:22.0  2005-09-09 12:24:22.0   \n",
       "2    2005-09-09 12:25:16.0    2005-09-09 12:25:40.0  2005-09-09 12:25:40.0   \n",
       "3    2005-09-09 12:25:51.0    2005-09-09 12:27:24.0  2005-09-09 12:27:24.0   \n",
       "4    2005-09-09 12:27:30.0    2005-09-09 12:27:30.0  2005-09-09 12:27:30.0   \n",
       "5    2005-09-09 12:27:41.0    2005-09-09 12:27:41.0  2005-09-09 12:27:41.0   \n",
       "6    2005-09-09 12:28:41.0    2005-09-09 12:28:41.0  2005-09-09 12:28:41.0   \n",
       "7    2005-09-09 12:28:58.0    2005-09-09 12:28:58.0  2005-09-09 12:28:58.0   \n",
       "8    2005-09-09 12:31:52.0    2005-09-09 12:31:52.0  2005-09-09 12:31:52.0   \n",
       "9    2005-09-09 12:32:28.0    2005-09-09 12:32:35.0  2005-09-09 12:32:35.0   \n",
       "10   2005-09-09 12:32:58.0    2005-09-09 12:32:58.0  2005-09-09 12:32:58.0   \n",
       "11   2005-09-09 12:28:50.0    2005-09-09 12:33:04.0  2005-09-09 12:33:04.0   \n",
       "12   2005-09-09 12:33:31.0    2005-09-09 12:33:31.0  2005-09-09 12:33:31.0   \n",
       "13   2005-09-09 12:33:39.0    2005-09-09 12:33:39.0  2005-09-09 12:33:39.0   \n",
       "14   2005-09-09 12:33:47.0    2005-09-09 12:33:47.0  2005-09-09 12:33:47.0   \n",
       "15   2005-09-09 12:35:47.0    2005-09-09 12:35:47.0  2005-09-09 12:35:47.0   \n",
       "16   2005-09-09 12:35:57.0                      NaN  2005-09-09 12:35:57.0   \n",
       "17   2005-09-09 12:35:51.0    2005-09-09 12:37:55.0  2005-09-09 12:37:55.0   \n",
       "18   2005-09-09 12:38:02.0    2005-09-09 12:38:02.0  2005-09-09 12:38:02.0   \n",
       "19   2005-09-09 12:38:11.0    2005-09-09 12:38:11.0  2005-09-09 12:38:11.0   \n",
       "20   2005-09-09 12:38:35.0    2005-09-09 12:38:35.0  2005-09-09 12:38:35.0   \n",
       "21   2005-09-09 12:39:52.0    2005-09-09 12:39:52.0  2005-09-09 12:39:52.0   \n",
       "22   2005-09-09 12:39:57.0    2005-09-09 12:39:57.0  2005-09-09 12:39:57.0   \n",
       "23   2005-09-09 12:40:59.0    2005-09-09 12:41:13.0  2005-09-09 12:41:13.0   \n",
       "24   2005-09-09 12:39:24.0    2005-09-09 12:41:24.0  2005-09-09 12:41:24.0   \n",
       "25   2005-09-09 12:41:41.0    2005-09-09 12:41:41.0  2005-09-09 12:41:41.0   \n",
       "26   2005-09-09 12:41:51.0    2005-09-09 12:41:51.0  2005-09-09 12:41:51.0   \n",
       "27   2005-09-09 12:41:54.0    2005-09-09 12:41:54.0  2005-09-09 12:41:54.0   \n",
       "28   2005-09-09 12:42:06.0    2005-09-09 12:42:06.0  2005-09-09 12:42:06.0   \n",
       "29   2005-09-09 12:42:13.0    2005-09-09 12:42:13.0  2005-09-09 12:42:13.0   \n",
       "..                     ...                      ...                    ...   \n",
       "75   2005-09-14 12:35:58.0    2005-09-14 12:35:58.0  2005-09-14 12:35:58.0   \n",
       "76   2005-09-14 12:36:06.0    2005-09-14 12:36:06.0  2005-09-14 12:36:06.0   \n",
       "77   2005-09-14 12:28:37.0    2005-09-14 12:36:12.0  2005-09-14 12:36:12.0   \n",
       "78   2005-09-14 12:36:57.0    2005-09-14 12:36:57.0  2005-09-14 12:36:57.0   \n",
       "79   2005-09-14 12:37:02.0    2005-09-14 12:37:02.0  2005-09-14 12:37:02.0   \n",
       "80   2005-09-14 12:38:21.0    2005-09-14 12:38:21.0  2005-09-14 12:38:21.0   \n",
       "81   2005-09-14 12:38:26.0    2005-09-14 12:38:26.0  2005-09-14 12:38:26.0   \n",
       "82   2005-09-14 12:38:29.0    2005-09-14 12:38:29.0  2005-09-14 12:38:29.0   \n",
       "83   2005-09-14 12:38:40.0    2005-09-14 12:38:40.0  2005-09-14 12:38:40.0   \n",
       "84   2005-09-14 12:38:47.0    2005-09-14 12:38:47.0  2005-09-14 12:38:47.0   \n",
       "85   2005-09-14 12:38:55.0    2005-09-14 12:38:55.0  2005-09-14 12:38:55.0   \n",
       "86   2005-09-14 12:39:02.0    2005-09-14 12:39:02.0  2005-09-14 12:39:02.0   \n",
       "87   2005-09-14 12:39:08.0    2005-09-14 12:39:08.0  2005-09-14 12:39:08.0   \n",
       "88   2005-09-14 12:40:03.0    2005-09-14 12:40:03.0  2005-09-14 12:40:03.0   \n",
       "89   2005-09-14 12:40:06.0    2005-09-14 12:40:06.0  2005-09-14 12:40:06.0   \n",
       "90   2005-09-14 12:40:11.0    2005-09-14 12:40:11.0  2005-09-14 12:40:11.0   \n",
       "91   2005-09-14 12:38:50.0    2005-09-14 12:40:17.0  2005-09-14 12:40:17.0   \n",
       "92   2005-09-14 12:40:35.0    2005-09-14 12:40:35.0  2005-09-14 12:40:35.0   \n",
       "93   2005-09-14 12:40:41.0    2005-09-14 12:40:41.0  2005-09-14 12:40:41.0   \n",
       "94   2005-09-14 12:40:42.0    2005-09-14 12:40:42.0  2005-09-14 12:40:42.0   \n",
       "95   2005-09-14 12:41:10.0    2005-09-14 12:41:10.0  2005-09-14 12:41:10.0   \n",
       "96   2005-09-14 12:41:16.0    2005-09-14 12:41:16.0  2005-09-14 12:41:16.0   \n",
       "97   2005-09-14 12:41:22.0    2005-09-14 12:41:22.0  2005-09-14 12:41:22.0   \n",
       "98   2005-09-14 12:41:29.0    2005-09-14 12:41:29.0  2005-09-14 12:41:29.0   \n",
       "99   2005-09-14 12:41:36.0    2005-09-14 12:41:36.0  2005-09-14 12:41:36.0   \n",
       "100  2005-09-14 12:42:05.0    2005-09-14 12:42:05.0  2005-09-14 12:42:05.0   \n",
       "101  2005-09-16 12:23:43.0    2005-09-16 12:23:43.0  2005-09-16 12:23:43.0   \n",
       "102  2005-09-16 12:23:50.0    2005-09-16 12:23:50.0  2005-09-16 12:23:50.0   \n",
       "103  2005-09-16 12:23:54.0    2005-09-16 12:23:54.0  2005-09-16 12:23:54.0   \n",
       "104  2005-09-16 12:23:55.0    2005-09-16 12:23:55.0  2005-09-16 12:23:55.0   \n",
       "\n",
       "     Step Duration (sec)  Correct Step Duration (sec)  \\\n",
       "0                   33.0                         33.0   \n",
       "1                   15.0                         15.0   \n",
       "2                   78.0                          NaN   \n",
       "3                  104.0                          NaN   \n",
       "4                    6.0                          6.0   \n",
       "5                   11.0                         11.0   \n",
       "6                   60.0                         60.0   \n",
       "7                    8.0                          8.0   \n",
       "8                   13.0                         13.0   \n",
       "9                   43.0                          NaN   \n",
       "10                  23.0                         23.0   \n",
