ch03_Descriptive_Statistics.ipynb

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    "from IPython.core.display import HTML\n",
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    "    styles = open(\"styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> \n",
    "# Computational Statistics for Data Analysis\n",
    "<font\\>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <div class=\"alert alert-error\"><strong><center><small>\"Statistics is the discipline of using data samples to support claims about populations.\"<small></center></strong> </div>\n",
    "\n",
    "In this notebook, we will get familiar with Descriptive statistics that comprise  concepts, terms, measures and tools that help to describe, show and summarize the data in a meaningful way. When analysing data, such as the price of flats renting per year, it is possible to use both descriptive and inferential statistics in order to analyse the results and draw some conclusions. We will discuss basic concepts,  terms and procedures, like mean, median, variance, correlation, etc.,  to explore, describe and summarize the given set of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statistics is based on 2 main concepts:\n",
    "\n",
    "* A **population** is a collection of objects, items (“units”) about which information is sought.\n",
    "\n",
    "* A **sample** is a part of the population that is observed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'>\n",
    "# 1 Descriptive Statistics.\n",
    "* 1.1 Getting data\n",
    "* 1.2 Data preparation\n",
    "* 1.3 Improving data as a pandas DataFrame\n",
    "* 1.4 Data cleaning \n",
    " <font\\>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \"Are the men more likely to become high income professionals i.e. to receive income bigger than 50K?\"\n",
    "\n",
    "Some people believe it is true, but **without data analysis** to support it, this claim is a case of **anecdotal evidence**:\n",
    "\n",
    "* There are a **small number of samples** (personal experience, friends, etc.).\n",
    "* There is a **selection bias**: most *believers* are interested in this claim because their first babies were late.\n",
    "* There is a **confirmation bias**: believers might be more likely to contribute data that confirm it.\n",
    "* Sources are **innaccurate**: personal stories are subject to memory deformations. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Getting Data\n",
    "\n",
    "Let us consider a public database, called “Adult” dataset hosted on the UCI’s Machine Learning Repository (https://archive.ics.uci.edu/ml/datasets/Adult), that contains approximately 32.000 observations about different financial parameters of US population."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Data preparation\n",
    "\n",
    "One of the reasons we are using a general-purpose language such as Python rather than a stats language like R is that for many projects the *hard* part is preparing the data, not doing the analysis.\n",
    "\n",
    "The most common steps are:\n",
    "\n",
    "1. **Getting the data**. Data can be directly read from a file or it might be necessary to scrap the web.\n",
    "2. **Parsing the data**.  Of course, this depends on what format it is in: plain text, fixed columns, CSV, XML, HTML, etc.\n",
    "3. **Cleaning the data**.  Survey responses and other data files are almost always incomplete.  Sometimes there are multiple codes for things like, *not asked*, *did not know*, and *declined to answer*. And there are almost always errors. A simple strategy is to remove or ignore incomplete records.\n",
    "4. **Building data structures**. Once you read the data, you usually want to store it in a data structure that lends itself to the analysis you want to do.\n",
    "\n",
    "If the data fits into memory, building a data structure is usually the way to go.   If not, you could build a database, which is an out-of-memory data structure. Most databases provide a mapping from keys to values, so they are like dictionaries.\n",
    "\n",
    "Let us read the dataset:"
   ]
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    "file = open('files/adult.data', 'r')"
   ]
  },
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   "execution_count": 65,
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   "source": [
    "def chr_int(a):\n",
    "    if a.isdigit():\n",
    "        return int(a)\n",
    "    else:\n",
    "        return 0\n",
    "                \n",
    "data=[]\n",
    "for line in file:\n",
    "     data1=line.split(', ')\n",
    "     if len(data1)==15:\n",
    "        data.append([chr_int(data1[0]),data1[1],chr_int(data1[2]),data1[3],chr_int(data1[4]),data1[5],data1[6],\\\n",
    "            data1[7],data1[8],data1[9],chr_int(data1[10]),chr_int(data1[11]),chr_int(data1[12]),data1[13],\\\n",
    "            data1[14]])"
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  {
   "cell_type": "code",
   "execution_count": 66,
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   },
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[50, 'Self-emp-not-inc', 83311, 'Bachelors', 13, 'Married-civ-spouse', 'Exec-managerial', 'Husband', 'White', 'Male', 0, 0, 13, 'United-States', '<=50K\\n']]\n"
     ]
    }
   ],
   "source": [
    "print data[1:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Importing data as a pandas DataFrame"
   ]
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    {
     "data": {
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       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>type_employer</th>\n",
       "      <th>fnlwgt</th>\n",
       "      <th>education</th>\n",
       "      <th>education_num</th>\n",
       "      <th>marital</th>\n",
       "      <th>occupation</th>\n",
       "      <th>relationship</th>\n",
       "      <th>race</th>\n",
       "      <th>sex</th>\n",
       "      <th>capital_gain</th>\n",
       "      <th>capital_loss</th>\n",
       "      <th>hr_per_week</th>\n",
       "      <th>country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> 39</td>\n",
       "      <td>        State-gov</td>\n",
       "      <td>  77516</td>\n",
       "      <td> Bachelors</td>\n",
       "      <td> 13</td>\n",
       "      <td>      Never-married</td>\n",
       "      <td>      Adm-clerical</td>\n",
       "      <td> Not-in-family</td>\n",
       "      <td> White</td>\n",
       "      <td>   Male</td>\n",
       "      <td> 2174</td>\n",
       "      <td> 0</td>\n",
       "      <td> 40</td>\n",
       "      <td> United-States</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> 50</td>\n",
       "      <td> Self-emp-not-inc</td>\n",
       "      <td>  83311</td>\n",
       "      <td> Bachelors</td>\n",
       "      <td> 13</td>\n",
       "      <td> Married-civ-spouse</td>\n",
       "      <td>   Exec-managerial</td>\n",
       "      <td>       Husband</td>\n",
       "      <td> White</td>\n",
       "      <td>   Male</td>\n",
       "      <td>    0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 13</td>\n",
       "      <td> United-States</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td> 38</td>\n",
       "      <td>          Private</td>\n",
       "      <td> 215646</td>\n",
       "      <td>   HS-grad</td>\n",
       "      <td>  9</td>\n",
       "      <td>           Divorced</td>\n",
       "      <td> Handlers-cleaners</td>\n",
       "      <td> Not-in-family</td>\n",
       "      <td> White</td>\n",
       "      <td>   Male</td>\n",
       "      <td>    0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 40</td>\n",
       "      <td> United-States</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td> 53</td>\n",
       "      <td>          Private</td>\n",
       "      <td> 234721</td>\n",
       "      <td>      11th</td>\n",
       "      <td>  7</td>\n",
       "      <td> Married-civ-spouse</td>\n",
       "      <td> Handlers-cleaners</td>\n",
       "      <td>       Husband</td>\n",
       "      <td> Black</td>\n",
       "      <td>   Male</td>\n",
       "      <td>    0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 40</td>\n",
       "      <td> United-States</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td> 28</td>\n",
       "      <td>          Private</td>\n",
       "      <td> 338409</td>\n",
       "      <td> Bachelors</td>\n",
       "      <td> 13</td>\n",
       "      <td> Married-civ-spouse</td>\n",
       "      <td>    Prof-specialty</td>\n",
       "      <td>          Wife</td>\n",
       "      <td> Black</td>\n",
       "      <td> Female</td>\n",
       "      <td>    0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 40</td>\n",
       "      <td>          Cuba</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age     type_employer  fnlwgt  education  education_num  \\\n",
       "0   39         State-gov   77516  Bachelors             13   \n",
