Lab1_linear_regression.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FH6WL_esdgkB"
   },
   "source": [
    "# Introduction to Linear Regression\n",
    "\n",
    "*Adapted from Chapter 3 of [An Introduction to Statistical Learning](https://www.statlearning.com/)*\n",
    "\n",
    "Will be using [Pandas](https://pandas.pydata.org/docs/user_guide/10min.html) and [scikit-learn](http://scikit-learn.org/stable/).\n",
    "\n",
    "Instructions:\n",
    "\n",
    "\n",
    "*   Questions are marked by the sign ⏩. Provide the answer after the question, either in a code cell or in a text cell (or both).\n",
    "*   Upload the notebook on the website of the course. Direct emails will be ignored. -- Deadline : one week after the day of the lab. \n",
    "* Your notebook is an individual work. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "x78kZUVbdgkI"
   },
   "outputs": [],
   "source": [
    "# imports\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "# this allows plots to appear directly in the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Hy16HyYydgkL"
   },
   "source": [
    "## I. The Dataset\n",
    "\n",
    "Let's take a look at some data, ask some questions about that data, and then use linear regression to answer those questions!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "mmQwLdnkdgkM"
   },
   "outputs": [],
   "source": [
    "# read data into a DataFrame\n",
    "data = pd.read_csv('https://raw.githubusercontent.com/justmarkham/scikit-learn-videos/master/data/Advertising.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fPWczLu-kchG"
   },
   "source": [
    "⏩ **1) Use `data.head()` and `data.head(10)`: describe the dataset.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "SJ9ruhsbkWYc"
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  Radio  Newspaper  Sales\n",
       "1  230.1   37.8       69.2   22.1\n",
       "2   44.5   39.3       45.1   10.4\n",
       "3   17.2   45.9       69.3    9.3\n",
       "4  151.5   41.3       58.5   18.5\n",
       "5  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iD3h_-qEdgkN"
   },
   "source": [
    "What are the features?\n",
    "- TV: advertising dollars spent on TV for a single product in a given market (in thousands of dollars)\n",
    "- Radio: advertising dollars spent on Radio\n",
    "- Newspaper: advertising dollars spent on Newspaper\n",
    "\n",
    "What is the response?\n",
    "- Sales: sales of a single product in a given market (in thousands of widgets)\n",
    "\n",
    "⏩ **2) Use data.shape. How many examples are contained in the dataset?**|\n",
    "there are 200 examples in this dataset\n",
    "\n",
    "⏩ **3) Use data.describe() and provide your comments.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "_QI87W7pdgkO"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 4)\n"
     ]
    },
    {
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>147.042500</td>\n",
       "      <td>23.264000</td>\n",