       "11                 176.0                          NaN   \n",
       "12                  10.0                         10.0   \n",
       "13                   8.0                          8.0   \n",
       "14                   8.0                          8.0   \n",
       "15                 120.0                        120.0   \n",
       "16                   6.0                          NaN   \n",
       "17                 122.0                          NaN   \n",
       "18                   7.0                          7.0   \n",
       "19                   9.0                          9.0   \n",
       "20                  24.0                         24.0   \n",
       "21                  20.0                         20.0   \n",
       "22                   5.0                          5.0   \n",
       "23                  76.0                          NaN   \n",
       "24                  68.0                          NaN   \n",
       "25                  13.0                         13.0   \n",
       "26                  10.0                         10.0   \n",
       "27                   3.0                          3.0   \n",
       "28                  12.0                         12.0   \n",
       "29                   7.0                          7.0   \n",
       "..                   ...                          ...   \n",
       "75                   9.0                          9.0   \n",
       "76                   8.0                          8.0   \n",
       "77                 232.0                          NaN   \n",
       "78                  45.0                         45.0   \n",
       "79                   5.0                          5.0   \n",
       "80                  12.0                         12.0   \n",
       "81                   5.0                          5.0   \n",
       "82                   3.0                          3.0   \n",
       "83                  11.0                         11.0   \n",
       "84                   7.0                          7.0   \n",
       "85                   5.0                          5.0   \n",
       "86                   7.0                          7.0   \n",
       "87                   6.0                          6.0   \n",
       "88                  55.0                         55.0   \n",
       "89                   3.0                          3.0   \n",
       "90                   5.0                          5.0   \n",
       "91                   9.0                          NaN   \n",
       "92                  14.0                         14.0   \n",
       "93                   6.0                          6.0   \n",
       "94                   1.0                          1.0   \n",
       "95                  28.0                         28.0   \n",
       "96                   6.0                          6.0   \n",
       "97                   6.0                          6.0   \n",
       "98                   7.0                          7.0   \n",
       "99                   7.0                          7.0   \n",
       "100                 26.0                         26.0   \n",
       "101                 10.0                         10.0   \n",
       "102                  7.0                          7.0   \n",
       "103                  4.0                          4.0   \n",
       "104                  1.0                          1.0   \n",
       "\n",
       "     Error Step Duration (sec)  Correct First Attempt  Incorrects  Hints  \\\n",
       "0                          NaN                      1           0      0   \n",
       "1                          NaN                      1           0      0   \n",
       "2                         78.0                      0           2      0   \n",
       "3                        104.0                      0           4      9   \n",
       "4                          NaN                      1           0      0   \n",
       "5                          NaN                      1           0      0   \n",
       "6                          NaN                      1           0      0   \n",
       "7                          NaN                      1           0      0   \n",
       "8                          NaN                      1           0      0   \n",
       "9                         43.0                      0           1      0   \n",
       "10                         NaN                      1           0      0   \n",
       "11                       176.0                      0           1      4   \n",
       "12                         NaN                      1           0      0   \n",
       "13                         NaN                      1           0      0   \n",
       "14                         NaN                      1           0      0   \n",
       "15                         NaN                      1           0      0   \n",
       "16                         6.0                      0           1      0   \n",
       "17                       122.0                      0           2      0   \n",
       "18                         NaN                      1           0      0   \n",
       "19                         NaN                      1           0      0   \n",
       "20                         NaN                      1           0      0   \n",
       "21                         NaN                      1           0      0   \n",
       "22                         NaN                      1           0      0   \n",
       "23                        76.0                      0           1      0   \n",
       "24                        68.0                      0           0      4   \n",
       "25                         NaN                      1           0      0   \n",
       "26                         NaN                      1           0      0   \n",
       "27                         NaN                      1           0      0   \n",
       "28                         NaN                      1           0      0   \n",
       "29                         NaN                      1           0      0   \n",