       "1   50  Self-emp-not-inc   83311  Bachelors             13   \n",
       "2   38           Private  215646    HS-grad              9   \n",
       "3   53           Private  234721       11th              7   \n",
       "4   28           Private  338409  Bachelors             13   \n",
       "\n",
       "              marital         occupation   relationship   race     sex  \\\n",
       "0       Never-married       Adm-clerical  Not-in-family  White    Male   \n",
       "1  Married-civ-spouse    Exec-managerial        Husband  White    Male   \n",
       "2            Divorced  Handlers-cleaners  Not-in-family  White    Male   \n",
       "3  Married-civ-spouse  Handlers-cleaners        Husband  Black    Male   \n",
       "4  Married-civ-spouse     Prof-specialty           Wife  Black  Female   \n",
       "\n",
       "   capital_gain  capital_loss  hr_per_week        country   income  \n",
       "0          2174             0           40  United-States  <=50K\\n  \n",
       "1             0             0           13  United-States  <=50K\\n  \n",
       "2             0             0           40  United-States  <=50K\\n  \n",
       "3             0             0           40  United-States  <=50K\\n  \n",
       "4             0             0           40           Cuba  <=50K\\n  "
      ]
     },
     "execution_count": 67,
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   ],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame(data) #  Two-dimensional size-mutable, potentially heterogeneous tabular data structure with labeled axes \n",
    "\n",
    "df.columns = ['age', 'type_employer', 'fnlwgt', 'education', \n",
    "                \"education_num\",\"marital\", \"occupation\", \"relationship\", \"race\",\"sex\",\n",
    "                \"capital_gain\", \"capital_loss\", \"hr_per_week\",\"country\",\"income\"]\n",
    "df.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
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    {
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       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>type_employer</th>\n",
       "      <th>fnlwgt</th>\n",
       "      <th>education</th>\n",
       "      <th>education_num</th>\n",
       "      <th>marital</th>\n",
       "      <th>occupation</th>\n",
       "      <th>relationship</th>\n",
       "      <th>race</th>\n",
       "      <th>sex</th>\n",
       "      <th>capital_gain</th>\n",
       "      <th>capital_loss</th>\n",
       "      <th>hr_per_week</th>\n",
       "      <th>country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>32556</th>\n",
       "      <td> 27</td>\n",
       "      <td>      Private</td>\n",
       "      <td> 257302</td>\n",
       "      <td> Assoc-acdm</td>\n",
       "      <td> 12</td>\n",
       "      <td> Married-civ-spouse</td>\n",
       "      <td>      Tech-support</td>\n",
       "      <td>      Wife</td>\n",
       "      <td> White</td>\n",
       "      <td> Female</td>\n",
       "      <td>     0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 38</td>\n",
       "      <td> United-States</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32557</th>\n",
       "      <td> 40</td>\n",
       "      <td>      Private</td>\n",
       "      <td> 154374</td>\n",
       "      <td>    HS-grad</td>\n",
       "      <td>  9</td>\n",
       "      <td> Married-civ-spouse</td>\n",
       "      <td> Machine-op-inspct</td>\n",
       "      <td>   Husband</td>\n",
       "      <td> White</td>\n",
       "      <td>   Male</td>\n",
       "      <td>     0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 40</td>\n",
       "      <td> United-States</td>\n",
       "      <td>  &gt;50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32558</th>\n",
       "      <td> 58</td>\n",
       "      <td>      Private</td>\n",
       "      <td> 151910</td>\n",
       "      <td>    HS-grad</td>\n",
       "      <td>  9</td>\n",
       "      <td>            Widowed</td>\n",
       "      <td>      Adm-clerical</td>\n",
       "      <td> Unmarried</td>\n",
       "      <td> White</td>\n",
       "      <td> Female</td>\n",
       "      <td>     0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 40</td>\n",
       "      <td> United-States</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32559</th>\n",
       "      <td> 22</td>\n",
       "      <td>      Private</td>\n",
       "      <td> 201490</td>\n",
       "      <td>    HS-grad</td>\n",
       "      <td>  9</td>\n",
       "      <td>      Never-married</td>\n",
       "      <td>      Adm-clerical</td>\n",
       "      <td> Own-child</td>\n",
       "      <td> White</td>\n",
       "      <td>   Male</td>\n",
       "      <td>     0</td>\n",
       "      <td> 0</td>\n",
       "      <td> 20</td>\n",
       "      <td> United-States</td>\n",
       "      <td> &lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32560</th>\n",
       "      <td> 52</td>\n",
       "      <td> Self-emp-inc</td>\n",
       "      <td> 287927</td>\n",
       "      <td>    HS-grad</td>\n",
       "      <td>  9</td>\n",
       "      <td> Married-civ-spouse</td>\n",
       "      <td>   Exec-managerial</td>\n",
       "      <td>      Wife</td>\n",
       "      <td> White</td>\n",
       "      <td> Female</td>\n",
       "      <td> 15024</td>\n",
       "      <td> 0</td>\n",
       "      <td> 40</td>\n",
       "      <td> United-States</td>\n",
       "      <td>  &gt;50K\\n</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       age type_employer  fnlwgt   education  education_num  \\\n",
       "32556   27       Private  257302  Assoc-acdm             12   \n",
       "32557   40       Private  154374     HS-grad              9   \n",
       "32558   58       Private  151910     HS-grad              9   \n",
       "32559   22       Private  201490     HS-grad              9   \n",
       "32560   52  Self-emp-inc  287927     HS-grad              9   \n",
       "\n",
       "                  marital         occupation relationship   race     sex  \\\n",
       "32556  Married-civ-spouse       Tech-support         Wife  White  Female   \n",
       "32557  Married-civ-spouse  Machine-op-inspct      Husband  White    Male   \n",
       "32558             Widowed       Adm-clerical    Unmarried  White  Female   \n",
       "32559       Never-married       Adm-clerical    Own-child  White    Male   \n",
       "32560  Married-civ-spouse    Exec-managerial         Wife  White  Female   \n",
       "\n",
       "       capital_gain  capital_loss  hr_per_week        country   income  \n",
       "32556             0             0           38  United-States  <=50K\\n  \n",
       "32557             0             0           40  United-States   >50K\\n  \n",
       "32558             0             0           40  United-States  <=50K\\n  \n",
       "32559             0             0           20  United-States  <=50K\\n  \n",
       "32560         15024             0           40  United-States   >50K\\n  "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32561, 15)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's count the number of items per country:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "country\n",
      "?                               583\n",
      "Cambodia                         19\n",
      "Canada                          121\n",
      "China                            75\n",
      "Columbia                         59\n",
      "Cuba                             95\n",
      "Dominican-Republic               70\n",
      "Ecuador                          28\n",
      "El-Salvador                     106\n",
      "England                          90\n",
      "France                           29\n",
      "Germany                         137\n",
      "Greece                           29\n",
      "Guatemala                        64\n",
      "Haiti                            44\n",
      "Holand-Netherlands                1\n",
      "Honduras                         13\n",
      "Hong                             20\n",
      "Hungary                          13\n",
      "India                           100\n",
      "Iran                             43\n",
      "Ireland                          24\n",
      "Italy                            73\n",
      "Jamaica                          81\n",
      "Japan                            62\n",
      "Laos                             18\n",
      "Mexico                          643\n",
      "Nicaragua                        34\n",
      "Outlying-US(Guam-USVI-etc)       14\n",
      "Peru                             31\n",
      "Philippines                     198\n",
      "Poland                           60\n",
      "Portugal                         37\n",
      "Puerto-Rico                     114\n",
      "Scotland                         12\n",
      "South                            80\n",
      "Taiwan                           51\n",
