HW2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Elizabeth.Ke.Zhang/anaconda/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import re\n",
    "from sklearn import linear_model\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.decomposition import PCA\n",
    "import seaborn as sns\n",
    "# from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'/Users/Elizabeth.Ke.Zhang/Desktop/NYU/9733 ML/Week 2'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('session_2_homework_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>USGG3M</th>\n",
       "      <th>USGG6M</th>\n",
       "      <th>USGG2YR</th>\n",
       "      <th>USGG3YR</th>\n",
       "      <th>USGG5YR</th>\n",
       "      <th>USGG10YR</th>\n",
       "      <th>USGG30YR</th>\n",
       "      <th>Output1</th>\n",
       "      <th>Easing</th>\n",
       "      <th>Tightening</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1/5/1981</td>\n",
       "      <td>13.52</td>\n",
       "      <td>13.09</td>\n",
       "      <td>12.289</td>\n",
       "      <td>12.28</td>\n",
       "      <td>12.294</td>\n",
       "      <td>12.152</td>\n",
       "      <td>11.672</td>\n",
       "      <td>18.015526</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1/6/1981</td>\n",
       "      <td>13.58</td>\n",
       "      <td>13.16</td>\n",
       "      <td>12.429</td>\n",
       "      <td>12.31</td>\n",
       "      <td>12.214</td>\n",
       "      <td>12.112</td>\n",
       "      <td>11.672</td>\n",
       "      <td>18.091398</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1/7/1981</td>\n",
       "      <td>14.50</td>\n",
       "      <td>13.90</td>\n",
       "      <td>12.929</td>\n",
       "      <td>12.78</td>\n",
       "      <td>12.614</td>\n",
       "      <td>12.382</td>\n",
       "      <td>11.892</td>\n",
       "      <td>19.447314</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1/8/1981</td>\n",
       "      <td>14.76</td>\n",
       "      <td>14.00</td>\n",
       "      <td>13.099</td>\n",
       "      <td>12.95</td>\n",
       "      <td>12.684</td>\n",
       "      <td>12.352</td>\n",
       "      <td>11.912</td>\n",
       "      <td>19.748510</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1/9/1981</td>\n",
       "      <td>15.20</td>\n",
       "      <td>14.30</td>\n",
       "      <td>13.539</td>\n",
       "      <td>13.28</td>\n",
       "      <td>12.884</td>\n",
       "      <td>12.572</td>\n",
       "      <td>12.132</td>\n",
       "      <td>20.572042</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1/12/1981</td>\n",
       "      <td>15.22</td>\n",
       "      <td>14.23</td>\n",
       "      <td>13.179</td>\n",
       "      <td>12.94</td>\n",
       "      <td>12.714</td>\n",
       "      <td>12.452</td>\n",
       "      <td>12.082</td>\n",
       "      <td>20.142185</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1/13/1981</td>\n",
       "      <td>15.24</td>\n",
       "      <td>14.10</td>\n",
       "      <td>13.309</td>\n",
       "      <td>12.97</td>\n",
       "      <td>12.684</td>\n",
       "      <td>12.532</td>\n",
       "      <td>12.082</td>\n",
       "      <td>20.181543</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1/14/1981</td>\n",
       "      <td>15.08</td>\n",
       "      <td>13.90</td>\n",
       "      <td>12.959</td>\n",
       "      <td>12.75</td>\n",
       "      <td>12.614</td>\n",
       "      <td>12.532</td>\n",
       "      <td>12.072</td>\n",
       "      <td>19.777288</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1/15/1981</td>\n",
       "      <td>15.25</td>\n",
       "      <td>14.09</td>\n",
       "      <td>13.259</td>\n",
       "      <td>13.02</td>\n",
       "      <td>12.774</td>\n",
       "      <td>12.622</td>\n",
       "      <td>12.252</td>\n",
       "      <td>20.298884</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1/16/1981</td>\n",
       "      <td>15.15</td>\n",
       "      <td>13.98</td>\n",
       "      <td>13.089</td>\n",
       "      <td>12.85</td>\n",
       "      <td>12.664</td>\n",
       "      <td>12.532</td>\n",
       "      <td>12.132</td>\n",