       "..                         ...                    ...         ...    ...   \n",
       "75                         NaN                      1           0      0   \n",
       "76                         NaN                      1           0      0   \n",
       "77                       232.0                      0           5      5   \n",
       "78                         NaN                      1           0      0   \n",
       "79                         NaN                      1           0      0   \n",
       "80                         NaN                      1           0      0   \n",
       "81                         NaN                      1           0      0   \n",
       "82                         NaN                      1           0      0   \n",
       "83                         NaN                      1           0      0   \n",
       "84                         NaN                      1           0      0   \n",
       "85                         NaN                      1           0      0   \n",
       "86                         NaN                      1           0      0   \n",
       "87                         NaN                      1           0      0   \n",
       "88                         NaN                      1           0      0   \n",
       "89                         NaN                      1           0      0   \n",
       "90                         NaN                      1           0      0   \n",
       "91                         9.0                      0           1      0   \n",
       "92                         NaN                      1           0      0   \n",
       "93                         NaN                      1           0      0   \n",
       "94                         NaN                      1           0      0   \n",
       "95                         NaN                      1           0      0   \n",
       "96                         NaN                      1           0      0   \n",
       "97                         NaN                      1           0      0   \n",
       "98                         NaN                      1           0      0   \n",
       "99                         NaN                      1           0      0   \n",
       "100                        NaN                      1           0      0   \n",
       "101                        NaN                      1           0      0   \n",
       "102                        NaN                      1           0      0   \n",
       "103                        NaN                      1           0      0   \n",
       "104                        NaN                      1           0      0   \n",
       "\n",
       "     Corrects                                        KC(Default)  \\\n",
       "0           1                                                NaN   \n",
       "1           1                                                NaN   \n",
       "2           1                                    Define Variable   \n",
       "3           1  Using small numbers~~Write expression, positiv...   \n",
       "4           1                                   Entering a given   \n",
       "5           1                                   Entering a given   \n",
       "6           1                                   Entering a given   \n",
       "7           1                                   Entering a given   \n",
       "8           2                                                NaN   \n",
       "9           1                                                NaN   \n",
       "10          1                                                NaN   \n",
       "11          1  Using small numbers~~Find X, Simple~~Using dif...   \n",
       "12          1                                                NaN   \n",
       "13          1                                                NaN   \n",
       "14          1                                    Define Variable   \n",
       "15          1  Using small numbers~~Write expression, positiv...   \n",
       "16          0  Find Y, Simple~~Using small numbers~~Using dif...   \n",
       "17          1                                   Entering a given   \n",
       "18          1                                   Entering a given   \n",
       "19          1                                   Entering a given   \n",
       "20          1                                   Entering a given   \n",
       "21          2                                                NaN   \n",
       "22          1                                                NaN   \n",
       "23          1                                                NaN   \n",
       "24          1  Using small numbers~~Find X, Simple~~Using dif...   \n",
       "25          1                                                NaN   \n",
       "26          1                                                NaN   \n",
       "27          1                                    Define Variable   \n",
       "28          1  Using small numbers~~Write expression, positiv...   \n",
       "29          1                                   Entering a given   \n",
       "..        ...                                                ...   \n",
       "75          1  [SkillRule: Eliminate Parens; {CLT nested; CLT...   \n",
       "76          1  [SkillRule: Remove positive coefficient; {ax/b...   \n",
       "77          1  Using small numbers~~Find X, Simple~~Using dif...   \n",
       "78          1                                   Entering a given   \n",
       "79          1                                   Entering a given   \n",
       "80          1                                                NaN   \n",
       "81          1                                                NaN   \n",
       "82          1                                    Define Variable   \n",
       "83          1  Using small numbers~~Write expression, positiv...   \n",
       "84          1                                   Entering a given   \n",
       "85          1                                   Entering a given   \n",
       "86          1                                   Entering a given   \n",