      "Thailand                         18\n",
      "Trinadad&Tobago                  19\n",
      "United-States                 29170\n",
      "Vietnam                          67\n",
      "Yugoslavia                       16\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "counts = df.groupby('country').size()\n",
    "\n",
    "print counts \n",
    "# also: df.outcome.value_counts()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "age\n",
      "17     395\n",
      "18     550\n",
      "19     712\n",
      "20     753\n",
      "21     720\n",
      "22     765\n",
      "23     877\n",
      "24     798\n",
      "25     841\n",
      "26     785\n",
      "27     835\n",
      "28     867\n",
      "29     813\n",
      "30     861\n",
      "31     888\n",
      "...\n",
      "75     45\n",
      "76     46\n",
      "77     29\n",
      "78     23\n",
      "79     22\n",
      "80     22\n",
      "81     20\n",
      "82     12\n",
      "83      6\n",
      "84     10\n",
      "85      3\n",
      "86      1\n",
      "87      1\n",
      "88      3\n",
      "90     43\n",
      "Length: 73, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "counts = df.groupby('age').size() # grouping by age\n",
    "print counts "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21790, 15)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml = df[(df.sex == 'Male')] # grouping by sex\n",
    "ml.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6662, 15)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml1 = df[(df.sex == 'Male')&(df.income=='>50K\\n')]\n",
    "ml1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's separate male from female according to the income. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10771, 15)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm =df[(df.sex == 'Female')]\n",
    "fm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1179, 15)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm1 =df[(df.sex == 'Female')&(df.income=='>50K\\n')]\n",
    "fm1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The rate of people with high income is:  24 %.\n",
      "The rate of men with high income is:  30 %.\n",
      "The rate of women with high income is:  10 %.\n"
     ]
    }
   ],
   "source": [
    "df1=df[(df.income=='>50K\\n')]\n",
    "\n",
    "print 'The rate of people with high income is: ', int(len(df1)/float(len(df))*100), '%.' \n",
    "print 'The rate of men with high income is: ', int(len(ml1)/float(len(ml))*100), '%.' \n",
    "print 'The rate of women with high income is: ', int(len(fm1)/float(len(fm))*100), '%.' "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Data Cleaning\n",
    "\n",
    "The most common steps are:\n",
    "\n",
    "+ **Sample the data**. If the amount of raw data is huge, processing all of them may require an extensive amount of processing power which may not be practical.  In this case, it is quite common to sample the input data to reduce the size of data that need to be processed.\n",
    "\n",
    "+ **Impute missing data**. It is quite common that some of the input records are incomplete in the sense that certain fields are missing or have input error.  In a typical tabular data format, we need to validate each record contains the same number of fields and each field contains the data type we expect. In case the record has some fields missing, we have the following choices: \n",
    "<small>\n",
    "* (a) Discard the whole record if it is incomplete; \n",
    "* (b) Infer the missing value based on the data from other records.  A common approach is to fill the missing data with the average, or the median.\n",
    "<small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Normalize numeric value**. Normalize data is about transforming numeric data into a uniform range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Reduce dimensionality**. High dimensionality can be a problem for some machine learning methods.  There are two ways to reduce the number of input features.  One is about $removing$ $irrelevant$ input variables, another one is about $removing$ $redundant$ input variables.\n",
    "+ **Add derived features**. In some cases, we may need to compute additional attributes from existing attributes (f.e. converting a geo-location to a zip code, or converting the age to an age group).\n",
    "+ **Discretize numeric value into categories**. Discretize data is about cutting a continuous value into ranges and assigning the numeric with the corresponding bucket of the range it falls on.  For numeric attribute, a common way to generalize it is to discretize it into ranges, which can be either constant width (variable height/frequency) or variable width (constant height).\n",
    "+ **Binarize categorical attributes**. Certain machine learning models only take binary input (or numeric input).  In this case, we need to convert categorical attribute into multiple binary attributes, while each binary attribute corresponds to a particular value of the category. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Select, combine, aggregate data**. Designing the form of training data is the most important part of the whole predictive modeling exercise because the accuracy largely depends on whether the input features are structured in an appropriate form that provide strong signals to the learning algorithm. Rather than using the raw data as it is, it is quite common that multiple pieces of raw data need to be combined together, or aggregating multiple raw data records along some dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'>\n",
    "## 2 Exploratory Data Analysis.\n",
    "\n",
    "<font\\>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Summarizing the data: \n",
    "#### 2.1.1 Sample Mean \n",
    "\n",
    "If you have a sample of $n$ values, $x_i$, the **sample mean** is the sum of the values divided by the number of values:\n",
    "\n",
    "$$ \\mu = \\frac{1}{n} \\sum_i x_i$$\n",
    "\n",
    "The **mean** is the most basic and important summary statistic. It describes the central tendency of a sample. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a small difference!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average age of men is:  39.4335474989 .\n",
      "The average age of women is:  36.8582304336 .\n"
     ]
    }
   ],
   "source": [
    "print 'The average age of men is: ', ml['age'].mean(), '.' \n",
    "print 'The average age of women is: ', fm['age'].mean(), '.'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This difference in sample means can be considered a first evidence of our hypothesis!\n",
    "\n",
    "\n",
    "**Comment: ** *Later, we will work with both concepts: the population mean and the sample mean. Do not confuse them! Remember, the first one is the mean of samples taken from the population and the second one is the mean of the whole population.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average age of high-income men is:  44.6257880516 .\n",
      "The average age of high-income women is:  42.1255301103 .\n"
     ]
    }
   ],
   "source": [
    "print 'The average age of high-income men is: ', ml1['age'].mean(), '.' \n",
    "print 'The average age of high-income women is: ', fm1['age'].mean(), '.'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.2 Sample Variance\n",
    "\n",
    "Usually, mean is not a sufficient descriptor of the data, we can do a little better with two numbers: mean and **variance**:\n",
    "\n",
    "$$ \\sigma^2 = \\frac{1}{n} \\sum_i (x_i - \\mu)^2 $$\n",
    "\n",
    "**Variance** $\\sigma^2$ describes the *spread* of data. The term $(x_i - \\mu)$ is called the *deviation from the mean*, so variance is the mean squared deviation.\n",
    "\n",
    "The square root of variance, $\\sigma$, is called the **standard deviation**. We define standard deviation because variance is hard to interpret (in the case the units are grams, the variance is in grams squared). Let's get the basic statistics for our example data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics of age for men: mu: 39.4335474989 var: 178.773751745 std: 13.3706301925\n",
      "Statistics of age for women: mu: 36.8582304336 var: 196.383706395 std: 14.0136970994\n"
     ]
    }
   ],
   "source": [
    "ml_mu = ml['age'].mean()\n",
    "fm_mu = fm['age'].mean()\n",
    "ml_var = ml['age'].var()\n",
    "fm_var = fm['age'].var()\n",
    "ml_std = ml['age'].std()\n",
    "fm_std = fm['age'].std()\n",
    "print 'Statistics of age for men: mu:', ml_mu, 'var:', ml_var, 'std:', ml_std\n",
    "print 'Statistics of age for women: mu:', fm_mu, 'var:', fm_var, 'std:', fm_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics of hours per week for men: mu: 42.4280862781 var: 146.888467171 std: 12.1197552439\n",
      "Statistics  of hours per week for women: mu: 36.410361155 var: 139.506797 std: 11.8112995475\n"
     ]
    }
   ],
   "source": [
    "ml_mu_hr = ml['hr_per_week'].mean()\n",