       "      <td>19.967575</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date  USGG3M  USGG6M  USGG2YR  USGG3YR  USGG5YR  USGG10YR  USGG30YR  \\\n",
       "0   1/5/1981   13.52   13.09   12.289    12.28   12.294    12.152    11.672   \n",
       "1   1/6/1981   13.58   13.16   12.429    12.31   12.214    12.112    11.672   \n",
       "2   1/7/1981   14.50   13.90   12.929    12.78   12.614    12.382    11.892   \n",
       "3   1/8/1981   14.76   14.00   13.099    12.95   12.684    12.352    11.912   \n",
       "4   1/9/1981   15.20   14.30   13.539    13.28   12.884    12.572    12.132   \n",
       "5  1/12/1981   15.22   14.23   13.179    12.94   12.714    12.452    12.082   \n",
       "6  1/13/1981   15.24   14.10   13.309    12.97   12.684    12.532    12.082   \n",
       "7  1/14/1981   15.08   13.90   12.959    12.75   12.614    12.532    12.072   \n",
       "8  1/15/1981   15.25   14.09   13.259    13.02   12.774    12.622    12.252   \n",
       "9  1/16/1981   15.15   13.98   13.089    12.85   12.664    12.532    12.132   \n",
       "\n",
       "     Output1  Easing  Tightening  \n",
       "0  18.015526     NaN         NaN  \n",
       "1  18.091398     NaN         NaN  \n",
       "2  19.447314     NaN         NaN  \n",
       "3  19.748510     NaN         NaN  \n",
       "4  20.572042     NaN         NaN  \n",
       "5  20.142185     NaN         NaN  \n",
       "6  20.181543     NaN         NaN  \n",
       "7  19.777288     NaN         NaN  \n",
       "8  20.298884     NaN         NaN  \n",
       "9  19.967575     NaN         NaN  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data.shape: (8300, 11)\n",
      "Easing days: 1585\n",
      "Tightening days: 773\n"
     ]
    }
   ],
   "source": [
    "print('data.shape:',data.shape)\n",
    "print('Easing days:',sum(data.Easing == 1))\n",
    "print('Tightening days:',sum(data.Tightening == 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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OnTs7/vOf/yQAPPHEE4mDBw+uPPPMMysBpk6dmpeRkbFt0aJFmXfeeWdKTW7b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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c25588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# matplotlib inline\n",
    "X_col = [col for col in data.columns if re.match(r'^USGG',col)]\n",
    "ax = data[X_col].plot()\n",
    "ax.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LR2way(X,y,df,out=True,Notreverse=True):\n",
    "    slopes = []\n",
    "    intercepts = []\n",
    "    in_dex = []\n",
    "    for x in X:\n",
    "        if Notreverse: \n",
    "            lr = linear_model.LinearRegression().fit(df[[x]],df[y])\n",
    "            in_dex.append(y + '-->' + x)\n",
    "        else:\n",
    "            lr = linear_model.LinearRegression().fit(df[[y]],df[x])\n",
    "            in_dex.append(x + '-->' + y)\n",
    "        slopes.append(lr.coef_)\n",
    "        intercepts.append(lr.intercept_)\n",
    "    ret = pd.DataFrame({'slopes':slopes,'intercepts':intercepts},index=in_dex)\n",
    "    print(in_dex)\n",
    "    if out:\n",
    "        display(ret)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Output1-->USGG3M', 'Output1-->USGG6M', 'Output1-->USGG2YR', 'Output1-->USGG3YR', 'Output1-->USGG5YR', 'Output1-->USGG10YR', 'Output1-->USGG30YR']\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Elizabeth.Ke.Zhang/anaconda/lib/python3.6/site-packages/scipy/linalg/basic.py:1226: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  warnings.warn(mesg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>intercepts</th>\n",
       "      <th>slopes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Output1--&gt;USGG3M</th>\n",
       "      <td>-11.723184</td>\n",
       "      <td>[2.507560943753729]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Output1--&gt;USGG6M</th>\n",
       "      <td>-12.097528</td>\n",
       "      <td>[2.4972347033674063]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Output1--&gt;USGG2YR</th>\n",
       "      <td>-13.055775</td>\n",
       "      <td>[2.4004493115970793]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Output1--&gt;USGG3YR</th>\n",
       "      <td>-13.861618</td>\n",
       "      <td>[2.45579265609239]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Output1--&gt;USGG5YR</th>\n",