       "87          1                                   Entering a given   \n",
       "88          2                                                NaN   \n",
       "89          1                                                NaN   \n",
       "90          1  [SkillRule: Remove positive coefficient; {ax/b...   \n",
       "91          1  Using small numbers~~Find X, Simple~~Using dif...   \n",
       "92          1                                                NaN   \n",
       "93          1                                                NaN   \n",
       "94          1                                    Define Variable   \n",
       "95          1  Using difficult numbers~~Using small numbers~~...   \n",
       "96          1                                   Entering a given   \n",
       "97          1                                   Entering a given   \n",
       "98          1                                   Entering a given   \n",
       "99          1                                   Entering a given   \n",
       "100         2                                                NaN   \n",
       "101         1                                                NaN   \n",
       "102         1                                                NaN   \n",
       "103         1                                  Identifying units   \n",
       "104         1                                    Define Variable   \n",
       "\n",
       "    Opportunity(Default)  \n",
       "0                    NaN  \n",
       "1                    NaN  \n",
       "2                      1  \n",
       "3                1~~1~~1  \n",
       "4                      1  \n",
       "5                      2  \n",
       "6                      3  \n",
       "7                      4  \n",
       "8                    NaN  \n",
       "9                    NaN  \n",
       "10                   NaN  \n",
       "11               2~~1~~2  \n",
       "12                   NaN  \n",
       "13                   NaN  \n",
       "14                     2  \n",
       "15               3~~2~~3  \n",
       "16               1~~4~~4  \n",
       "17                     5  \n",
       "18                     6  \n",
       "19                     7  \n",
       "20                     8  \n",
       "21                   NaN  \n",
       "22                   NaN  \n",
       "23                   NaN  \n",
       "24               5~~2~~5  \n",
       "25                   NaN  \n",
       "26                   NaN  \n",
       "27                     3  \n",
       "28               6~~3~~6  \n",
       "29                     9  \n",
       "..                   ...  \n",
       "75                  1~~4  \n",
       "76                  4~~5  \n",
       "77             18~~7~~18  \n",
       "78                    22  \n",
       "79                    23  \n",
       "80                   NaN  \n",
       "81                   NaN  \n",
       "82                     7  \n",
       "83             19~~7~~19  \n",
       "84                    24  \n",
       "85                    25  \n",
       "86                    26  \n",
       "87                    27  \n",
       "88                   NaN  \n",
       "89                   NaN  \n",
       "90                  5~~6  \n",
       "91             20~~8~~20  \n",
       "92                   NaN  \n",
       "93                   NaN  \n",
       "94                     8  \n",
       "95             21~~21~~8  \n",
       "96                    28  \n",
       "97                    29  \n",
       "98                    30  \n",
       "99                    31  \n",
       "100                  NaN  \n",
       "101                  NaN  \n",
       "102                  NaN  \n",
       "103                    7  \n",
       "104                   13  \n",
       "\n",
       "[105 rows x 19 columns]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Inspect some of the training data\n",
    "traindata.head(n=105)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "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>Row</th>\n",
       "      <th>Anon Student Id</th>\n",
       "      <th>Problem Hierarchy</th>\n",
       "      <th>Problem Name</th>\n",
       "      <th>Problem View</th>\n",
       "      <th>Step Name</th>\n",
       "      <th>Step Start Time</th>\n",
       "      <th>First Transaction Time</th>\n",
       "      <th>Correct Transaction Time</th>\n",
       "      <th>Step End Time</th>\n",
       "      <th>Step Duration (sec)</th>\n",
       "      <th>Correct Step Duration (sec)</th>\n",
       "      <th>Error Step Duration (sec)</th>\n",
       "      <th>Correct First Attempt</th>\n",
       "      <th>Incorrects</th>\n",
       "      <th>Hints</th>\n",
       "      <th>Corrects</th>\n",
       "      <th>KC(Default)</th>\n",
       "      <th>Opportunity(Default)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10039</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>2/300*X = 10</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>NaN</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10482</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_06, Section CTA1_06-3</td>\n",
       "      <td>FOR05</td>\n",
       "      <td>1</td>\n",
       "      <td>xScale</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>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Changing axis intervals</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11024</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit ES_03, Section ES_03-6</td>\n",
       "      <td>EG52</td>\n",
       "      <td>1</td>\n",
       "      <td>2.9 = -2x+3.7+x</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>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>[SkillRule: Consolidate vars, no coeff; CLT]</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11476</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_08, Section CTA1_08-3</td>\n",
       "      <td>REAL10</td>\n",
       "      <td>1</td>\n",