    "fm_mu_hr = fm['hr_per_week'].mean()\n",
    "ml_var_hr = ml['hr_per_week'].var()\n",
    "fm_var_hr = fm['hr_per_week'].var()\n",
    "ml_std_hr = ml['hr_per_week'].std()\n",
    "fm_std_hr = fm['hr_per_week'].std()\n",
    "print 'Statistics of hours per week for men: mu:', ml_mu_hr, 'var:', ml_var_hr, 'std:', ml_std_hr\n",
    "print 'Statistics  of hours per week for women: mu:', fm_mu_hr, 'var:', fm_var_hr, 'std:', fm_std_hr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.3 Sample Median\n",
    "\n",
    "The statistical median is an order statistic that gives the *middle* value of a sample. It is a value more robust to ouliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median age per men and women:  38.0 35.0\n",
      "Median age per men and women with high-income:  44.0 41.0\n"
     ]
    }
   ],
   "source": [
    "ml_median= ml['age'].median()\n",
    "fm_median= fm['age'].median()\n",
    "print \"Median age per men and women: \", ml_median, fm_median\n",
    "\n",
    "ml_median_age= ml1['age'].median()\n",
    "fm_median_age= fm1['age'].median()\n",
    "print \"Median age per men and women with high-income: \", ml_median_age, fm_median_age\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median hours per week per men and women:  40.0 40.0\n"
     ]
    }
   ],
   "source": [
    "ml_median_hr= ml['hr_per_week'].median()\n",
    "fm_median_hr= fm['hr_per_week'].median()\n",
    "print \"Median hours per week per men and women: \", ml_median_hr, fm_median_hr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.4 Summarizing the data: Quantiles & Percentiles\n",
    "\n",
    "Order the sample $\\{ x_i \\}$, then find $x_p$ so that it divides the data into two parts where:\n",
    "\n",
    "+ a fraction $p$ of the data values are less than or equal to $x_p$ and\n",
    "+ the remaining fraction $(1 − p)$ are greater than $x_p$.\n",
    "\n",
    "That value $x_p$ is the pth-quantile, or 100×pth percentile.\n",
    "\n",
    "**5-number summary**: $x_{min}, Q_1, Q_2, Q_3, x_{max}$, where $Q_1$ is the 25×pth percentile,\n",
    "$Q_2$ is the 50×pth percentile and $Q_3$ is the 75×pth percentile."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most common representation of a distribution is a **histogram**, which is a graph that shows the frequency of each value. Let us visualize the histogram for the age of the male and female populations in our example: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iIpJBcZPKWOBRADOrAb4D/NjddwEuAc4uTXgiIpIlcZPKtsDfou3xQB/gN9H+o0BdwnGJ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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1086ed950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "ml_age=ml['age']\n",
    "ml_age.hist(normed=0, histtype='stepfilled', bins=20)\n",
    "\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Male samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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f5yxgN0nr5v/v9yN1Jmm471LSZvnnFsBngF/Tze9ylZymRdIkYG+gD6kN8HvA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\nmVlpnFTMzKw0TipmZlYaJxUzMyvN/wf3xQ0pXCZg8AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e7a2310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age=fm['age']\n",
    "\n",
    "fm_age.hist(normed=0, histtype='stepfilled', bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Female samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare both populations: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aWa+t3/hYtmKKi+KMV6Zxdm1rbhn64p9+n42YelNTV7d0Y339slxdrzcPrVv3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6eb310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "fm_age.hist(normed=0, histtype='stepfilled', alpha=.5, bins=20)   # default number of bins = 10\n",
    "ml_age.hist(normed=0, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75), bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LgH9z92cK2N4WoC5ruY5oT6WtNoPjdW3Vue3QYzO7C3gsz3oSG2L76o1fufL6qTOuLSRk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\nRCSY/w+zcj/4zhfunAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6eba10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(normed=1, histtype='stepfilled', alpha=.5, bins=20)   # default number of bins = 10\n",
    "ml_age.hist(normed=1, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75), bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('PMF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Data Distributions\n",
    "\n",
    "Summarizing can be dangerous: very different data can be described by the same statistics. It must be validated by inspecting the data.\n",
    "\n",
    "We can look at the **data distribution**, which describes how often (frequency) each value appears.\n",
    "\n",
    "\n",
    "We can normalize the frequencies of the histogram by dividing/normalizing by $n$, the number of samples. The normalized histogram is called **Probability Mass Function (PMF)**.\n",
    "\n",
    "Let's visualize and compare the MPF of male and female age in our example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EmiBTRERioyQjIiKxUZIREZHYNPsJMs3sbuAUYJW7HxIeS91cZ2ZWBdwHdCG4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\nkoyIiMTmfwEjIWSuSYeuJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c29e250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(normed=1, histtype='stepfilled', bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4fu5B+vK8CriU4JaPu939V4X+fO4KPZn7COY7y5bGuc42A1e7+8HAQOCKcG62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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1086ac090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(normed=1, histtype='stepfilled', bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **cumulative distribution function (CDF)**, or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found to have a value less than or equal to x. For our example, the CDFs will be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iZ2A98CpgVeeAiNgJOA84IjOvazyhJOlRGt/DyMwHgWOBi4CrgbMz85qIWB0Rq+th7wb+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\nWf3warWuGgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108efea10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(normed=1, histtype='step', cumulative=True, linewidth=3.5, bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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exh+IiOcDpwKHZObdBe+7YAi+/sAHP3PlK1qQabKcg84wX3IOQ0Zzbnw5Z2UQexjXAEsj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\nfs9I8eCq3gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e7f5650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(normed=1, histtype='step', cumulative=True, linewidth=3.5, bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TZiJwF4C7LzKzfmY2ABhWoO5EYFxc/y7gKZRkRKQr2pOlMtPtqA5penfTi8XW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\n5zndBgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eed9410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(bins=10, normed=1, histtype='stepfilled', alpha=.5)   # default number of bins = 10\n",
    "fm_age.hist(bins=10, normed=1, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75))\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QFQwREQmigiEiIkH+F8ygHB571QeQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f138e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(normed=1, histtype='step', cumulative=True,  linewidth=3.5, bins=20)\n",
    "fm_age.hist(normed=1, histtype='step', cumulative=True,  linewidth=3.5, bins=20, color=sns.desaturate(\"indianred\", .75))\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean sample difference is  2.57531706528\n"
     ]
    }
   ],
   "source": [
    "print \"The mean sample difference is \", ml_age.mean() - fm_age.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Outliers\n",
    "\n",
    "**Ouliers** are data samples with a value that is far from the central tendency.\n",
    "\n",
    "We can find outliers by:\n",
    "\n",
    "+ Computing samples that are *far* from the median.\n",
    "+ Computing samples whose value *exceeds the mean* by 2 or 3 standard deviations.\n",
    "\n",
    "This expression will return a series of boolean values that you can then index the series by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37.0"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['age'].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how many outliers we can detect in our example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df[(df.income == '>50K\\n') & (df['age'] < df['age'].median() - 15)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df[(df.income == '>50K\\n') & (df['age'] > df['age'].median() + 35)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we think that outliers correspond to errors, an option is to trim the data by discarting the highest and lowest values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32492, 15)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = df.drop(df.index[(df.income=='>50K\\n') & (df['age']>df['age'].median() + 35) & (df['age'] > df['age'].median() -15)])\n",