       "      <td>-15.436649</td>\n",
       "      <td>[2.568741597117226]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Output1--&gt;USGG10YR</th>\n",
       "      <td>-18.063370</td>\n",
       "      <td>[2.7869910490846768]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Output1--&gt;USGG30YR</th>\n",
       "      <td>-21.085905</td>\n",
       "      <td>[3.0695608627521898]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    intercepts                slopes\n",
       "Output1-->USGG3M    -11.723184   [2.507560943753729]\n",
       "Output1-->USGG6M    -12.097528  [2.4972347033674063]\n",
       "Output1-->USGG2YR   -13.055775  [2.4004493115970793]\n",
       "Output1-->USGG3YR   -13.861618    [2.45579265609239]\n",
       "Output1-->USGG5YR   -15.436649   [2.568741597117226]\n",
       "Output1-->USGG10YR  -18.063370  [2.7869910490846768]\n",
       "Output1-->USGG30YR  -21.085905  [3.0695608627521898]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr1 = LR2way(X_col,'Output1',df = data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['USGG3M-->Output1', 'USGG6M-->Output1', 'USGG2YR-->Output1', 'USGG3YR-->Output1', 'USGG5YR-->Output1', 'USGG10YR-->Output1', 'USGG30YR-->Output1']\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>intercepts</th>\n",
       "      <th>slopes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USGG3M--&gt;Output1</th>\n",
       "      <td>4.675134</td>\n",
       "      <td>[0.383960901227975]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG6M--&gt;Output1</th>\n",
       "      <td>4.844370</td>\n",
       "      <td>[0.39018695732704445]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG2YR--&gt;Output1</th>\n",
       "      <td>5.438888</td>\n",
       "      <td>[0.41518505902501124]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG3YR--&gt;Output1</th>\n",
       "      <td>5.644458</td>\n",
       "      <td>[0.4063541363030711]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG5YR--&gt;Output1</th>\n",
       "      <td>6.009421</td>\n",
       "      <td>[0.38606095754164854]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG10YR--&gt;Output1</th>\n",
       "      <td>6.481316</td>\n",
       "      <td>[0.34775440245779426]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG30YR--&gt;Output1</th>\n",
       "      <td>6.869355</td>\n",
       "      <td>[0.3047124217524948]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    intercepts                 slopes\n",
       "USGG3M-->Output1      4.675134    [0.383960901227975]\n",
       "USGG6M-->Output1      4.844370  [0.39018695732704445]\n",
       "USGG2YR-->Output1     5.438888  [0.41518505902501124]\n",
       "USGG3YR-->Output1     5.644458   [0.4063541363030711]\n",
       "USGG5YR-->Output1     6.009421  [0.38606095754164854]\n",
       "USGG10YR-->Output1    6.481316  [0.34775440245779426]\n",
       "USGG30YR-->Output1    6.869355   [0.3047124217524948]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr2 = LR2way(X_col,'Output1',df = data,Notreverse=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Elizabeth.Ke.Zhang/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \n",
      "/Users/Elizabeth.Ke.Zhang/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "data['Binary_Output'] = np.nan\n",
    "data.Binary_Output[data.Easing == 1] = 0\n",
    "data.Binary_Output[data.Tightening == 1] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NAs in Binary_Output: 5942\n"
     ]
    }
   ],
   "source": [
    "print('NAs in Binary_Output:', sum(np.isnan(data.Binary_Output)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "logit_data shape: (2358, 12)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>USGG3M</th>\n",
       "      <th>USGG6M</th>\n",
       "      <th>USGG2YR</th>\n",
       "      <th>USGG3YR</th>\n",
       "      <th>USGG5YR</th>\n",
       "      <th>USGG10YR</th>\n",
       "      <th>USGG30YR</th>\n",
       "      <th>Output1</th>\n",
       "      <th>Easing</th>\n",
       "      <th>Tightening</th>\n",
       "      <th>Binary_Output</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11/2/1981</td>\n",
       "      <td>12.69</td>\n",