       "      <td>yScale</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>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Changing axis intervals</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11948</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit ES_04, Section ES_04-12</td>\n",
       "      <td>EG58</td>\n",
       "      <td>7</td>\n",
       "      <td>xR2</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>NaN</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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Row Anon Student Id                Problem Hierarchy Problem Name  \\\n",
       "0  10039      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1       PROP01   \n",
       "1  10482      52vEY7f17k  Unit CTA1_06, Section CTA1_06-3        FOR05   \n",
       "2  11024      52vEY7f17k      Unit ES_03, Section ES_03-6         EG52   \n",
       "3  11476      52vEY7f17k  Unit CTA1_08, Section CTA1_08-3       REAL10   \n",
       "4  11948      52vEY7f17k     Unit ES_04, Section ES_04-12         EG58   \n",
       "\n",
       "   Problem View        Step Name  Step Start Time  First Transaction Time  \\\n",
       "0             1     2/300*X = 10              NaN                     NaN   \n",
       "1             1           xScale              NaN                     NaN   \n",
       "2             1  2.9 = -2x+3.7+x              NaN                     NaN   \n",
       "3             1           yScale              NaN                     NaN   \n",
       "4             7              xR2              NaN                     NaN   \n",
       "\n",
       "   Correct Transaction Time  Step End Time  Step Duration (sec)  \\\n",
       "0                       NaN            NaN                  NaN   \n",
       "1                       NaN            NaN                  NaN   \n",
       "2                       NaN            NaN                  NaN   \n",
       "3                       NaN            NaN                  NaN   \n",
       "4                       NaN            NaN                  NaN   \n",
       "\n",
       "   Correct Step Duration (sec)  Error Step Duration (sec)  \\\n",
       "0                          NaN                        NaN   \n",
       "1                          NaN                        NaN   \n",
       "2                          NaN                        NaN   \n",
       "3                          NaN                        NaN   \n",
       "4                          NaN                        NaN   \n",
       "\n",
       "   Correct First Attempt  Incorrects  Hints  Corrects  \\\n",
       "0                    NaN         NaN    NaN       NaN   \n",
       "1                    NaN         NaN    NaN       NaN   \n",
       "2                    NaN         NaN    NaN       NaN   \n",
       "3                    NaN         NaN    NaN       NaN   \n",
       "4                    NaN         NaN    NaN       NaN   \n",
       "\n",
       "                                    KC(Default) Opportunity(Default)  \n",
       "0                                           NaN                  NaN  \n",
       "1                       Changing axis intervals                   28  \n",
       "2  [SkillRule: Consolidate vars, no coeff; CLT]                   27  \n",
       "3                       Changing axis intervals                   65  \n",
       "4                                           NaN                  NaN  "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Inspect some of the training data\n",
    "testdata.head(n=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0                    R1C1\n",
       "1                    R1C2\n",
       "2                    R3C1\n",
       "3                    R3C2\n",
       "4                    R4C1\n",
       "5                    R5C1\n",
       "6                    R6C1\n",
       "7                    R7C2\n",
       "8          ValidEquations\n",
       "9           7/10*X = 1400\n",
       "10           7X/10 = 1400\n",
       "11                   R7C1\n",
       "12                   R1C1\n",
       "13                   R1C2\n",
       "14                   R3C1\n",
       "15                   R3C2\n",
       "16                   R4C2\n",
       "17                   R4C1\n",
       "18                   R5C1\n",
       "19                   R6C1\n",
       "20                   R7C2\n",
       "21         ValidEquations\n",
       "22        3/5*X = 1200000\n",
       "23         3X/5 = 1200000\n",
       "24                   R7C1\n",
       "25                   R1C1\n",
       "26                   R1C2\n",
       "27                   R3C1\n",
       "28                   R3C2\n",
       "29                   R4C1\n",
       "               ...       \n",
       "232714               R2C1\n",
       "232715               R4C1\n",
       "232716               R5C1\n",
       "232717               R1C2\n",
       "232718               R2C2\n",
       "232719               R3C2\n",
       "232720               R6C2\n",
       "232721               R7C1\n",
       "232722               R6C1\n",
       "232723               R1C1\n",
       "232724               R2C1\n",
       "232725               R3C1\n",
       "232726               R4C1\n",
       "232727               R5C1\n",
       "232728               R1C2\n",
       "232729               R2C2\n",
       "232730               R3C2\n",
       "232731               R6C2\n",
       "232732               R7C2\n",
       "232733               R7C1\n",
       "232734               R6C1\n",
       "232735               R1C1\n",
       "232736               R3C1\n",
       "232737               R2C1\n",
       "232738               R4C1\n",
       "232739               R5C1\n",
       "232740               R1C2\n",
       "232741               R2C2\n",
       "232742               R3C2\n",
       "232743               R6C2\n",
       "Name: Step Name, Length: 232744, dtype: object"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traindata['Step Name']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's begin asking some basic questions of the data\n",
    "\n",
    "### How many students are interacting with the system?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of students:  174\n"