    "df2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ml1_age=ml1['age']\n",
    "fm1_age=fm1['age']\n",
    "\n",
    "ml2_age = ml1_age.drop(ml1_age.index[(ml1_age > df['age'].median() + 35) & (ml1_age > df['age'].median() - 15)])\n",
    "fm2_age = fm1_age.drop(fm1_age.index[(fm1_age > df['age'].median() + 35) & (fm1_age > df['age'].median() - 15)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Men statistics: Mean: 44.3179821239 Std: 10.0197498572 Median: 44.0 Min: 19 Max: 72\n"
     ]
    }
   ],
   "source": [
    "mu2ml = ml2_age.mean()\n",
    "std2ml = ml2_age.std()\n",
    "md2ml = ml2_age.median()\n",
    "# Computing the mean, std, median, min and max for the high-income male population\n",
    "print \"Men statistics: Mean:\", mu2ml, \"Std:\", std2ml, \"Median:\", md2ml, \"Min:\", ml2_age.min(), \"Max:\", ml2_age.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Women statistics: Mean: 44.3179821239 Std: 10.0197498572 Median: 44.0 Min: 19 Max: 72\n"
     ]
    }
   ],
   "source": [
    "mu3ml = fm2_age.mean()\n",
    "std3ml = fm2_age.std()\n",
    "md3ml = fm2_age.median()\n",
    "# Computing the mean, std, median, min and max for the high-income female population\n",
    "print \"Women statistics: Mean:\", mu2ml, \"Std:\", std2ml, \"Median:\", md2ml, \"Min:\", fm2_age.min(), \"Max:\", fm2_age.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean difference with outliers is: 2.58.\n",
      "The mean difference without outliers is: 2.44.\n"
     ]
    }
   ],
   "source": [
    "print 'The mean difference with outliers is: %4.2f.' % (ml_age.mean() - fm_age.mean())\n",
    "print \"The mean difference without outliers is: %4.2f.\" % (ml2_age.mean() - fm2_age.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare visually the age distributions before and after removing the outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10f199a10>"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Mg6eSzr3yEDn/rjRqX/W5GrBBuk3dpu7j06oXOP3zP/K1bQ5LGVOu5a7RU3m3BH6/yffa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\nczUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eee2a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(13.4,5))\n",
    "\n",
    "df.age[(df.income == '>50K\\n')].plot(alpha=.25, color='blue')\n",
    "df2.age[(df2.income == '>50K\\n')].plot(alpha=.45,color='red')\n",
    "\n",
    "plt.ylabel('Age')\n",
    "plt.xlabel('Samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what is happening near the mode:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "countx,divisionx = np.histogram(ml2_age, normed=True) \n",
    "county,divisiony = np.histogram(fm2_age, normed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Wu2LG9AZBlPTBTcteCJyXcXWMyZ1qx4SOx+36OFlE3gDm4K6YXRk3yFq38SC/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\nGGNMZv4fVYU4zy8rQLAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f505750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "val = [(divisionx[i]+divisionx[i+1])/2 for i in range(len(divisionx)-1)]\n",
    "plt.plot(val, countx-county, 'o-') \n",
    "plt.title('Differences in promoting men vs. women')\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Differences',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is still some evidence for our hypothesis!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Remember:\n",
      " We have the following mean values for men, women and the difference:\n",
      "Originally:  39.4335474989 36.8582304336 2.57531706528\n",
      "For high-income:  44.6257880516 42.1255301103 2.50025794137\n",
      "After cleaning:  44.3179821239 41.877028181 2.44095394288\n",
      "\n",
      "The same for the median:\n",
      "38.0 35.0 3.0\n",
      "44.0 41.0 3.0\n",
      "44.0 41.0 3.0\n"
     ]
    }
   ],
   "source": [
    "print \"Remember:\\n We have the following mean values for men, women and the difference:\\nOriginally: \", ml_age.mean(), fm_age.mean(),  ml_age.mean()- fm_age.mean() # The difference between the mean values of male and female populations.\n",
    "print \"For high-income: \", ml1_age.mean(), fm1_age.mean(), ml1_age.mean()- fm1_age.mean() # The difference between the mean values of male and female populations.\n",
    "print \"After cleaning: \", ml2_age.mean(), fm2_age.mean(), ml2_age.mean()- fm2_age.mean() # The difference between the mean values of male and female populations.\n",
    "\n",
    "print \"\\nThe same for the median:\"\n",
    "print ml_age.median(), fm_age.median(), ml_age.median()- fm_age.median() # The difference between the mean values of male and female populations.\n",
    "print ml1_age.median(), fm1_age.median(), ml1_age.median()- fm1_age.median() # The difference between the mean values of male and female populations.\n",
    "print ml2_age.median(), fm2_age.median(), ml2_age.median()- fm2_age.median(), # The difference between the mean values of male and female populations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5 Measuring asymmetry (optional).\n",
    "\n",
    "** Skewness** is a statistic that measures the asymmetry of set of $n$ data samples $x_i$:\n",
    "\n",
    "$$ g_1 = \\frac{\\frac{1}{n} \\sum_i (x_i - \\mu)^2 }{\\frac{1}{n} \\sum_i (x_i - \\mu)^3 }$$\n",
    "\n",
    "The numerator is the mean squared deviation (or variance) and the denominator the mean cubed deviation.\n",
    "\n",
    "Negative deviation indicates that the distribution \"skews left\" (it extends farther to the left than to the right).\n",
    "\n",
    "** Skewness** can be affected by outliers!!! A simpler alternative is to look at the relationship between mean ($\\mu$) and median ($\\mu_{\\frac{1}{2}}$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The skewness of the male population is: 0.266444383843\n",
      "The skewness of the female population is: 0.386333524913\n"
     ]
    }
   ],
   "source": [
    "def skewness(x):\n",
    "    res=0\n",
    "    m=x.mean()\n",
    "    s=x.std()\n",
    "    for i in x:\n",
    "        res+=(i-m)*(i-m)*(i-m)\n",
    "    res/=(len(x)*s*s*s)\n",
    "    return res\n",
    "\n",
    "print \"The skewness of the male population is:\", skewness(ml2_age)\n",
    "print \"The skewness of the female population is:\", skewness(fm2_age)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** 2.6 Pearson's median skewness coefficient** is a more robust alternative:\n",
    "\n",
    "$$ g_p = \\frac{3(\\mu - \\mu_{\\frac{1}{2}})}{\\sigma} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Write a function to compute $g_1$ and $g_p$ of the pregnancy length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson's coefficient of the male population is: 9.55830402221\n",
      "The Pearson's coefficient of the female population is: 26.4067269073\n"
     ]
    }
   ],
   "source": [
    "def pearson(x):\n",
    "    return 3*(x.mean()-x.median())*x.std()\n",
    "\n",
    "print \"The Pearson's coefficient of the male population is:\", pearson(ml2_age)\n",
    "print \"The Pearson's coefficient of the female population is:\", pearson(fm2_age)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.6 Relative Risk\n",
    "\n",
    "Let's say that a person is \"early\" promoted if he/she is promoted before the age of 41, \"on time\" if he/she is promoted of age 41, 42, 43 or 44, and \"late\" promoted if he/she is ascended to get income bigger than 50K after being 44 years old. Let us compute the probability of being early, on time and late promoted for men and women:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6601, 15) (1171, 15)\n"
     ]
    }
   ],
   "source": [
    "#ml1 = df[(df.sex == 'Male')&(df.income=='>50K\\n')]\n",
    "\n",
    "ml2 = ml1.drop(ml1.index[(ml1['age'] > df['age'].median() + 35) & (ml1['age'] > df['age'].median() - 15)])\n",
    "fm2 = fm1.drop(fm1.index[(fm1['age'] > df['age'].median() + 35) & (fm1['age'] > df['age'].median() - 15)])\n",
    "\n",
    "print ml2.shape, fm2.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Men grouped in 3 categories:\n",
      "Young: 38 %.\n",
      "Elder: 48 %.\n",
      "Average age: 14 %.\n"
     ]
    }
   ],
   "source": [
    "print \"Men grouped in 3 categories:\"\n",
    "print \"Young:\",int(round(100*len(ml2_age[ml2_age<41])/float(len(ml2_age.index)))),\"%.\"\n",
    "print \"Elder:\", int(round(100*len(ml2_age[ml2_age >44])/float(len(ml2_age.index)))),\"%.\"\n",
    "print \"Average age:\", int(round(100*len(ml2_age[(ml2_age>40) & (ml2_age< 45)])/float(len(ml2_age.index)))),\"%.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Women grouped in 3 categories:\n",
      "Young: 48 %.\n",
      "Elder: 37 %.\n",
      "Average age: 15 %.\n"
     ]
    }
   ],
   "source": [
    "print \"Women grouped in 3 categories:\"\n",
    "print \"Young:\",int(round(100*len(fm2_age[fm2_age <41])/float(len(fm2_age.index)))),\"%.\"\n",