       "      <td>12.87</td>\n",
       "      <td>14.119</td>\n",
       "      <td>14.44</td>\n",
       "      <td>14.614</td>\n",
       "      <td>14.572</td>\n",
       "      <td>14.412</td>\n",
       "      <td>21.820650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11/4/1981</td>\n",
       "      <td>12.30</td>\n",
       "      <td>12.50</td>\n",
       "      <td>14.119</td>\n",
       "      <td>14.13</td>\n",
       "      <td>14.324</td>\n",
       "      <td>14.182</td>\n",
       "      <td>13.962</td>\n",
       "      <td>21.015864</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11/5/1981</td>\n",
       "      <td>12.18</td>\n",
       "      <td>12.59</td>\n",
       "      <td>14.209</td>\n",
       "      <td>14.23</td>\n",
       "      <td>14.434</td>\n",
       "      <td>14.192</td>\n",
       "      <td>14.062</td>\n",
       "      <td>21.159323</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11/6/1981</td>\n",
       "      <td>11.68</td>\n",
       "      <td>12.20</td>\n",
       "      <td>13.869</td>\n",
       "      <td>13.88</td>\n",
       "      <td>14.074</td>\n",
       "      <td>13.942</td>\n",
       "      <td>13.852</td>\n",
       "      <td>20.241872</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11/9/1981</td>\n",
       "      <td>11.19</td>\n",
       "      <td>11.63</td>\n",
       "      <td>13.179</td>\n",
       "      <td>13.25</td>\n",
       "      <td>13.544</td>\n",
       "      <td>13.392</td>\n",
       "      <td>13.562</td>\n",
       "      <td>18.804600</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>11/10/1981</td>\n",
       "      <td>11.15</td>\n",
       "      <td>11.57</td>\n",
       "      <td>13.229</td>\n",
       "      <td>13.23</td>\n",
       "      <td>13.634</td>\n",
       "      <td>13.402</td>\n",
       "      <td>13.552</td>\n",
       "      <td>18.813639</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>11/12/1981</td>\n",
       "      <td>10.60</td>\n",
       "      <td>11.25</td>\n",
       "      <td>12.779</td>\n",
       "      <td>12.85</td>\n",
       "      <td>13.234</td>\n",
       "      <td>13.192</td>\n",
       "      <td>13.212</td>\n",
       "      <td>17.805298</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>11/13/1981</td>\n",
       "      <td>10.78</td>\n",
       "      <td>11.31</td>\n",
       "      <td>12.839</td>\n",
       "      <td>12.93</td>\n",
       "      <td>13.314</td>\n",
       "      <td>13.182</td>\n",
       "      <td>13.262</td>\n",
       "      <td>17.997884</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>11/16/1981</td>\n",
       "      <td>10.63</td>\n",
       "      <td>11.10</td>\n",
       "      <td>12.699</td>\n",
       "      <td>12.79</td>\n",
       "      <td>13.214</td>\n",
       "      <td>13.072</td>\n",
       "      <td>13.112</td>\n",
       "      <td>17.620769</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>11/17/1981</td>\n",
       "      <td>10.63</td>\n",
       "      <td>11.08</td>\n",
       "      <td>12.719</td>\n",
       "      <td>12.85</td>\n",
       "      <td>13.214</td>\n",
       "      <td>13.182</td>\n",
       "      <td>13.252</td>\n",
       "      <td>17.726563</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date  USGG3M  USGG6M  USGG2YR  USGG3YR  USGG5YR  USGG10YR  USGG30YR  \\\n",
       "0   11/2/1981   12.69   12.87   14.119    14.44   14.614    14.572    14.412   \n",
       "1   11/4/1981   12.30   12.50   14.119    14.13   14.324    14.182    13.962   \n",
       "2   11/5/1981   12.18   12.59   14.209    14.23   14.434    14.192    14.062   \n",
       "3   11/6/1981   11.68   12.20   13.869    13.88   14.074    13.942    13.852   \n",
       "4   11/9/1981   11.19   11.63   13.179    13.25   13.544    13.392    13.562   \n",
       "5  11/10/1981   11.15   11.57   13.229    13.23   13.634    13.402    13.552   \n",
       "6  11/12/1981   10.60   11.25   12.779    12.85   13.234    13.192    13.212   \n",
       "7  11/13/1981   10.78   11.31   12.839    12.93   13.314    13.182    13.262   \n",
       "8  11/16/1981   10.63   11.10   12.699    12.79   13.214    13.072    13.112   \n",
       "9  11/17/1981   10.63   11.08   12.719    12.85   13.214    13.182    13.252   \n",
       "\n",
       "     Output1  Easing  Tightening  Binary_Output  \n",
       "0  21.820650     1.0         NaN            0.0  \n",
       "1  21.015864     1.0         NaN            0.0  \n",
       "2  21.159323     1.0         NaN            0.0  \n",
       "3  20.241872     1.0         NaN            0.0  \n",
       "4  18.804600     1.0         NaN            0.0  \n",
       "5  18.813639     1.0         NaN            0.0  \n",
       "6  17.805298     1.0         NaN            0.0  \n",
       "7  17.997884     1.0         NaN            0.0  \n",
       "8  17.620769     1.0         NaN            0.0  \n",
       "9  17.726563     1.0         NaN            0.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_data = data[pd.notnull(data.Binary_Output)]\n",
    "logit_data.index = np.arange(len(logit_data))\n",
    "print('logit_data shape:',logit_data.shape)\n",
    "logit_data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit1 = linear_model.LogisticRegression().fit(logit_data[['USGG3M']],logit_data.Binary_Output)\n",
    "logit2 = linear_model.LogisticRegression().fit(logit_data[X_col],logit_data.Binary_Output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs1 = logit1.predict_proba(logit_data[['USGG3M']])\n",
    "probs2 = logit2.predict_proba(logit_data[X_col])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.45516287 0.54483713]\n",
      " [0.47250538 0.52749462]\n",
      " [0.47785688 0.52214312]\n",
      " [0.50019561 0.49980439]\n",
      " [0.52208739 0.47791261]]\n",
      "[[0.69936635 0.30063365]\n",
      " [0.64002689 0.35997311]\n",
      " [0.49756229 0.50243771]\n",
      " [0.3899371  0.6100629 ]\n",
      " [0.40744327 0.59255673]]\n"
     ]
    }
   ],
   "source": [
    "print(probs1[0:5])\n",
    "print(probs2[0:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EUm84XAh3MXbm2oDhlmOvEe1wTYvGy6Camv92C0KIikE9nDI0eO9wYVCzcYxs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\nMAkTERGZhEmYiIjIJEzCREREJvl/reOmoATd/rUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e9d6550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = logit_data[X_col].plot()\n",
    "plt.plot(20*logit_data.Binary_Output)\n",
    "plt.plot(logit_data.Output1,'r-',label = 'Output1')\n",
    "ax.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>USGG3M</th>\n",
       "      <th>USGG2YR</th>\n",
       "      <th>USGG5YR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USGG3M</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.984314</td>\n",
       "      <td>0.960315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG2YR</th>\n",
       "      <td>0.984314</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.991637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG5YR</th>\n",
       "      <td>0.960315</td>\n",
       "      <td>0.991637</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           USGG3M   USGG2YR   USGG5YR\n",
       "USGG3M   1.000000  0.984314  0.960315\n",
       "USGG2YR  0.984314  1.000000  0.991637\n",
       "USGG5YR  0.960315  0.991637  1.000000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrmat = data[['USGG3M','USGG2YR','USGG5YR']].corr()\n",
    "corrmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "#sns.heatmap(corrmat, vmax=1., square=False).xaxis.tick_top()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>USGG3M</th>\n",
       "      <th>USGG6M</th>\n",
       "      <th>USGG2YR</th>\n",
       "      <th>USGG3YR</th>\n",
       "      <th>USGG5YR</th>\n",
       "      <th>USGG10YR</th>\n",
       "      <th>USGG30YR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USGG3M</th>\n",
       "      <td>11.760393</td>\n",
       "      <td>11.855287</td>\n",
       "      <td>12.303031</td>\n",
       "      <td>11.942035</td>\n",
       "      <td>11.188856</td>\n",
       "      <td>9.924865</td>\n",
       "      <td>8.587987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG6M</th>\n",
       "      <td>11.855287</td>\n",
       "      <td>12.000510</td>\n",
       "      <td>12.512434</td>\n",
       "      <td>12.158422</td>\n",
       "      <td>11.406959</td>\n",
       "      <td>10.128890</td>\n",