     ]
    }
   ],
   "source": [
    "# Take the column of anonimized student IDs and count the number of unique entries\n",
    "print('Number of students: ', len(np.unique(traindata['Anon Student Id'])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How long does it take a student to solve any problem step on average?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    181599.000000\n",
       "mean         17.924024\n",
       "std          35.179534\n",
       "min           0.000000\n",
       "25%           5.000000\n",
       "50%           8.000000\n",
       "75%          17.000000\n",
       "max        1067.000000\n",
       "Name: Correct Step Duration (sec), dtype: float64"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csd = traindata['Correct Step Duration (sec)']\n",
    "csd.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So ignoring all the students that did not solve a problem step correctly, the average duraction for any problem step was about 18 seconds.\n",
    "\n",
    "Let's histogram this data to see the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "hist = plt.hist(np.array(csd.dropna()),bins=100,density=True,log=False,range=(0,100))\n",
    "plt.xlabel('Time to correct answer (sec)')\n",
    "plt.ylabel('Fraction')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "counts, bins = hist[0], hist[1]\n",
    "cdf = np.cumsum(counts)\n",
    "plt.plot(bins[1::], cdf)\n",
    "plt.xlabel('Time to correct answer (sec)')\n",
    "plt.ylabel('Cumulative fraction')\n",
    "plt.axis((0,100,0,1.0))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The histogram shows visually what mere statistics hints at. The distribution of students is heavily weighted towards those who are solving problems in under 20 seconds. The cumulative distribution function (CDF) shows that roughly 80% of successful students solve the problem within 20 seconds. After 40 seconds, 90% of successful students have finished the problem. Almost no students take longer than 80 seconds."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Completion time by problem\n",
    "\n",
    "OK, let's ask a slightly harder question: how are students doing problem by problem? The answer will take several parts.\n",
    "\n",
    "First, let's get the number of unique problems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The unique identifier for each problem is the 'Problem Name'\n",
    "problems = traindata['Problem Name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of unique problems:  1021\n"
     ]
    }
   ],
   "source": [
    "# Get just the uniques\n",
    "problems = np.unique(problems)\n",
    "print('Number of unique problems: ', len(problems))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, let's compute which problems need the largest time on average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "pmedian_times = {}\n",
    "for p in problems:\n",
    "    pmedian_times[p] = traindata[traindata['Problem Name'] == p]['Correct Step Duration (sec)'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "import operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "sorted_times = sorted(pmedian_times.items(), key=operator.itemgetter(1), reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The hardest top-5 problem and its average correct duration (sec).\n",
      "[('JAN13C', 65.0), ('TRANSFORMN022', 32.0), ('EG-FACTOR45', 30.0), ('JAN13A', 25.5), ('LIT76A', 23.5)]\n",
      "The earliest top-5 problem and its average correct duration (sec).\n",
      "[('TRANSFORMG038', 1.5), ('TRANSFORMA045', 1.5), ('TRANSFORMA035', 1.25), ('TRANSFORMG039', 1.25), ('TRANSFORMN005', 1.0)]\n"
     ]
    }
   ],
   "source": [
    "print(\"The hardest top-5 problem and its average correct duration (sec).\")\n",
    "print(sorted_times[:5])\n",
    "\n",
    "print(\"The earliest top-5 problem and its average correct duration (sec).\")\n",
    "print(sorted_times[len(sorted_times)-5:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statistical results of problem difficulty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist = plt.hist(np.array(list(pmedian_times.values())),bins=15,density=True,log=False,range=(0,25))\n",
    "plt.xlabel('Time to correct answer (sec)')\n",
    "plt.ylabel('Number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we take the time to correct answer as the difficulty of a problem, the histogram shows visually the difficulties of all the problems. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "There are many other interesting characteristic in this dataset.\n",
    "Like, \n",
    "* After some practices, students may become better at solving problems.\n",
    "* Same problem step for different students may request different knowledge components. Or for some problems, there is only one correct knowledge components\n",
    "\n",
    "These may be some things you need to take consider into for the feature engineering part. We leave them for you to explore deeper."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 0: Initialize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn\n",
    "import random\n",
    "pd.options.display.max_columns = None\n",
    "pd.options.display.max_rows = 1000\n",
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "traindata_origin = pd.read_csv('data/train.csv',sep = '\\t')\n",
    "testdata_origin = pd.read_csv('data/test.csv',sep = '\\t')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 1: Preprocess Data\n",
    "## 1.1 Split Problem hierarchy\n",
    "First, we should split 2 columns and remove the origin one.\n",
    "\n",
    "#### Train Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#temp_df = traindata_origin['Problem Hierarchy'].str.split(',')\n",
    "temp_train = traindata_origin\n",
    "temp_train['Problem Unit'] = traindata_origin['Problem Hierarchy'].str.split(',',1).str[0]\n",
    "temp_train['Problem Section'] = traindata_origin['Problem Hierarchy'].str.split(',',1).str[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp_train = temp_train.reindex(columns = ['Row','Anon Student Id','Problem Hierarchy','Problem Unit','Problem Section',\\\n",