    "print \"Elder:\", int(round(100*len(fm2_age[fm2_age >44])/float(len(fm2_age.index)))),\"%.\"\n",
    "print \"Average age:\", int(round(100*len(fm2_age[(fm2_age>40) & (fm2_age< 45)])/float(len(fm2_age.index)))),\"%.\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **relative risk** is the ratio of two probabilities. In order to get the relative risk \\cite{Downey} of early promotion, we need to consider the  fraction of both probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The male mean: 44.3179821239\n",
      "The female mean: 41.877028181\n"
     ]
    }
   ],
   "source": [
    "print \"The male mean:\", ml2_age.mean()\n",
    "print \"The female mean:\", fm2_age.mean()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The relative risk of female early promotion is:  21.1254400822\n"
     ]
    }
   ],
   "source": [
    "ml2_young = len(ml2_age[(ml2_age<41)])/float(len(ml2_age.index))\n",
    "fm2_young  = len(fm2_age[(fm2_age<41)])/float(len(fm2_age.index))\n",
    "print \"The relative risk of female early promotion is: \", 100*(1-ml2_young/fm2_young)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that women are 21% more likely to get high gains before 41 years than men."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The relative risk of male late promotion is:  128.971570897\n"
     ]
    }
   ],
   "source": [
    "ml2_elder = len(ml2_age[(ml2_age>44)])/float(len(ml2_age.index))\n",
    "fm2_elder  = len(fm2_age[(fm2_age>44)])/float(len(fm2_age.index))\n",
    "print \"The relative risk of male late promotion is: \", 100*ml2_elder/fm2_elder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that men are 29% more likely to get high gains after 44 years than women."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussions.\n",
    "\n",
    "After exploring the data, we obtained some apparent effects that seem to support our first assumption:\n",
    "\n",
    "+ **Data description:** The mean age for ascending male professionals is 44 years old while for female professionals it is 41 years.\n",
    "\n",
    "+ **Relative risk:** Female professionals are 21%  more likely to be ascended before 41 years of age, while men are 29% more likely to be ascended being at least 45 years old.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Continous distributions\n",
    "\n",
    "So far, we have built **empirical distributions** (which represent the distributions of values in a sample), based on observations, but many real problems are well approximated by fitting **continous distributions functions (CDF)**. \n",
    "\n",
    "They are called in this way because the distribution is described by an analytical continous function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.1 The exponential distribution\n",
    "\n",
    "The CDF of the exponential distribution is:\n",
    "\n",
    "$$ CDF(x) = 1 -  \\exp^{- \\lambda x}$$ \n",
    "\n",
    "And its PDF is:\n",
    "\n",
    "$$ PDF(x) = \\lambda \\exp^{- \\lambda x}$$\n",
    "\n",
    "The parameter $\\lambda$ determines the shape of the distribution, the mean of the distribution is $1/\\lambda$ and its variance is $1/\\lambda^2$. The median is $ln(2)/\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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EAxORxKhwyKBSmdxGwEXAJ4CXgIPz2fR1iQYlIokbVrmJ9KLoAPjDhKJxA/AeFQ0RAfU4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f107b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 3\n",
    "x=np.arange(0,2.5,0.1)\n",
    "y= 1 - np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential CDF: $\\lambda$ =%.2f' % l ,fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vA0sII6xubbJZ7QixMeUiOrfjR8CngMXA4cD5fT41u/aLmHIRUy4S0uy4+ZMo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\nRESkLSocIiLSFhUOERFpy/8CwhExk9yHdgAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ecb7f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "\n",
    "import scipy.stats as stats\n",
    "i\n",
    "\n",
    "l = 3\n",
    "x=np.arange(0,2.5,0.1)\n",
    "y= l * np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential PDF: $\\lambda$ =%.2f' % l, fontsize=15)\n",
    "plt.xlabel('x', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a lot of real world events that can be described with this distribution.\n",
    "* The time until a radioactive particle decays,\n",
    "* The time it takes before your next telephone call,\n",
    "* The time until default (on payment to company debt holders) in reduced form credit risk modeling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The random variable $X$ of the lifelengths of some batteries is associated with a probability density function of the form:\n",
    "\n",
    "$$ PDF(x) = \\frac{1}{4} \\exp^{- \\frac{x}{4}}$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ad78pyfglVi7m7wbeB8wEcsDfcoXSlHSjEpE06A6J2dGSXOQKpV7gvwhNXG8C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\niAqJiIg0RIVEREQa8v8B7+Q2xbjeufoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ecb74d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 0.25\n",
    "x=np.arange(0,25,0.1)\n",
    "y= l * np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential: $\\lambda$ =%.2f' % l ,fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('PDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.2 The normal distribution\n",
    "\n",
    "The **normal, or Gaussian distribution** is the most used one because it describes a lot of phenomena and because it is amenable for analysis. \n",
    "\n",
    "Its CDF has no closed-form expression and its more common representation is the PDF:\n",
    "\n",
    "$$ PDF(x) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp \\left(-\\frac{(x-\\mu)^2}{2 \\sigma^2} \\right)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NRGYut28d8pspH1jWW6sFpHH4Ju5a4xpBlPzQdx5j+lL2GomIHAD8tuSuG0Tk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\nTayQGGOMqYkVEmOMMTWxQmKMMaYm/w/EMihjEs1nnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1086ccc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u=6 # mean\n",
    "s=2 # standard deviation\n",
    "x=np.arange(0,15,0.1)\n",
    "y=(1/(np.sqrt(2*np.pi*s*s)))*np.exp(-(((x-u)**2)/(2*s*s)))\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Gaussian PDF: $\\mu$=%.1f, $\\sigma$=%.1f' % (u,s),fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('Probability density',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examples:\n",
    "    * Measures of size of living tissue (length, height, skin area, weight);\n",
    "    * The length of inert appendages (hair, claws, nails, teeth) of biological specimens, in the direction of growth; presumably the thickness of tree bark also falls under this category;\n",
    "    * Certain physiological measurements, such as blood pressure of adult humans.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Central Limit Theorem\n",
    "\n",
    "The normal distribution is also important, because it is involved in the Central Limit Theorem:\n",
    "\n",
    "> Take the mean of $n$ random samples from ANY arbitrary distribution with a $well$ $defined$ standard deviation $\\sigma$ and mean $\\mu$. As $n$ gets bigger the **distribution of the sample mean** will always converge to a Gaussian (normal) distribution with mean $\\mu$ and standard deviation $\\frac{\\sigma}{\\sqrt{n}}$.\n",
    "\n",
    "Colloquially speaking, the theorem states the distribution of an average tends to be normal, even when the distribution from which the average is computed is decidedly non-normal. This explains the ubiquity of the Gaussian distribution in science and statistics. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Uniform Distribution\n",
    "\n",
    "The uniform distribution is obviously non-normal.  Let's call it the $parent$ $distribution$.\n",
    "\n",
    "To compute an average, two samples are drawn ($n=2$), at random, from the parent distribution and averaged. Then another sample of two is drawn and another value of the average computed.  This process is repeated, over and over, and averages of two are computed.  \n",
    "\n",
    "Repeatedly taking more elements ($n = 3,4...$) from the parent distribution, and computing the averages, produces a normal probability density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wGuBbwNbShylSEaZ0veQeNn8CeCHwrtkJUUAJTjXZ7Zzbkvt5E3CttfaThJ8aDDnnLp/d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\ncEREREREZNz4HwP1KSreRgZvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b615dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 4, sharey=True, squeeze=True, figsize=(14, 5))\n",
    "x = np.linspace(0, 1, 100)\n",
    "for i in range(4):\n",
    "    f = np.mean(np.random.random((10000, i+1)), 1)\n",
    "    m, s = np.mean(f), np.std(f, ddof=1)\n",
    "    fn = (1/(s*np.sqrt(2*np.pi)))*np.exp(-(x-m)**2/(2*s**2))  # normal pdf            \n",
    "    ax[i].hist(f, 40, normed=True, color=[0, 0.2, .8, .6]) \n",
    "    ax[i].set_title('n=%d' %(i+1))\n",