       "      <td>30.554000</td>\n",
       "      <td>14.022500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>85.854236</td>\n",
       "      <td>14.846809</td>\n",
       "      <td>21.778621</td>\n",
       "      <td>5.217457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>1.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>74.375000</td>\n",
       "      <td>9.975000</td>\n",
       "      <td>12.750000</td>\n",
       "      <td>10.375000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>149.750000</td>\n",
       "      <td>22.900000</td>\n",
       "      <td>25.750000</td>\n",
       "      <td>12.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>218.825000</td>\n",
       "      <td>36.525000</td>\n",
       "      <td>45.100000</td>\n",
       "      <td>17.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>296.400000</td>\n",
       "      <td>49.600000</td>\n",
       "      <td>114.000000</td>\n",
       "      <td>27.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TV       Radio   Newspaper       Sales\n",
       "count  200.000000  200.000000  200.000000  200.000000\n",
       "mean   147.042500   23.264000   30.554000   14.022500\n",
       "std     85.854236   14.846809   21.778621    5.217457\n",
       "min      0.700000    0.000000    0.300000    1.600000\n",
       "25%     74.375000    9.975000   12.750000   10.375000\n",
       "50%    149.750000   22.900000   25.750000   12.900000\n",
       "75%    218.825000   36.525000   45.100000   17.400000\n",
       "max    296.400000   49.600000  114.000000   27.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print (data.shape) #there are 200 examples in this dataset\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1rfwzraC7K2U"
   },
   "source": [
    "⏩ **4) Use data['Name_column'].hist() to draw the histogram of the sales. Set the parameters in order to plot 20 bins (= bars of the histogram. On the histogram, locate the 25% quantile given by the describe() method of the previous question.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 25% percentile is 10.375000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "DSdLnlfJ7Pnw"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
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      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Sales'].hist(bins = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-K7YVQQTAnX-"
   },
   "source": [
    "⏩ **5) Comment the result of data.boxplot(). What is the interest of this plot?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The box plot shows that the advertising spent on the TV is on average more than the others, follows newspapers, radio, and then shows that the sales is on average less than the money spent on advertising."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "xPhTyJY__fUY"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HNPAzgdQdgkP"
   },
   "source": [