    "                                    'Problem Name','Problem View','Step Name','Step Start Time',\\\n",
    "                                    'First Transaction Time','Correct Transaction Time',\\\n",
    "                                    'Step End Time','Step Duration (sec)','Correct Step Duration (sec)',\\\n",
    "                                    'Error Step Duration (sec)','Correct First Attempt','Incorrects',\\\n",
    "                                    'Hints','Corrects','KC(Default)','Opportunity(Default)'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "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>Row</th>\n",
       "      <th>Anon Student Id</th>\n",
       "      <th>Problem Hierarchy</th>\n",
       "      <th>Problem Unit</th>\n",
       "      <th>Problem Section</th>\n",
       "      <th>Problem Name</th>\n",
       "      <th>Problem View</th>\n",
       "      <th>Step Name</th>\n",
       "      <th>Step Start Time</th>\n",
       "      <th>First Transaction Time</th>\n",
       "      <th>Correct Transaction Time</th>\n",
       "      <th>Step End Time</th>\n",
       "      <th>Step Duration (sec)</th>\n",
       "      <th>Correct Step Duration (sec)</th>\n",
       "      <th>Error Step Duration (sec)</th>\n",
       "      <th>Correct First Attempt</th>\n",
       "      <th>Incorrects</th>\n",
       "      <th>Hints</th>\n",
       "      <th>Corrects</th>\n",
       "      <th>KC(Default)</th>\n",
       "      <th>Opportunity(Default)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9938</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>Unit CTA1_13</td>\n",
       "      <td>Section CTA1_13-1</td>\n",
       "      <td>PROP04</td>\n",
       "      <td>1</td>\n",
       "      <td>R1C1</td>\n",
       "      <td>2005-09-09 12:23:34.0</td>\n",
       "      <td>2005-09-09 12:24:07.0</td>\n",
       "      <td>2005-09-09 12:24:07.0</td>\n",
       "      <td>2005-09-09 12:24:07.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Row Anon Student Id                Problem Hierarchy  Problem Unit  \\\n",
       "0  9938      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1  Unit CTA1_13   \n",
       "\n",
       "      Problem Section Problem Name  Problem View Step Name  \\\n",
       "0   Section CTA1_13-1       PROP04             1      R1C1   \n",
       "\n",
       "         Step Start Time First Transaction Time Correct Transaction Time  \\\n",
       "0  2005-09-09 12:23:34.0  2005-09-09 12:24:07.0    2005-09-09 12:24:07.0   \n",
       "\n",
       "           Step End Time  Step Duration (sec)  Correct Step Duration (sec)  \\\n",
       "0  2005-09-09 12:24:07.0                 33.0                         33.0   \n",
       "\n",
       "   Error Step Duration (sec)  Correct First Attempt  Incorrects  Hints  \\\n",
       "0                        NaN                      1           0      0   \n",
       "\n",
       "   Corrects KC(Default) Opportunity(Default)  \n",
       "0         1         NaN                  NaN  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp_train.head(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "traindata_pre = temp_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#temp_df = traindata_origin['Problem Hierarchy'].str.split(',')\n",
    "temp_test = testdata_origin\n",
    "temp_test['Problem Unit'] = testdata_origin['Problem Hierarchy'].str.split(',',1).str[0]\n",
    "temp_test['Problem Section'] = testdata_origin['Problem Hierarchy'].str.split(',',1).str[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp_test = temp_test.reindex(columns = ['Row','Anon Student Id','Problem Hierarchy','Problem Unit','Problem Section',\\\n",
    "                                    'Problem Name','Problem View','Step Name','Step Start Time',\\\n",
    "                                    'First Transaction Time','Correct Transaction Time',\\\n",
    "                                    'Step End Time','Step Duration (sec)','Correct Step Duration (sec)',\\\n",
    "                                    'Error Step Duration (sec)','Correct First Attempt','Incorrects',\\\n",
    "                                    'Hints','Corrects','KC(Default)','Opportunity(Default)'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "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>Row</th>\n",
       "      <th>Anon Student Id</th>\n",
       "      <th>Problem Hierarchy</th>\n",
       "      <th>Problem Unit</th>\n",
       "      <th>Problem Section</th>\n",
       "      <th>Problem Name</th>\n",
       "      <th>Problem View</th>\n",
       "      <th>Step Name</th>\n",
       "      <th>Step Start Time</th>\n",
       "      <th>First Transaction Time</th>\n",
       "      <th>Correct Transaction Time</th>\n",
       "      <th>Step End Time</th>\n",
       "      <th>Step Duration (sec)</th>\n",
       "      <th>Correct Step Duration (sec)</th>\n",
       "      <th>Error Step Duration (sec)</th>\n",
       "      <th>Correct First Attempt</th>\n",
       "      <th>Incorrects</th>\n",
       "      <th>Hints</th>\n",
       "      <th>Corrects</th>\n",
       "      <th>KC(Default)</th>\n",
       "      <th>Opportunity(Default)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10039</td>\n",
       "      <td>52vEY7f17k</td>\n",
       "      <td>Unit CTA1_13, Section CTA1_13-1</td>\n",
       "      <td>Unit CTA1_13</td>\n",
       "      <td>Section CTA1_13-1</td>\n",
       "      <td>PROP01</td>\n",
       "      <td>1</td>\n",
       "      <td>2/300*X = 10</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>NaN</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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Row Anon Student Id                Problem Hierarchy  Problem Unit  \\\n",
       "0  10039      52vEY7f17k  Unit CTA1_13, Section CTA1_13-1  Unit CTA1_13   \n",
       "\n",
       "      Problem Section Problem Name  Problem View     Step Name  \\\n",
       "0   Section CTA1_13-1       PROP01             1  2/300*X = 10   \n",
       "\n",
       "   Step Start Time  First Transaction Time  Correct Transaction Time  \\\n",