    "    ax[i].plot(x, fn, color=[1, 0, 0, .6], linewidth=5)\n",
    "plt.suptitle('Demonstration of the central limit theorem for a uniform distribution', y=1.05)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.6 Kernel density estimates\n",
    "\n",
    "In some instances, we may not be interested in the parameters of a particular distribution of data, but just a **continous representation** of the data at hand. In this case, we can estimate the distribution non-parametrically (i.e. making no assumptions about the form of the underlying distribution) using kernel density estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10e72a710>]"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XZazToTNGAO20xrgK1sBGNZWKFkYRDP4ZYH3f97cBLgduz/icNCRNmrQCGMRX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\nspL4TaGZZtqYAjbpCTMWwGLRHYnKAfj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rGFud4Ll2+ODK/J6nndoJna342DAaoev3Aa+h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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1086c1810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats.distributions import norm\n",
    "\n",
    "# Some random data\n",
    "y = np.random.random(15) * 10\n",
    "x = np.linspace(0, 10, 100)\n",
    "\n",
    "x1 = np.random.normal(-1, 2, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 3, 10)\n",
    "y = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n",
    "x = np.linspace(min(y), max(y), 100)\n",
    "\n",
    "\n",
    "# Smoothing parameter\n",
    "s = 0.4\n",
    "\n",
    "# Calculate the kernels\n",
    "kernels = np.transpose([norm.pdf(x, yi, s) for yi in y])\n",
    "\n",
    "plt.plot(x, kernels, 'k:')\n",
    "plt.plot(x, kernels.sum(1), 'r')\n",
    "plt.plot(y, np.zeros(len(y)), 'go', ms=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ef43490>]"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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03PGBpk0eB/zDw7vzRd75QOSma0Tm3Cvyq7NFbpotcvgXRf5yushx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\nYER5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108ddf850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import kde\n",
    "\n",
    "x1 = np.random.normal(-1, 0.5, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 1, 10)\n",
    "y = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n",
    "x = np.linspace(min(y), max(y), 100)\n",
    "\n",
    "s = 0.4 # Smoothing parameter\n",
    "\n",
    "kernels = np.transpose([norm.pdf(x, yi, s) for yi in y]) # Calculate the kernels\n",
    "density = kde.gaussian_kde(y)\n",
    "\n",
    "plt.plot(x, kernels, 'k:')\n",
    "plt.plot(x, kernels.sum(1), 'r')\n",
    "plt.plot(y, np.zeros(len(y)), 'bo', ms=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10c110f10>]"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nmfwvesy+mKambV8EQbBsxZU3eFVNXWLdztZmZs6uJU3dvu4OHr/7RgvD8MV87T/tNiez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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c110b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xgrid = np.linspace(x.min(), x.max(), 200)\n",
    "plt.hist(y, bins=28, normed=True)\n",
    "plt.plot(xgrid, density(xgrid), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy implements a Gaussian KDE that automatically chooses an appropriate bandwidth. Let's create a bi-modal distribution of data that is not easily summarized by a parametric distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create a bi-modal distribution with a mixture of Normals.\n",
    "x1 = np.random.normal(-1, 2, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 3, 10)\n",
    "\n",
    "# Append by row\n",
    "x = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.22770327,  0.05692582,  0.11385163,  0.11385163,  0.05692582,\n",
       "         0.11385163,  0.05692582,  0.        ,  0.05692582,  0.05692582,\n",
       "         0.05692582,  0.22770327,  0.        ,  0.05692582,  0.        ,\n",
       "         0.05692582,  0.05692582,  0.11385163]),\n",
       " array([-3.25125594, -2.54858705, -1.84591816, -1.14324928, -0.44058039,\n",
       "         0.2620885 ,  0.96475738,  1.66742627,  2.37009516,  3.07276404,\n",
       "         3.77543293,  4.47810182,  5.1807707 ,  5.88343959,  6.58610848,\n",
       "         7.28877736,  7.99144625,  8.69411514,  9.39678402]),\n",
       " <a list of 18 Patch objects>)"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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J0hxrdY2/2uY4lV4L6addj93/7AsH9u3ttv8zO388dvzEaxf1UsPP9z1Lr7ul1zGGoYZ+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6f51d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=18, normed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d5948d0>]"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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f7FtER791xaMt/g/wpLuPA04BuszRe2ZWDnwTmJgI0TzgK1ktKrkHif5fW/pH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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6d6c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "density = kde.gaussian_kde(x)\n",
    "xgrid = np.linspace(x.min(), x.max(), 200)\n",
    "plt.hist(x, bins=18, normed=True)\n",
    "plt.plot(xgrid, density(xgrid), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'>\n",
    "## 4 Estimation\n",
    "\n",
    "\n",
    "<font\\> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MN+yPU2vdd8X2C/WvB4GHqHULFamMwFbaOCWp5acWC0r9cx6pn83E2VlRn/1OYImkCeB5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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6f5a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.normal(0.0, 1.0, 10000)\n",
    "a = plt.hist(x,50,normed='True')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**Definition:** *Estimation* is the process of inferring the parameters (e.g. mean) of a distribution from a statistic of samples drown from a population.\n",
    "\n",
    "For example: What is the estimated mean $\\hat{\\mu}$ of the following normal data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use our definition of empirical mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The empirical mean of the sample is  0.00110566955034\n"
     ]
    }
   ],
   "source": [
    "print 'The empirical mean of the sample is ', x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Sample mean\n",
    "\n",
    "+ The process is called **estimation** and the statistic we used **estimator**.\n",
    "\n",
    "+ The median is also an estimator (more robust to outliers). \n",
    "\n",
    "+ \"Is median better than sample mean?\" is a question with at least two different answers. We can use two different objectives to answer this question: the minimization of error or the maximization to get the right answer. \n",
    "\n",
    "+ If there are no outliers, we can use the **sample mean** to minimize **mean squared error** (where $m$ is the number of times you play the estimation game, not the size of the sample!):\n",
    "\n",
    "$$ MSE = \\frac{1}{m} \\sum(\\hat{\\mu} - \\mu)^2$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  0.000946002368116\n"
     ]
    }
   ],
   "source": [
    "NTs=200\n",
    "mu=0.0\n",
    "var=1.0\n",
    "err = 0.0\n",
    "NPs=1000\n",
    "for i in range(NTs):\n",
    "    x = np.random.normal(mu, var, NPs)\n",
    "    err += (x.mean()-mu)**2\n",
    "\n",
    "print 'MSE: ', err/NTs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Variance\n",
    "\n",
    "We can also estimate the variance with:\n",
    "\n",
    "$$ \\hat{\\sigma}^2 = \\frac{1}{n} \\sum_i (x_i - \\mu)^2 $$\n",
    "\n",
    "This estimator works for large samples, but it is biased for small samples. We can use this one:\n",
    "\n",
    "$$ \\hat{\\sigma}^2_{n-1} = \\frac{1}{n-1} \\sum_i (x_i - \\mu)^2 $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Other concepts: Standard scores\n",
    "\n",
    "$$ z_i = \\frac{x_i - \\mu}{\\sigma}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This measure is dimensionless and its distribution has mean 0 and variance 1.\n",
    "\n",
    "It inherits the \"shape\" of $X$: if it is normally distributed, so is $Z$. If $X$ is skewed, so is $Z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 Covariance\n",
    "\n",
    "**Covariance** is a measure of the tendency of two variables to vary together. \n",
    "\n",
    "If we have two series $X$ and $Y$ with $X=\\{x_i\\}$ and $Y=\\{y_i\\}$, and they vary together, their deviations $x_i - \\mu_X$ and $y_i - \\mu_Y$ tend to have the same sign.\n",
    "\n",
    "If we multiply them together, the product is positive, when the deviations have the same sign, and negative, when they have the opposite sign. So adding up the products gives a measure of the tendency to vary together.\n",
    "\n",
    "Covariance is the mean of the products:\n",
    "\n",
    "$$ Cov(X,Y) = \\frac{1}{n} \\sum_{i=1}^n (x_i - \\mu_X)*(y_i - \\mu_Y), $$\n",
    "\n",
    "where $n$ is the length of the two series.\n",
