{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 05 How parameters change as data is shifted and scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe width=\"700\" height=\"400\" src=\"https://www.youtube.com/embed/JFlI4Vxtzxo/\" frameborder=\"0\" allowfullscreen></iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<iframe width=\"700\" height=\"400\" src=\"https://www.youtube.com/embed/JFlI4Vxtzxo/\" frameborder=\"0\" allowfullscreen></iframe>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import Series, DataFrame\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[khanacademy](https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/linear-transformations-data/v/how-parameters-change-as-data-is-shifted-and-scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![How parameters change as data is shifted and scaled fig 1](./imgs/04-05-01.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([7, 7, 5, 8, 10, 13, 5, 3, 2, 3, 5, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = DataFrame({'Data': x, \n",
    "               'Data+5': x+5,\n",
    "               'Data*5': x*5})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Data</th>\n",
       "      <th>Data+5</th>\n",
       "      <th>Data*5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>12</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>12</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>13</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10</td>\n",
       "      <td>15</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>13</td>\n",
       "      <td>18</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6</td>\n",
       "      <td>11</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Data  Data+5  Data*5\n",
       "0      7      12      35\n",
       "1      7      12      35\n",
       "2      5      10      25\n",
       "3      8      13      40\n",
       "4     10      15      50\n",
       "5     13      18      65\n",
       "6      5      10      25\n",
       "7      3       8      15\n",
       "8      2       7      10\n",
       "9      3       8      15\n",
       "10     5      10      25\n",
       "11     6      11      30"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_std_df = df.describe()[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "median_iqr_df = DataFrame({'Data': [np.median(df['Data']), stats.iqr(df['Data'])],\n",
    " 'Data+5': [np.median(df['Data+5']), stats.iqr(df['Data+5'])],\n",
    " 'Data*5': [np.median(df['Data*5']), stats.iqr(df['Data*5'])]\n",
    "}, index=['median', 'iqr'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.concat([df, mean_std_df, median_iqr_df])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Data</th>\n",
       "      <th>Data+5</th>\n",
       "      <th>Data*5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>35.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>35.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>40.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>13.000000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>65.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>15.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>10.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>15.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>30.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>6.166667</td>\n",
       "      <td>11.166667</td>\n",
       "      <td>30.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.128559</td>\n",
       "      <td>3.128559</td>\n",
       "      <td>15.642793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>median</th>\n",
       "      <td>5.500000</td>\n",
       "      <td>10.500000</td>\n",
       "      <td>27.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>iqr</th>\n",
       "      <td>2.750000</td>\n",
       "      <td>2.750000</td>\n",
       "      <td>13.750000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Data     Data+5     Data*5\n",
       "0        7.000000  12.000000  35.000000\n",
       "1        7.000000  12.000000  35.000000\n",
       "2        5.000000  10.000000  25.000000\n",
       "3        8.000000  13.000000  40.000000\n",
       "4       10.000000  15.000000  50.000000\n",
       "5       13.000000  18.000000  65.000000\n",
       "6        5.000000  10.000000  25.000000\n",
       "7        3.000000   8.000000  15.000000\n",
       "8        2.000000   7.000000  10.000000\n",
       "9        3.000000   8.000000  15.000000\n",
       "10       5.000000  10.000000  25.000000\n",
       "11       6.000000  11.000000  30.000000\n",
       "mean     6.166667  11.166667  30.833333\n",
       "std      3.128559   3.128559  15.642793\n",
       "median   5.500000  10.500000  27.500000\n",
       "iqr      2.750000   2.750000  13.750000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Data</th>\n",
       "      <th>Data+5</th>\n",
       "      <th>Data*5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>6.166667</td>\n",
       "      <td>11.166667</td>\n",
       "      <td>30.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.128559</td>\n",
       "      <td>3.128559</td>\n",
       "      <td>15.642793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>median</th>\n",
       "      <td>5.500000</td>\n",
       "      <td>10.500000</td>\n",
       "      <td>27.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>iqr</th>\n",
       "      <td>2.750000</td>\n",
       "      <td>2.750000</td>\n",
       "      <td>13.750000</td>\n",
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      ],
      "text/plain": [
       "            Data     Data+5     Data*5\n",
       "mean    6.166667  11.166667  30.833333\n",
       "std     3.128559   3.128559  15.642793\n",
       "median  5.500000  10.500000  27.500000\n",
       "iqr     2.750000   2.750000  13.750000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[-4:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
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   "execution_count": null,
   "metadata": {},
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   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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