       "0              NaN                     NaN                       NaN   \n",
       "\n",
       "   Step End Time  Step Duration (sec)  Correct Step Duration (sec)  \\\n",
       "0            NaN                  NaN                          NaN   \n",
       "\n",
       "   Error Step Duration (sec)  Correct First Attempt  Incorrects  Hints  \\\n",
       "0                        NaN                    NaN         NaN    NaN   \n",
       "\n",
       "   Corrects KC(Default) Opportunity(Default)  \n",
       "0       NaN         NaN                  NaN  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp_test.head(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "testdata_pre = temp_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Map string to Integer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp_train = traindata_pre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp_test = testdata_pre"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Anon Student Id"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "sids = list(set(temp_train['Anon Student Id']).union(set(temp_test['Anon Student Id'])))\n",
    "sid_dict = {}\n",
    "for index, sid in enumerate(sids):\n",
    "    sid_dict[sid] = index\n",
    "temp_train['Anon Student Id'] = temp_train['Anon Student Id'].apply(lambda x:sid_dict[x])\n",
    "temp_test['Anon Student Id'] = temp_test['Anon Student Id'].apply(lambda x:sid_dict[x])\n",
    "#     sid_dict[index] = sid\n",
    "#     temp_train.loc[temp_train['Anon Student Id'] == sid, 'Anon Student Id'] = index\n",
    "#     temp_test.loc[temp_test['Anon Student Id'] == sid, 'Anon Student Id'] = index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Problem Hierarchy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "prohies = list(set(temp_train['Problem Hierarchy']).union(set(temp_test['Problem Hierarchy'])))\n",
    "prohie_dict = {}\n",
    "for index, prohie in enumerate(prohies):\n",
    "    prohie_dict[prohie] = index\n",
    "temp_train['Problem Hierarchy'] = temp_train['Problem Hierarchy'].apply(lambda x:prohie_dict[x])\n",
    "temp_test['Problem Hierarchy'] = temp_test['Problem Hierarchy'].apply(lambda x:prohie_dict[x])\n",
    "#     prohie_dict[index] = prohie\n",
    "#     temp_train.loc[temp_train['Problem Hierarchy'] == prohie, 'Problem Hierarchy'] = index\n",
    "#     temp_test.loc[temp_test['Problem Hierarchy'] == prohie, 'Problem Hierarchy'] = index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Problem Unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "prounis = list(set(temp_train['Problem Unit']).union(set(temp_test['Problem Unit'])))\n",
    "prouni_dict = {}\n",
    "for index, prouni in enumerate(prounis):\n",
    "    prouni_dict[prouni] = index\n",
    "temp_train['Problem Unit'] = temp_train['Problem Unit'].apply(lambda x:prouni_dict[x])\n",
    "temp_test['Problem Unit'] = temp_test['Problem Unit'].apply(lambda x:prouni_dict[x])\n",
    "#     prouni_dict[index] = prouni\n",
    "#     temp_train.loc[temp_train['Problem Unit'] == prouni, 'Problem Unit'] = index\n",
    "#     temp_test.loc[temp_test['Problem Unit'] == prouni, 'Problem Unit'] = index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Problem Section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "prosecs = list(set(temp_train['Problem Section']).union(set(temp_test['Problem Section'])))\n",
    "prosec_dict = {}\n",
    "for index, prosec in enumerate(prosecs):\n",
    "    prosec_dict[prosec] = index\n",
    "temp_train['Problem Section'] = temp_train['Problem Section'].apply(lambda x:prosec_dict[x])\n",
    "temp_test['Problem Section'] = temp_test['Problem Section'].apply(lambda x:prosec_dict[x])\n",
    "#     prosec_dict[index] = prosec\n",
    "#     temp_train.loc[temp_train['Problem Section'] == prosec, 'Problem Section'] = index\n",
    "#     temp_test.loc[temp_test['Problem Section'] == prosec, 'Problem Section'] = index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Problem Name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pronams = list(set(temp_train['Problem Name']).union(set(temp_test['Problem Name'])))\n",
    "pronam_dict = {}\n",
    "for index,pronam in enumerate(pronams):\n",
    "    pronam_dict[pronam] = index\n",
    "temp_train['Problem Name'] = temp_train['Problem Name'].apply(lambda x:pronam_dict[x])\n",
    "temp_test['Problem Name'] = temp_test['Problem Name'].apply(lambda x:pronam_dict[x])\n",
    "#     pronam_dict[index] = pronam\n",
    "#     temp_train.loc[temp_train['Problem Name'] == pronam, 'Problem Name'] = index\n",
    "#     temp_test.loc[temp_test['Problem Name'] == pronam, 'Problem Name'] = index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Step Name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "stenams = list(set(temp_train['Step Name']).union(set(temp_test['Step Name'])))\n",
    "stenam_dict = {}\n",
    "for index,stenam in enumerate(stenams):\n",
    "    stenam_dict[stenam] = index\n",
    "temp_train['Step Name'] = temp_train['Step Name'].apply(lambda x:stenam_dict[x])\n",
    "temp_test['Step Name'] = temp_test['Step Name'].apply(lambda x:stenam_dict[x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp_train.to_csv('train_cor.csv',sep='\\t',index = False)\n",
    "temp_test.to_csv('test_cor.csv',sep='\\t', index = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_df = pd.read_csv('train_pre.csv',sep = '\\t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas\n",
    "import numpy\n",
    "\n",
    "names = ['Personal CFAR', 'Problem CFAR','Anon Student Id','Problem Unit', 'Problem Section', 'Step Name', 'Problem Name', 'Problem View', 'Correct First Attempt', 'KC_num', 'Step CFAR', 'KC CFAR']\n",
    "correlations = x_df[names].corr()\n",
    "# plot correlation matrix\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "ax = fig.add_subplot(222)\n",
    "cax = ax.matshow(correlations, vmin=-1, vmax=1)\n",
    "fig.colorbar(cax)\n",
    "ticks = numpy.arange(0,len(names),1)\n",
    "ax.set_xticks(ticks)\n",
    "ax.set_yticks(ticks)\n",
    "ax.set_xticklabels(names)\n",
    "ax.set_yticklabels(names)\n",
    "plt.savefig('./1.jpg')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}