    "\n",
    "It is a measure that is difficult to interpret."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cov(X, X) = 18.89\n",
      "Var(X) = 18.89\n",
      "Cov(X, Y) = 0.18\n"
     ]
    }
   ],
   "source": [
    "def Cov(X, Y):\n",
    "    def _get_dvis(V):\n",
    "        return [v - np.mean(V) for v in V]\n",
    "    dxis = _get_dvis(X)\n",
    "    dyis = _get_dvis(Y)\n",
    "    return np.sum([x * y for x, y in zip(dxis, dyis)])/len(X)\n",
    "\n",
    "\n",
    "X = [5, -1, 3.3, 2.7, 12.2]\n",
    "X= np.array(X)\n",
    "Y = [10, 12, 8, 9, 11]\n",
    "\n",
    "print \"Cov(X, X) = %.2f\" % Cov(X, X)\n",
    "print \"Var(X) = %.2f\" % np.var(X)\n",
    "\n",
    "print \"Cov(X, Y) = %.2f\" % Cov(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create some examples of positive and negative correlations like those showing the relations of stock market with respect to the economic growth or the gasoline prices with respect to the world oil production:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "MAXN=100\n",
    "\n",
    "MAXN=40\n",
    "X=np.array([[1,9],[3, 2], [5,3],[5.5,4],[6,4],[6.5,4],[7,3.5],[7.5,3.8],[8,4],\n",
    "            [8.5,4],[9,4.5],[9.5,7],[10,9],[10.5,11],[11,11.5],[11.5,12],[12,12],[12.5,12],[13,10]])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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rW9T8DvDVzPzZ/CfqGVAPyMxPd9oySZKkJWg7UPiTwKGLPHcIjqmRJEkT1sXspzsA13dw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\njSRJ6gWLGkmS1AsWNZIkqRf+fypJnbepL1vTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d5b30d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='b',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('Economic growth(T)',fontsize=15)\n",
    "plt.ylabel('Stock market returns(T)',fontsize=15)\n",
    "plt.gcf().set_size_inches((20,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7xtrzQf0ZzVe+ajJ2OuwFHA9sBg5acvelwHbg5G6XXSWur49qtt+42LzMXu0Z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\nz6qXq/2629oxLefQ7D3b0q7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110459c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.array([[1,8],[2, 7], [3,6],[4,8],[5,8],[6,7],[7,7],[8,5],[9,5],[10,6],[11,4],[12,5],[13,3],[14,2],[15,2],[16,1]])\n",
    "plt.subplot(1,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='b',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('World Oil Production(T)',fontsize=15)\n",
    "plt.ylabel('Gasoline prices(T)',fontsize=15)\n",
    "plt.gcf().set_size_inches((20,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5 Pearson's Correlation\n",
    "\n",
    "Shell we take into account the variance? An alternative is to divide the deviations by $\\sigma$, which yields standard scores, and compute the product of standard scores:\n",
    "\n",
    "$$ p_i = \\frac{(x_i - \\mu_X)}{\\sigma_X} \\frac{(y_i - \\mu_Y)}{\\sigma_Y} $$\n",
    " \n",
    "The mean of these products is:\n",
    "\n",
    "$$ \\rho = \\frac{1}{n} \\sum p_i = \\frac{1}{n} \\sum  \\frac{(x_i - \\mu_X)}{\\sigma_X} \\frac{(y_i - \\mu_Y)}{\\sigma_Y}  $$\n",
    "\n",
    "Or we can rewrite $\\rho$ by factoring out $\\sigma_X$ and $\\sigma_Y$:\n",
    "\n",
    "$$ \\rho = \\frac{Cov(X,Y)}{\\sigma_X \\sigma_Y}$$\n",
    "\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr(X, X) = 2.00000\n",
      "Corr(X, Y) = 0.16906\n"
     ]
    }
   ],
   "source": [
    "def Corr(X, Y):\n",
    "    assert len(X) == len(Y)\n",
    "    return Cov(X, Y) / np.prod([np.std(V) for V in [X, Y]])\n",
    "\n",
    "print \"Corr(X, X) = %.5f\" % Corr(X, X)\n",
    "\n",
    "Y=np.random.random(len(X))\n",
    "\n",
    "print \"Corr(X, Y) = %.5f\" % Corr(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When $\\rho = 0$, we cannot say that there is no relationship between the variables!\n",
    "\n",
    "Pearson's coefficient only measures **linear** correlations!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.6 Spearman’s rank correlation\n",
    "\n",
    "Pearson’s correlation works well if the relationship between variables is linear and if the variables are roughly normal. But it is not robust in the presence of **outliers**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spearman’s rank correlation is an alternative that mitigates the effect of outliers and skewed distributions. To compute Spearman’s correlation, we have to compute the rank of each value, which is its index in the sorted sample. \n",
    "\n",
    "For example, in the sample {7, 1, 2, 5} the rank of the value 5 is 3, because it appears third if we sort the elements. \n",
    "\n",
    "Then, we compute the Pearson’s correlation, **but for the ranks**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ranks:  [4.0, 1.0, 2.0, 3.0]\n",
      "Pearson rank coefficient: 0.28\n",
      "[1.0, 2.0, 3.0, 4.0, 5.0]\n",
      "[2.0, 1.0, 3.0, 5.0, 4.0]\n",
      "Spearman rank coefficient: 0.80\n"
     ]
    },
    {
     "data": {
      "image/png": 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GD8/7GGRcVQ1z2VkzZ2fac3kc+NPM/HkGVwT+YY0/m4yQszPV+czM7wGvzsyXAb8AvDoi\nfmV4nRrmc5ScnWn/fC67msGVqU+7kmm981l1WQDnMbjE9mh3r6kPMbj31LD9wC0Amflp4HkRsX1r\nY46UE6b8oZ3M/BTwrTVWqWEuR8kJ05/LhzPzc93y/wJfYHBLm2FTn88Rc0IFHyjLzO92i6cw2ENf\n+cHcqc9n971LOaGC+YyIeeB1DD6usFqedc1n7YehfnDPqM4SsGeEdeaBY5ONVsywMmcLvCIiPs/g\nE+t/1n0mpSY1zOUoqprLiDgLOAf49IqnqprPNXJWMZ8RMQfcD/wMcOMqGaqYzxFyVjGfDO7g/efA\nj5/g+XXNZ+17FqN+CGRla271h0dG+X73Azsy8xeBfwRun2ykDZv2XI6imrmMiB8D/gW4unvnvlIV\n81nIWcV8ZuaT3eGdeeBXu2P/K019PkfIOfX5jIhfZ3DO77OsvZcz8nzWXhYr7zO1gx++c+1q68x3\nY1upmDMzv7O8+5qZdwLPqfDOujXMZVEtcxkRz2FwS/1/zszVXhCqmM9SzlrmcyjPt4GPA7+04qkq\n5nPZiXJWMp+vAPZHxFeAQ8BrIuLWFeusaz5rL4v7GPwnSWdFxCkM/lOlhRXrLABvAYiIlwOPZuZW\n7+YXc0bE9uX/BCoizgOaEW6WuNVqmMuiGuay+/43A0cy810nWG3q8zlKzkrm8wUR8bxu+bnAXmDl\nlTk1zGcxZw3zmZnXZuaOzDwbuBT498x8y4rV1jWfVZ+zyMzHI+KPgE8yOJF0c2Z+ISLe1j3/nsy8\nIyJe1/0nS/8H/E6NORncIPEPIuJxBpepXbrVOSPiEPAq4AXdfb0OAM9ZzljDXI6SkwrmEngl8NvA\nf0XE8ovFtQzunlzTfBZzUsd8ngHc0p0PmAM+kJn31PZvfZSc1DGfK7UAm5lP7w0lSSqq/TCUJKkC\nloUkqciykCQVWRaSpCLLQpJUZFlIkoosC0lSkWUhSSr6fzUXDRE/fzhUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111c66390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def list2rank(l):\n",
    "    #l is a list of numbers\n",
    "    # returns a list of 1-based index; mean when multiple instances\n",
    "    return [np.mean([i+1 for i, sorted_el in enumerate(sorted(l)) if sorted_el == el]) for el in l]\n",
    "\n",
    "l = [7, 1, 2, 5]\n",
    "print \"ranks: \", list2rank(l)\n",
    "\n",
    "def spearmanRank(X, Y):\n",
    "    # X and Y are same-length lists\n",
    "    print list2rank(X) \n",
    "    print list2rank(Y)\n",
    "    return Corr(list2rank(X), list2rank(Y))\n",
    "\n",
    "X = [10, 20, 30, 40, 1000]\n",
    "Y = [-70, -1000, -50, -10, -20]\n",
    "plt.plot(X,'ro')\n",
    "plt.plot(Y,'go')\n",
    "\n",
    "print \"Pearson rank coefficient: %.2f\" % Corr(X, Y)\n",
    "print \"Spearman rank coefficient: %.2f\" % spearmanRank(X, Y)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Obtain for the Anscombe's quartet [2] given in the figures bellow, the different estimators (mean, variance, covariance for each pair, Pearson's correlation and Spearman's rank correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xdICzSin3AZ8HTgOPRMQ3DxpIkqazkJ96JeWSpgetlPJx4K9HxKcnODxbZZwt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\nE/hgKeWbI+KhhvMeQ67GekS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8C/XHgGdHxDOAy4EfmtXf14uq2kFVrVBVq6yvM37ceVyy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\nSZIqY0GTJEmqjAVNkiSpMv8FcQJErNfSRBEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111e1ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.array([[10.0, 8.04, 10.0, 9.14, 10.0, 7.46, 8.0, 6.58],\n",
    "[8.0, 6.95, 8.0, 8.14, 8.0, 6.77, 8.0, 5.76],\n",
    "[13.0,7.58,13.0,8.74,13.0,12.74,8.0,7.71],\n",
    "[9.0,8.81,9.0,8.77,9.0,7.11,8.0,8.84],\n",
    "[11.0,8.33,11.0,9.26,11.0,7.81,8.0,8.47],\n",
    "[14.0,9.96,14.0,8.10,14.0,8.84,8.0,7.04],\n",
    "[6.0,7.24,6.0,6.13,6.0,6.08,8.0,5.25],\n",
    "[4.0,4.26,4.0,3.10,4.0,5.39,19.0,12.50],\n",
    "[12.0,10.84,12.0,9.13,12.0,8.15,8.0,5.56],\n",
    "[7.0,4.82,7.0,7.26,7.0,6.42,8.0,7.91],\n",
    "[5.0,5.68,5.0,4.74,5.0,5.73,8.0,6.89]])\n",
    "\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "plt.scatter(X[:,2],X[:,3],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "plt.scatter(X[:,4],X[:,5],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "plt.scatter(X[:,6],X[:,7],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "plt.gcf().set_size_inches((10,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Main reference\n",
    "[1] *Think Stats: Probability and Statistics for Programmers*, by Allen B. Downey, published by O'Reilly Media.\n",
    "http://www.greenteapress.com/thinkstats/\n",
    "\n",
    "[2] Anscombe's quartet, https://en.wikipedia.org/wiki/Anscombe%27s_quartet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}