       "      <td>8.768702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG2YR</th>\n",
       "      <td>12.303031</td>\n",
       "      <td>12.512434</td>\n",
       "      <td>13.284203</td>\n",
       "      <td>12.977542</td>\n",
       "      <td>12.279514</td>\n",
       "      <td>11.005377</td>\n",
       "      <td>9.600181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG3YR</th>\n",
       "      <td>11.942035</td>\n",
       "      <td>12.158422</td>\n",
       "      <td>12.977542</td>\n",
       "      <td>12.708647</td>\n",
       "      <td>12.068078</td>\n",
       "      <td>10.856033</td>\n",
       "      <td>9.497246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG5YR</th>\n",
       "      <td>11.188856</td>\n",
       "      <td>11.406959</td>\n",
       "      <td>12.279514</td>\n",
       "      <td>12.068078</td>\n",
       "      <td>11.543082</td>\n",
       "      <td>10.463386</td>\n",
       "      <td>9.212159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG10YR</th>\n",
       "      <td>9.924865</td>\n",
       "      <td>10.128890</td>\n",
       "      <td>11.005377</td>\n",
       "      <td>10.856033</td>\n",
       "      <td>10.463386</td>\n",
       "      <td>9.583483</td>\n",
       "      <td>8.510632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>USGG30YR</th>\n",
       "      <td>8.587987</td>\n",
       "      <td>8.768702</td>\n",
       "      <td>9.600181</td>\n",
       "      <td>9.497246</td>\n",
       "      <td>9.212159</td>\n",
       "      <td>8.510632</td>\n",
       "      <td>7.624304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             USGG3M     USGG6M    USGG2YR    USGG3YR    USGG5YR   USGG10YR  \\\n",
       "USGG3M    11.760393  11.855287  12.303031  11.942035  11.188856   9.924865   \n",
       "USGG6M    11.855287  12.000510  12.512434  12.158422  11.406959  10.128890   \n",
       "USGG2YR   12.303031  12.512434  13.284203  12.977542  12.279514  11.005377   \n",
       "USGG3YR   11.942035  12.158422  12.977542  12.708647  12.068078  10.856033   \n",
       "USGG5YR   11.188856  11.406959  12.279514  12.068078  11.543082  10.463386   \n",
       "USGG10YR   9.924865  10.128890  11.005377  10.856033  10.463386   9.583483   \n",
       "USGG30YR   8.587987   8.768702   9.600181   9.497246   9.212159   8.510632   \n",
       "\n",
       "          USGG30YR  \n",
       "USGG3M    8.587987  \n",
       "USGG6M    8.768702  \n",
       "USGG2YR   9.600181  \n",
       "USGG3YR   9.497246  \n",
       "USGG5YR   9.212159  \n",
       "USGG10YR  8.510632  \n",
       "USGG30YR  7.624304  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covmat = data[X_col].cov()\n",
    "covmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "standardisedX = scale(data[X_col])\n",
    "standardisedX = pd.DataFrame(standardisedX, index=data.index, columns=X_col)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>USGG3M</th>\n",
       "      <th>USGG6M</th>\n",
       "      <th>USGG2YR</th>\n",
       "      <th>USGG3YR</th>\n",
       "      <th>USGG5YR</th>\n",
       "      <th>USGG10YR</th>\n",
       "      <th>USGG30YR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.579328</td>\n",
       "      <td>2.380401</td>\n",
       "      <td>1.879560</td>\n",
       "      <td>1.861457</td>\n",
       "      <td>1.849871</td>\n",
       "      <td>1.831892</td>\n",
       "      <td>1.739428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.596825</td>\n",
       "      <td>2.400609</td>\n",
       "      <td>1.917973</td>\n",
       "      <td>1.869872</td>\n",
       "      <td>1.826323</td>\n",
       "      <td>1.818970</td>\n",
       "      <td>1.739428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.865114</td>\n",
       "      <td>2.614237</td>\n",
       "      <td>2.055165</td>\n",
       "      <td>2.001721</td>\n",
       "      <td>1.944063</td>\n",
       "      <td>1.906193</td>\n",
       "      <td>1.819108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.940935</td>\n",
       "      <td>2.643106</td>\n",
       "      <td>2.101810</td>\n",
       "      <td>2.049410</td>\n",
       "      <td>1.964668</td>\n",
       "      <td>1.896501</td>\n",
       "      <td>1.826352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.069247</td>\n",
       "      <td>2.729712</td>\n",
       "      <td>2.222539</td>\n",
       "      <td>2.141985</td>\n",
       "      <td>2.023538</td>\n",
       "      <td>1.967572</td>\n",
       "      <td>1.906032</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     USGG3M    USGG6M   USGG2YR   USGG3YR   USGG5YR  USGG10YR  USGG30YR\n",
       "0  2.579328  2.380401  1.879560  1.861457  1.849871  1.831892  1.739428\n",
       "1  2.596825  2.400609  1.917973  1.869872  1.826323  1.818970  1.739428\n",
       "2  2.865114  2.614237  2.055165  2.001721  1.944063  1.906193  1.819108\n",
       "3  2.940935  2.643106  2.101810  2.049410  1.964668  1.896501  1.826352\n",
       "4  3.069247  2.729712  2.222539  2.141985  2.023538  1.967572  1.906032"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "standardisedX.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.33464166,  5.35280333,  5.7438603 , ..., -3.48714976,\n",
       "       -3.49353631, -3.50782993])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 1. Covariance matrix\n",
    "covmat = standardisedX.cov()\n",
    "\n",
    "## 2. Eigen values and Eigen vectors. \n",
    "##    Loadings are eigen vectors and eigen values represent the importance\n",
    "eig_val,eig_vec = np.linalg.eig(covmat)\n",
    "\n",
    "## 3. calculate principal components\n",
    "def calcpc(variables, loadings):\n",
    "    # find the number of samples in the data set and the number of variables \n",
    "    numsamples, numvariables = variables.shape\n",
    "    # make a vector to store the component\n",
    "    pc = np.zeros(numsamples)\n",
    "    # calculate the value of the component for each sample\n",
    "    for i in range(numsamples):\n",
    "        valuei = 0\n",
    "        for j in range(numvariables):\n",
    "            valueij = variables.iloc[i, j]\n",
    "            loadingj = loadings[j]\n",
    "            valuei = valuei + (valueij * loadingj) \n",
    "        pc[i] = valuei\n",
    "    return pc\n",
    "\n",
    "# calculate first principal component...\n",
    "pc1 = calcpc(standardisedX, eig_vec[:,0])\n",
    "pc1\n",
    "# the same process to get pc2,pc3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#print(eig_val,eig_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            USGG3M    USGG6M   USGG2YR   USGG3YR   USGG5YR  USGG10YR  USGG30YR\n",
      "USGG3M    1.000120  0.998053  0.984432  0.976945  0.960431  0.934984  0.907053\n",
      "USGG6M    0.998053  1.000120  0.991121  0.984646  0.969307  0.944610  0.916828\n",
      "USGG2YR   0.984432  0.991121  1.000120  0.998912  0.991756  0.975501  0.954034\n",
      "USGG3YR   0.976945  0.984646  0.998912  1.000120  0.996506  0.983812  0.964940\n",
      "USGG5YR   0.960431  0.969307  0.991756  0.996506  1.000120  0.994952  0.982093\n",
      "USGG10YR  0.934984  0.944610  0.975501  0.983812  0.994952  1.000120  0.995755\n",
      "USGG30YR  0.907053  0.916828  0.954034  0.964940  0.982093  0.995755  1.000120\n"
     ]
    }
   ],
   "source": [
    "print(covmat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7gPumWJ8k6SGYJNz3B9YPzG/ol/2TJEcCy6vq09saKMnpSdYkWbNp06YFFytJmswk4Z4R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\nuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSg/4/RZH08Lv0L98AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddb92e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 4. Display the importance of the factors\n",
    "ratio = eig_val/sum(eig_val)\n",
    "x = np.arange(7) + 1\n",
    "plt.bar(x,height=ratio)\n",
    "plt.xticks(x, ['F' + str(i) for i in x])\n",
    "plt.title('Importance of principal components')\n",
    "plt.show()\n",
    "#print(ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zMfA33gkhzBFzyb9rUlcSbYmhTf4AXc+HgTfDillQtjm0dZ+l19e/zoIdC7hr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6fee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [0.25,0.5,2,3,5,10,30]\n",
    "plt.plot(x,eig_vec[:,0])\n",
    "plt.plot(x,eig_vec[:,1])\n",
    "plt.plot(x,eig_vec[:,2])\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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}