    "⏩ **5) Use data.plot(kind='scatter', x=..., y=...) to vizualize the relationship between the features and the response. Comment about the relevance of the use of a linear model.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation between TV ads and sales is positively stronger than Radio's ads. However, Newspaper's ads doesn't seem to be correlated (effective) with getting high sales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "wEW30651dgkQ"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Newspaper', ylabel='Sales'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QhnySbAIylmlnj2Nmh0CDmQceeEDNzc2qra1VZWVl7Oexxx6LPebGG2/UvHnzdM011+jss8/Wu+++q2eeeUalpaUBthxAWBTSBpF+1rcJC46ZHQLNmclkJ4VIJKK6ujrV1dV53yAABcfNRNygJErwTRSQpbt67dEt8cKKZAohIdamqchC+HskY0QCMAAELd9E3CBlGpCdSPM8x09ktlVfISXEelUTyE2F9PdIxpg6MwCA/NT066VJpw1I2sG6NcpQaAmxpk9FFtrfIxFGZgAg5DpOP+Q7yuBWbR6vuTnlYvJUpC1/D68RzABAB507QZvzEBJNP4wb2lfnDu2jtf+7L3ZbNqMMpu/15OWUi4lTkab/PfxCMAMAStwJVpQU6UDLsdjvtuUhJJp+WNe4X18c1k+rb6jNaZTB9ITYdNWQw8b0v4dfyJkBACXuBDsGMpJdeQjp6qNISplfk4zJtXkKsSaMyX8PPxHMACh4yTrBzmzqFL2sj2JqQmyh1oQx9e/hJ6aZABS8dJ1gZzbkIXg5/WBqQmyhTrmY+vfwE8EMgIKXrhPszIZO0Y/6KKYlxLr1nm1N+jbt7+EnppkAFLxkeQed2ZaHUIjTD/m854MtRzV98TpdcE+9Zi1Zr0l3P6fpi9epuVPuFMwTcTLZU8Bi0WhU5eXlam5uVllZWdDNAWCo5pZjXbYEcHM1U5BX+4U4/ZDLe56+eF3SUZ0wroQyXTb9N8EMAHTQuRPMNxDItu6JrVMctmtoOqwL7qlPev/qG2r5e/gsm/6bnBkA6KBz3kG+eQiZ1j1hf51gUXzObuTMAIBHsql7wv46wSrUlVBhQTADAB7JtO5JIRZ7Mw3F5+xGMAMAaTQ0HdbqbXuyDioyvdovpGJvuR5LP+S7+svk9xZ25MwAQBL55rFkWvekEKY4bMgJyrX4nA3vLewYmQGAJNzIY8nkar8Qpjhsygmq6dcrq32rbHpvYcXIDAAk0J7H0lnHPJZMOrtMr/YXTRvTpc5NWArcuXUsTRTm92YTghkASMDtpbrplniHeX+dMC97DvN7swnBDICchbnAW1B5LGHcXyfMOUFhfm82IZgBkLVCSHj0Y6PGQhHmYxnm92YTEoABZK1QEh4LcaNGr4T5WIb5vdmCvZkAxGQybeT3HjYmTGWFMY8lKGE+lmF+b0FgbyYAWclm2sivhEeTprIyyWMxIegKSjbvPYw5Qe3C/N5MRzADIOPNECX/Eh6zaVOQTAq6/FbI7x1mIWcGKHDZ7gvkR4E3m/YqKpT8oUQK5b2zTYH5GJkBClwu00ZeFnhraDqs37/6XtZtCoKtBdPcmBKz9b1ng5EnexDMAAUul2kjLwq8Jeo4kukeiWj1tj2B56fYVjDNzc7ZtveeC1umOkEwAxS8fOpkuJnwmKjj6KybPgqkpv96Xey2IK+UbSuY5mbnbNt7z1YhjDyFCTkzAAKvk5EsR6az8pIiRT84FndbkDkaQW0QmUsOh9t5SGHfHDOTkSeYg5EZAIHvC5Su47j+wuEaM6QibkSmXdBXyn5uEJnPNJEX00Jh3hwz7CNPYUMwAyAmqDoZ6TqOr43+dNor4aByNPwMBPOZJvKicw46CPZSoWxTEJb6SAQzADyV6cly5KfL9Pp7UZ3oMAvSseNIV6w86CtlrwPBfHM4vOycw1osLswjT2FbqUUwA8ATmZws061g6thxFMqVcjJuTBOFuXP2QphHnsK2UotgBoAnMjlZJnpMN0mnV5Vp0be+4Gt9G9O5MU0U5s7ZS2EbeQrjSi2CGQCuy+Rk6Xz8785OSHrtvWjC5y3kztjNkamwdc7IThhrBLE0G4DrMjlZ5rP0taZfL006bYB1J9x8Bb2EHuEQxpVajMwAcF0mJ0vTE3pNVMgjU3BPGPPPGJkB4LpMCqqFveialwp1ZAruCdsoX8RJd3lkuWg0qvLycjU3N6usrCzo5iAEwlKXwWvNLce6JOt2Xs2UyWMAeMfkUb5s+m+CGSBDYavL4JdMTpYmn1ARXlyYmI1gpgOCGbhl+uJ1SeeYbazLABQqLkzskE3/Tc4MkAG3N+nL5PWy3UjQS6a1B3YL+vOUqgYS7MRqJiADftVlMO2K0bT2wG4mfJ7CWDAOjMwAGXGjLkMmV6OmXTGa1h7YzYTPUz71jWAuRmYAj2V6NWraFaNp7YHdTPk8hbFgHBiZATKSz9Vcplejpl0xpmvPk399lxwaZMyUzzf1jcKJYAbIQK5Xc9kkDpt2xZiuPf++arsm3f2cpi9ep+aWYz61yhtBJ6QWApM+32ErGAemmYCM5Fr+O5vE4WSv0W7BE1t9TZRM1552L77dFLcTtk1MSEgtFCaV0GdbiPBhZAbIUC5Xc9lejSZ6jXZBJN6mak+7NkeeLE/3gwkJqYXEtBERtoUID0ZmgAzlcjWX7dVoeUmR6r52ui64p77LcwWReNv+nte8tUfTf70+5WPdWp7uF1MSUgtJoY6IUGnYe64EM21tbdqyZYuqq6tVUVHhxlMCxqrpl90JadG0MV32H0p1NepGTRu3T55tGdQJt20ViF+1g2znRUec7XfIVkxj+ienYGbevHkaNWqUZs+erba2Nk2cOFFr165VSUmJ/vCHP6i2ttblZgL2yvZqNJ9ESa9OnunaNPaUCus6J5MSUk1ER5y/VNOYNuaYmSynnJn/+q//0ujRoyVJv//979XY2Kg333xT8+bN0y233OJqA4GwyHR+Pp+lo17lgLS3KdEJo6KkSA9NH5vX8weBJbqpkU+UH7+3QCl0OQUze/fu1aBBgyRJTz31lK644gqNGDFCs2fP1pYtWzJ+njVr1ujiiy9WVVWVIpGIVq5cGXf/zJkzFYlE4n7OO++8XJqMEArzctpcEiW9PnkumjZG5w/vH3fb2OoKPXfDJGuv1P1ISLXxc0pHnD9T6uoUipymmQYOHKjXX39dlZWV+vOf/6xf/OIXkqSWlhZ179494+c5cuSIRo8erVmzZunyyy9P+JiLLrpIS5Ysif1+0kkn5dJkhEghDH/nkij5cuP+lPfnmwOSb/KmiUmQXiak2vw5JZ8of0xj+iunYGbWrFn6xje+ocrKSkUiEV144YWSpJdfflmf/exnM36eKVOmaMqUKSkfU1xcHBsFQuHq2BEueGKr9fPQmXbsmSRKJuo0E3Hr5Jlt8qYNnboXCak250vQEefPpLo6hSCnYKaurk4jR47Url27dMUVV6i4uFiS1L17d/3whz90tYHPPfecBgwYoJNPPlkTJ07Uj3/8Yw0YMCDp41tbW9Xa2hr7PRqNutoe+CvTjtqW5bRedOyJOs2Ogj552typ58r2Zd90xO7IdiUjcpfz0uyvf/3rkqQPP/wwdtuMGTPyb1EHU6ZM0RVXXKHq6mo1Njbq1ltv1QUXXKCNGzfGAqjOFi5cqNtuu83VdiA46Trqzkwf/s6nY080mpOs0+woyJOn7Z16rsIwTUNHnL+w19Uxaeo4p2Cmra1Nd9xxhx588EH97W9/01tvvaWhQ4fq1ltv1SmnnKLZs2e70rgrr7wy9u+RI0fq7LPPVnV1tf74xz9q6tSpCf/PTTfdpPnz58d+j0ajGjJkiCvtgb8y6ag7M3n4O9eOPdVoTrpO886po/TNcz6Tf+NzlG+nbtLJMhthmKYJe0fsp6Dq6nj1/TFx6jinYObHP/6xHn74Yd1111266qqrYrePGjVK//7v/+5aMNNZZWWlqqurtX379qSPKS4uTjpqA7uk6wg7smH4O9eOPdVoTt3XTk/5nOcO7Zt9Q9PI5gSZa6du4skyG2GapimUAndh4vX3x8Sp45yWZi9dulS//OUv9e1vfztu9dKZZ56pN99807XGdbZv3z7t2rVLlZWVnr0GzJGuI+zIhuHvXDr2dEtkIx/XRPGjVsrBlqOavnidLrinXrOWrM9ox+xca7mEocaJafsQoXB4+f0xddl+TiMz7777roYNG9bl9hMnTujYseQnts4OHz6st99+O/Z7Y2OjNm/erD59+qhPnz6qq6vT5ZdfrsrKSu3YsUM333yz+vXrp8suuyyXZsMy6a5ub7vkDKuGv3O5Ws9kNMev3IZcr8aybV9Y8myYpkEQvP7+mJoPllMwc8YZZ+j5559XdXV13O2/+93vNGZM5ifQDRs2aNKkSbHf23NdZsyYoQceeEBbtmzR0qVLdfDgQVVWVmrSpEl67LHHVFpamkuzYaFUHWF5SZF1nUO2HXsmozmOMtg4KU/5nCCz7dRNPVnmimka+Mnr74+p+WA5BTMLFizQP/7jP+rdd9/ViRMn9Pjjj2vbtm1aunSp/vCHP2T8PLW1tXKc5Cfip59+OpfmIUTCdnWb7fvJZDRn+uJ1ns9fu3GCzLRTN/VkmYqticoIH6+/P6bmg+WUM3PxxRfrscce01NPPaVIJKIf/ehHeuONN/T73/8+VkAPcFOm+xrZIpv3kyr3wq/5az8DDJv2TMoljwjwkh/fHxPzwSJOqqGREIhGoyovL1dzc7PKysqCbg4KWL5X74lGc1Zv26NZS9Yn/T9LZo3VpNOSF5nMRvsIUKKrMbdXMDS3HOsyHWfiaiY/jwmQKb++P16PmGfTf+dcNA9AZtxaJplomsbPERM/i6jZML2YSx4R01Hwg1/fH5PywTIOZioqKhTpNGyVzP79qTe8AwqJlzUZ/Jy/DiLAMOlk2Vk2eUS2182BnUz+/rgt42Dmvvvu87AZQDj5sczY77LzhXSCTCWbUTETi4wBYZJxMOP2vktAIfBjmbENUzJhlOmoWFjq5gAmy2k1U0cffPCBotFo3A+Aj/iZ0xK2FV82yGRVRyYBLYD85JQAfOTIEf3Lv/yLli9frn379nW5v62tLe+GAWFgak0GuCOTUTEb6+bAfySH5yenkZkbb7xRzz77rH7xi1+ouLhYDz30kG677TZVVVVp6dKlbrcRsJqJNRngrlSjYjbVzYH/qFXkjpzqzHzmM5/R0qVLVVtbq7KyMr3yyisaNmyY/uM//kPLli3TU0895UVbc0KdGZiCnJbCZUvdHPiPWkXJeV5nZv/+/aqpqZEklZWVxZZin3/++br66qtzeUqEWOfh0zAOp2bynlgFVLhI0kYiJIe7J6dgZujQodqxY4eqq6t1+umna/ny5TrnnHP0+9//XieffLLLTYStEtXWqCgp0oEOw6e2X51SPwTZCHtAG8YLFS+FbVPVIOWUMzNr1iz99a9/lSTddNNNsdyZ66+/Xv/8z//sagNhvoamw1q9bU+XfYAS1dY40GkeuL3Whq1S1Q8xVee/V7K/H5Ap8j5yQ3K4e3Iambn++utj/540aZLefPNNbdiwQaeeeqpGjx7tWuNgtlSjEvuOtCYcPu3M5uFU24aIC2GkDMGgKGBuWO3onqxGZl5++WX96U9/irtt6dKlmjhxor73ve/p5z//uVpbW11tIMyV6gSWbvi0MxtrbdhWP6QQRsrgP792bg8rVju6I6uRmbq6OtXW1mrKlCmSpC1btmj27NmaOXOmTj/9dN11112qqqpSXV2dF22FQdKNSvzTl07J6vlsHE61aYg42d+rM1NHlWAu8j7yQ3K4O7Iamdm8ebO+/OUvx35/9NFHde655+pXv/qVrr/+et1///1avny5642EedKdwNocJayt0ZkbtTaCyvkwuX5I52NSCCNlHZEH5B+bgnqTUcE7P1mNzBw4cEADBw6M/V5fX6+LLroo9vvYsWO1a9cu91oHY2VyAku0AWJn+QynmrCSyO9NHtNJdkx+MHl4Vs9jawdkwmei0JD3ARNkNTIzcOBANTY2SpKOHj2qV155RePGjYvdf+jQIRUVccIIkl9XpJmMSrQPn46trujyQesmaWx1hZbOPifWyWTbdhNWErW/x9U31GrJrLFafUNt3HvyW7Jjcs8z230bKQuSCZ+JQkTeB4KW1cjMRRddpB/+8If6yU9+opUrV6qkpERf+tKXYve/+uqrOvXUU11vZKHLpHZDEFekmYxKNDQd1vqdB7r83xOS1u88oMa9R1RRUpR1201bSWRC/ZB0x+TJOV+UpJSrmWzugEz7TBQS8j4QtKyCmdtvv11Tp07VxIkT1bt3bz388MM66aSTYvf/+te/1uTJk11vZKHKJkAJYmlkJiewTJIDFzyxI2XbEwVzJB12le6Y7Gs5mvDvFZYOiM+EP1JdXJkQ1KMwZRXM9O/fX88//7yam5vVu3dvde/ePe7+3/3ud+rdu7erDSxkmQYoQV+RpjqBpcut6R6JpGz7FQ+sjRvZaQ/mSDrsKtNj0vnvFZYOiM+Et8hHgslyqgBcXl7eJZCRpD59+sSN1CB32dRuyLbeiZ8rPdLl1nR+f51t7DRF1R7MmbySKCiFfkwK/f17Ld98JFaYwUs5BTPwXjYBSqZXpEGVHE+VHJiu7Sc6/d4xmDMl6dCkk7QpxyQohf7+vZJPYTy2OoAfctrOAN7LZsg806WRQZUcT5VbU15SlLDt3SLSiRSDNu35D0EmHZo47F7oiZiF/v69kk8+ElsdwA+MzBgq2yHz2y8dqbKe8bFpWc8e+vGlIyWZUXI8WVGoRFfTZ1VXpHyujsFcUMWmTF4GXOgFuAr9/bst13wkE847KAwEMwbLZsj8X1e+pugHx+Nui35wXLesfE1S+iurlxr25dna3CWq1fK77403Ov+BkzQKSa75SLbtXwZ7Mc1ksEyHzDNZzZTuyuqmx7foT1t2BzpF0nlVjWnVdTtiGTAKTS7fR1aYwS8EMxZItHS2Y62HTDrWSacN0ITh/VNuLWDaPLbJ+Q+cpAtHJkUrC0Eu30e2OoBfCGYskyjp9OwM80t+MHlEymDG1EqpYamDAruYmOBtgmy/jyaPsCI8CGYsc92yzXqhU0Cy6Z2DqigpUvSD4ymvfva3HM3oNZgiSS+THCSvjiEjBf5gFY47TB5hRXgQzBgkXSe1+Z0DSXNjDrQc09hTKrR+xydF5jpf/aSbGmnHFEl6QeQgMVLgjUTfu6CrarvJlOCXEVZ4iWDGAJl2Uv/6xGspn+eaScN0St9e2rHviLpHImpzHO1vORp7jmTz1+2yncdOdpI05eTppXTHUnL/Kp6RAnel+t6FIcGb4BeFhGDGAJl0Ug1Nh/Xau9GUz3NK316qKCnSgid2JD2BJZq/bpfpPHayk+Ttl47Uv658rWBOnqmOpeTuVXyYRgpMkep7V/e101P+XxtGLwl+UUgIZgKWaSeV7kqxd3F31fTrpemL16U8gXWev+7RLaLjJ5ysRlGSnSQv+fkLXWrdpNv92mbtx/LRde/oh49vSfo4N67iwzBSYJJ037vIx/VTbF2FQ/CLjsJ27k2EYCZg6Tqp199tVk2/XmlzNA63tmnNW00Zn8Bynb9OdZI8kGCvlXS7X9s6YtPx5HBOTZ+Uj3XjKp6l4O7KJDi0eRUOwS+kwppqJJgJWLpO6jdrd+gro6s0tH9vDe3XSw0pKstu2nUg6X2SPyMEySTb/dq24e5kJ4fxp/bVyw37u+wvdf4wd6oVU6/DXZkEhzavwiH4hVRYU41sZxCwof17a+wpyevErN95QH/ddUDTF69LGchI0pghme9nlKtMV0R1lmr3a5skOzk4jnTu0PgRmhOOdKzthGu7A7MjtHuyKc9v4z5PuW4/gPAotC1XCGYMMGP8KSnvv2XFa11qy3Q2trpCE0b09/wEluokWVFS1OX2bvG/dmHT3iypTg5/adinY20nunyh1jXud23jyUR7WLXnQXmhoemwVm/bozVv7dHqbXtCd/ILe3AY9veH1AptXyymmQxwemVZyvtfey/1KiZJmvlxQJRqnt+tJLBkr/HjS0fqlk6rmc6qjq9905lNw93pTg6J3qcXCZde1+tINJXWLkzz7TZPI2Ui7O8PqRXaVCPBjAFS5UN8rqo07ZJsSTr90+WSEp/AKkqKugQf+XRKqU6SiW5vX2Fle65HrlNskl0Jl4mm0tqFcb497MXcwv7+kFih5dkxzWSIZEPCP750ZMr/1y2ihFNIHef5UyWB5SNZLkHn28My3J1qii3T/bFMl2wqrV1Y59uBMArLuTcTjMwYItVoR6pKs+cP65/yg5lpvQk36xB0fq4wDXenmsabu2yT9VdBma5Ws2mkCShUYTr3pkMwY5hEQ8KJOtCRVWW647JROnPIySmfL13ntPXdZi14YqsrU1DpahqEYbg71cnBq7okfha8Yv8uhF0hFJDrLAzn3nQijpNkPDkkotGoysvL1dzcrLKy1Im2psslum5oOqwL7qlPev/Y6gq98s7BhKMJ2eZFpMqNCVOORTpuXQUFVfAq0d+xXSH+PWGWXIORTL5PhRjomCyb/ptgpgAkCzK+UH1yypVGq2+odS1oyua58JGggsPmlmNJ95wK02om2CXf4D7V9+n+aZ8vmEq5Nsmm/2aaqQAkm/74xtjBKYOZbPIi3C6fXuhXSEHurePG/l2A2/KpZpvu+3TV0g16ZefBnJ4bZiCYMZSbnXmyPI+GpsMp/182eRFu1TRIdPU19pQKzRh/is6oKs/5WNgWHJmwt04hzLPDDvkG96bUiIJ3CGYM42WeROfOyc06BG49V6Krr/U7DsRONtkeC9M3WksWZBVawSsglXyD+0KpEVXIqDNjmKt/+0qXK5A125v0vd9u9OT13KxDkO9zpatxImVfH8erGjv5OthyVNMXr9MF99Rr1pL1mnT3c5q+eF1sHyf21gE+kW9wXwg1ogodIzMGaWg6rL807Et4318a9nky3Nk+BbXmrSZt2nVAX/hMhb40vH9ez5Xrap5MapxkM/QbZN5JOpnM/3u11BuwTaYjv6mmk8NeI6rQEcwErP3L1z0S0bNv7kn52Jca9rn+xfJiGibXXItshoIzGfo1Ie8kkUyDrEIqeAWkkyoYyeQ8FkSNKPiHYCYgqTbzSybNBtQ5yWeFgNuSXX0lksnQr6l5J9kGWSTiAqmDkfZl1x0lO48l+j5x4WA/cmZ80tB0WKu37YntaZNqM79kzh3a1/U2JcpRCXL/nUR5Nx1lkzNiat6JqUFWWHX+7mV7P8zSee83N89jyfabg/kYmfFYsqXGqeq7JDL+1L6uf8FMnIbpeIX0+rvN+s3aHVq/85Njle3Qr4nDx4W2m21Q0k09mL7SDZkx8TwG/wU6MrNmzRpdfPHFqqqqUiQS0cqVK+PudxxHdXV1qqqqUs+ePVVbW6utW7cG09gcJRqB2bgzu0BmwvD+euDbZ7nZLElmjxDU9Oulr4yu0u+uHq/VN9RqyayxWn1DrZbOPierjqY9OMrnObxQSLvZBiXdSjZTV7ohOyafx+CfQEdmjhw5otGjR2vWrFm6/PLLu9x/11136d5779VvfvMbjRgxQrfffrsuvPBCbdu2TaWlpQG0ODvJEj1PZLiBxMKpo3TeUPdHZNrZMkKQLmckk4J4puWdMEfvrXRJ1mve2mPsSjdkx5bzGLwVaDAzZcoUTZkyJeF9juPovvvu0y233KKpU6dKkh5++GENHDhQjzzyiL773e/62dScpBv+7CbpRILb27+E0875jCft6sjEaZhMhWGawLQgKyzSffc27TqY8n6mJuxi83kM7jA2Z6axsVG7d+/W5MmTY7cVFxdr4sSJWrt2bdJgprW1Va2trbHfo9Go521NJt3w51nVFXH5IO38/BLaPEJg0kosmCXdd2/MkJNT3s/UhF1sPo/BHcYGM7t375YkDRw4MO72gQMHaufOnUn/38KFC3Xbbbd52rZMpRv+9Hszv1TTMW6NEPi1B1I2BfE6tslxnC7ts23fJqSX7rs3YcQApiZCiJHOwmVsMNMu0mlZreM4XW7r6KabbtL8+fNjv0ejUQ0ZMsSz9qWTaPjzc1WluuH/jZDkz5fPj+kYv6d8MlnBUFFSlLKWz/hT+8pxFFd12bZpKiSX6Lv3heqTY6OeTE0A4WFsnZlBgwZJ+mSEpt2ePXu6jNZ0VFxcrLKysrifILUPfz4xZ7yGD+gtSXrt3ai+9rMX4/bi8ZIfqzb8XhmSyQqGdLV81v7vvi7bR7CaxQ6Z1IYpLynS/dM+r7Ed9t5Zv+OA5i7bpOaWY8audEN2qBMEyeCRmZqaGg0aNEirVq3SmDEfXSkdPXpU9fX1+slPfhJw67JzsOWoZi5ZrwOdApcXtjd5nt/hx/5EQeyBlG4awfn4tbPFahazZTsCeN2yzXrlnYNxt3XOq2Jqwk5hWAAA9wQ6MnP48GFt3rxZmzdvlvRR0u/mzZv1zjvvKBKJaN68ebrjjju0YsUKvfbaa5o5c6ZKSkr0rW99K8hmZ6Tj1cJVSzd0CWSkj1YyeV1pN5PpGBteI5FUtVoy2bQyFa/ajPxkMwJoYoVruIc6Qego0JGZDRs2aNKkSbHf23NdZsyYod/85je68cYb9cEHH+iaa67RgQMHdO655+qZZ54xusZMLnsuebkM1I+CUm69RraJuKlWMGSzaWU+bYZ/sh0BpDJseAUxGmwiFi98ItBgpra2Vk6KDQUjkYjq6upUV1fnX6PylMueS152nH4UlMr3NfIdLk40TZDNppUdsZrFXNkGJ1SG9U7QnWihB6pMsXVlbAKwjZINa6cytrrC8y+dH6Xz83kNr4aL021aOf7UvhrXafNOVrOYK9vgxNSNRm12sOWopi9epwvuqdesJes16e7nfFvI0FGhB6pMsXVlbAKwjbLN06goKdJDM8Z61JpP+FFQKtfX8HK4OFGbJHVpH4W27JDLCCDLr91lSqHKQt7CgCm2xAhmXJRNnsbYUyr00PSxvg4J+rFqI9vX8GO4uHObvCoYCO9lG5xQGdY9pnWihRqoFvoUWzIEMy5Kd7Vw2yVncELtpNCHi5GdXIMTAtb8mdaJFmqgyjkzMXJmXJYqd6SmXy9NOm1AQXzhMkVeA3LBd8l/pnaihfZZ4JyZWMRJtZwoBKLRqMrLy9Xc3Ox6NeBUGf2FdrWQj+aWY12Giws9Mx9wmxsrkKYvXpdyrzn4o1DOmdn03wQzOUi0LG7kp8t0x2WjdObgk115Db8FvdRSIgAEvODmMt5C6US94vZ5NuznTIKZDrwIZhJdnbSz7Yud6EQXRHIyAG94MZoS9k7UbdSFyU02/Tc5M1lKV0umfb8lW3y01DJ+hcL6HQdUe/dq32tHAHCXV1s6FFqeSr6oC+M9gpkspcvo92O/Jbd8cqLret+BlmP6p4fX+98owEWFvqNyUPum4RPsEeYPlmZnKdNaMjas9U93olu/84D1BZhMyAWC/xjW/4ipK5AKiWlL2sOKkZkstS+L6xZJ/TgbThKZBGa2XrmZUnYdwWBY/yMs4w0eAaU/CGZysGjaGJ0/rH/C+2w6SQzt31tjT6lI+Rhbv2h0ZoWLYf14fuzNhuQIKP3BNFMO2itPvrrroG5esUWvvReN3WfbSeKh6WNVe/dqHeg0YtFN0vmWftFMK7sOfzGsH69QK+WapFC3XvATwUwezhxysv5w3ZfyPkkEmddRXlKk526YpH96eL3W7zwQu/38j/MLbERnVtgY1k+MLR2CQ0DpPYIZF+R6kjAlSbG8pEi/u3p8aL5odGaFrZB3VLZd2BP2CSi9QzAToFR5HUGUBg/LF43ODAzr28WUCzvYiwrAAWloOqwL7qlPev/qG2rpdPNA2XVIVKq1BXs+IZFs+m9GZgJCXoe3mKOGFJ7RxjAjYR9uIJgJCHkd/qAzA8zGhR3cQJ2ZgFB7AAC4sIM7CGYC5EYxq0Lfewbu4zMFP3FhBzeQAGyAXPI6yP6H2/hMISgk7CORbPpvghlLkf0Pt/GZQtBI2EdHrGYKObL/4TY+UzABCfvIFTkzPnMjHyGT7H8gG3ym4CfysuA2RmZ84mY+Atn/iYW9FLqX+EzBD+Rl2cv08yvBjE/c3LqAcv3xOEHmj88U/GDaFi5Iz5bzK9NMPmjPR2jrlGvdMR8hW24s6w6LVCdIZI5SAfCSF+dBeM+W8ysjMz7wosIl5fo/QuKqe/L5TNly9YbgUOnXPjadXxmZ8YGX+Qg1/Xpp0mkDjPlA+Y3EVffl8pmy5eoNwSEvyz42nV8JZnzwSYXLrvdVlBSpT8lJ/jcqJDhBBo/pA2SCSr/2sen8SjDjk0XTxqisZ9fh9vbKl8hNLidI8jrcZdPVG4JFrp9dbApAyZnxyb4jrTrQcqzL7Sck4+YebbNo2pgupdATnSDJ6/CGTVdvCBa5fvbJ9PwaNIIZn5D85p1MT5AmLgs1vXZDJljWjWy5Vek3DN8f09kSgBLM+ISrV++lOkGalpUftlEiW67eEA5h+/7YwPStJghmfMLVa7BMGxkzcZQoH7ZcvSEcwvb9Qf5IAPYRyW/BMWlkLMyrfwq9VAC8F+bvD3LHyIyPuHoNjkkjY6aNEgE24fuDRBiZCQBXr8EwZWTMpFEiwDZ8f5AIIzMoGKaMjJk0SgTYhu8PEmFkBgXHhJExU0aJABvx/UFnEcfplEUVMtFoVOXl5WpublZZWVnQzQHiBD1KBNiM70+4ZdN/M80UMhSRsovptRsAk/H9QTuCmZCgiBQAoFCRMxMSqYpIAQAQZgQzIUARKcBd7KwO2IVpphCgiJSdyG8yD9O1gJ0IZkKAIlJ2ocM0V6Z7/hCIAmYhmAkBikjZhU3yzJTJzuoVJUUEooCByJkJCYpI2YH8JnNlMl1Loj1gJkZmXBL0sLMppfqRGvlN5ko3Xds9orQjN5n+7YI+XwBhQzCTJ9PyHygiZTbym8yVbrq2LU2t9EwCUdPOF0BYMM2UJ4adkY32DrN7JBJ3e/dIRBOG9ycQDViq6Vo3AlHOF4A3GJnJQyYJg3RO6GzRtDGau2xT3GeH/CYzpJquLS8pyivRnvMF4B2jg5m6ujrddtttcbcNHDhQu3fvDqhF8ch/QC7IbzJfsunafAJRzheAd4wOZiTpjDPO0P/8z//Efu/evXuArYlH/gPyQX6TffIJRDlfAN4xPpjp0aOHBg0aFHQzEqK+C1CYcglEOV8A3jE+AXj79u2qqqpSTU2NvvnNb6qhoSHl41tbWxWNRuN+vORWfRf2ggHCj3pQgDcijuOkWXAYnD/96U9qaWnRiBEj9Le//U2333673nzzTW3dulV9+/ZN+H8S5dlIUnNzs8rKyjxra675DyzVBAoP+VJAetFoVOXl5Rn130YHM50dOXJEp556qm688UbNnz8/4WNaW1vV2toa+z0ajWrIkCGeBzO5mr54XdJhZ0rbAwAKVTbBjPE5Mx316tVLo0aN0vbt25M+pri4WMXFxT62Kncs1QQAIH/G58x01NraqjfeeEOVlZVBN8UVmSzVBAAAqRkdzNxwww2qr69XY2OjXn75ZX39619XNBrVjBkzgm6aK1iqCQBA/owOZv7v//5P06ZN02mnnaapU6fqpJNO0ksvvaTq6uqgm+YKStsDAJA/qxKAc5FNAlEQmluOdakoymomAEChC20CcBhR2h4AgPwQzBiC0vYAAOTG6JwZAACAdAhmAACA1QhmAACA1QhmAACA1QhmAACA1QhmAACA1QhmAACA1QhmAACA1QhmAACA1QhmAACA1QhmAACA1dibCaHW0HRYO/e3sIEnAIQYwQxC6WDLUV23bLPWbG+K3TZheH8tmjZG5SVFAbYMAOA2ppkQStct26wX394bd9uLb+/V3GWbAmoRAMArBDMInYamw1qzvUltjhN3e5vjaM32JjXuPRJQywAAXiCYQejs3N+S8v4d+whmACBMCGYQOtV9SlLef0pfEoEBIEwIZhA6Q/v31oTh/dU9Eom7vXskognD+7OqCQBChmAGobRo2hh9cVi/uNu+OKyfFk0bE1CLAABeYWk2Qqm8pEhLZ5+jxr1HtGPfEerMAECIEcwg1Gr6EcQAQNgxzQQAAKxGMAMAAKxGMAMAAKxGMAMAAKxGMAMAAKxGMAMAAKxGMAMAAKxGMAMAAKxGMAMAAKxGMAMAAKxGMAMAAKzG3kwAgNBpaDqsnftb2GS2QBDMAABC42DLUV23bLPWbG+K3TZheH8tmjZG5SVFAbYMXmKaCQAQGtct26wX394bd9uLb+/V3GWbAmoR/EAwAwAIhYamw1qzvUltjhN3e5vjaM32JjXuPRJQy+A1ghkAQCjs3N+S8v4d+whmwopgBgAQCtV9SlLef0pfEoHDimAGABAKQ/v31oTh/dU9Eom7vXskognD+7OqKcQIZgAAobFo2hh9cVi/uNu+OKyfFk0bE1CL4AeWZgMAQqO8pEhLZ5+jxr1HtGPfEerMFAiCGQBA6NT0I4gpJEwzAQAAqxHMAAAAqxHMAAAAqxHMAAAAqxHMAAAAqxHMAAAAqxHMAAAAqxHMAAAAqxHMAAAAqxHMAAAAq4V+OwPHcSRJ0Wg04JYAAIBMtffb7f14KqEPZg4dOiRJGjJkSMAtAQAA2Tp06JDKy8tTPibiZBLyWOzEiRN67733VFpaqkgk4upzR6NRDRkyRLt27VJZWZmrz41PcJz9w7H2D8faPxxr/7h5rB3H0aFDh1RVVaVu3VJnxYR+ZKZbt24aPHiwp69RVlbGF8QHHGf/cKz9w7H2D8faP24d63QjMu1IAAYAAFYjmAEAAFYjmMlDcXGxFixYoOLi4qCbEmocZ/9wrP3DsfYPx9o/QR3r0CcAAwCAcGNkBgAAWI1gBgAAWI1gBgAAWI1gBgAAWI1gJke/+MUvVFNTo0996lM666yz9PzzzwfdJOutWbNGF198saqqqhSJRLRy5cq4+x3HUV1dnaqqqtSzZ0/V1tZq69atwTTWcgsXLtTYsWNVWlqqAQMG6NJLL9W2bdviHsPxzt8DDzygM888M1ZAbNy4cfrTn/4Uu59j7J2FCxcqEolo3rx5sds43u6oq6tTJBKJ+xk0aFDs/iCOM8FMDh577DHNmzdPt9xyizZt2qQvfelLmjJlit55552gm2a1I0eOaPTo0frZz36W8P677rpL9957r372s59p/fr1GjRokC688MLY/lvIXH19vebMmaOXXnpJq1at0vHjxzV58mQdOXIk9hiOd/4GDx6sO++8Uxs2bNCGDRt0wQUX6JJLLomd2DnG3li/fr1++ctf6swzz4y7nePtnjPOOEPvv/9+7GfLli2x+wI5zg6yds455zjf+9734m777Gc/6/zwhz8MqEXhI8lZsWJF7PcTJ044gwYNcu68887YbR9++KFTXl7uPPjggwG0MFz27NnjSHLq6+sdx+F4e6miosJ56KGHOMYeOXTokDN8+HBn1apVzsSJE53vf//7juPwmXbTggULnNGjRye8L6jjzMhMlo4ePaqNGzdq8uTJcbdPnjxZa9euDahV4dfY2Kjdu3fHHffi4mJNnDiR4+6C5uZmSVKfPn0kcby90NbWpkcffVRHjhzRuHHjOMYemTNnjr7yla/o7/7u7+Ju53i7a/v27aqqqlJNTY2++c1vqqGhQVJwxzn0G026be/evWpra9PAgQPjbh84cKB2794dUKvCr/3YJjruO3fuDKJJoeE4jubPn6/zzz9fI0eOlMTxdtOWLVs0btw4ffjhh+rdu7dWrFih008/PXZi5xi759FHH9Urr7yi9evXd7mPz7R7zj33XC1dulQjRozQ3/72N91+++0aP368tm7dGthxJpjJUSQSifvdcZwut8F9HHf3XXvttXr11Vf1wgsvdLmP452/0047TZs3b9bBgwf13//935oxY4bq6+tj93OM3bFr1y59//vf1zPPPKNPfepTSR/H8c7flClTYv8eNWqUxo0bp1NPPVUPP/ywzjvvPEn+H2emmbLUr18/de/evcsozJ49e7pEonBPe6Y8x91dc+fO1ZNPPqnVq1dr8ODBsds53u456aSTNGzYMJ199tlauHChRo8erZ/+9KccY5dt3LhRe/bs0VlnnaUePXqoR48eqq+v1/33368ePXrEjinH2329evXSqFGjtH379sA+1wQzWTrppJN01llnadWqVXG3r1q1SuPHjw+oVeFXU1OjQYMGxR33o0ePqr6+nuOeA8dxdO211+rxxx/Xs88+q5qamrj7Od7ecRxHra2tHGOXffnLX9aWLVu0efPm2M/ZZ5+tb3/729q8ebOGDh3K8fZIa2ur3njjDVVWVgb3ufYstTjEHn30UaeoqMhZvHix8/rrrzvz5s1zevXq5ezYsSPoplnt0KFDzqZNm5xNmzY5kpx7773X2bRpk7Nz507HcRznzjvvdMrLy53HH3/c2bJlizNt2jSnsrLSiUajAbfcPldffbVTXl7uPPfcc877778f+2lpaYk9huOdv5tuuslZs2aN09jY6Lz66qvOzTff7HTr1s155plnHMfhGHut42omx+F4u+UHP/iB89xzzzkNDQ3OSy+95Hz1q191SktLY31gEMeZYCZHP//5z53q6mrnpJNOcr7whS/ElrQid6tXr3YkdfmZMWOG4zgfLflbsGCBM2jQIKe4uNiZMGGCs2XLlmAbbalEx1mSs2TJkthjON75+853vhM7T/Tv39/58pe/HAtkHIdj7LXOwQzH2x1XXnmlU1lZ6RQVFTlVVVXO1KlTna1bt8buD+I4RxzHcbwb9wEAAPAWOTMAAMBqBDMAAMBqBDMAAMBqBDMAAMBqBDMAAMBqBDMAAMBqBDMAAMBqBDMAAMBqBDMAQmXmzJm69NJLY7/X1tZq3rx5gbUHgPcIZgAEYubMmYpEIopEIurRo4c+85nP6Oqrr9aBAwdcfZ3HH39c//Zv/+bqcwIwS4+gGwCgcF100UVasmSJjh8/rtdff13f+c53dPDgQS1btsy11+jTp49rzwXATIzMAAhMcXGxBg0apMGDB2vy5Mm68sor9cwzz0iS2traNHv2bNXU1Khnz5467bTT9NOf/jTu/7e1tWn+/Pk6+eST1bdvX914443qvN1c52mmAwcOaPr06aqoqFBJSYmmTJmi7du3e/5eAXiHYAaAERoaGvTnP/9ZRUVFkqQTJ05o8ODBWr58uV5//XX96Ec/0s0336zly5fH/s8999yjX//611q8eLFeeOEF7d+/XytWrEj5OjNnztSGDRv05JNP6i9/+Yscx9Hf//3f69ixY56+PwDeYZoJQGD+8Ic/qHfv3mpra9OHH34oSbr33nslSUVFRbrttttij62pqdHatWu1fPlyfeMb35Ak3Xfffbrpppt0+eWXS5IefPBBPf3000lfb/v27XryySf14osvavz48ZKk//zP/9SQIUO0cuVKXXHFFZ68TwDeIpgBEJhJkybpgQceUEtLix566CG99dZbmjt3buz+Bx98UA899JB27typDz74QEePHtXnP/95SVJzc7Pef/99jRs3Lvb4Hj166Oyzz+4y1dTujTfeUI8ePXTuuefGbuvbt69OO+00vfHGG968SQCeY5oJQGB69eqlYcOG6cwzz9T999+v1tbW2GjM8uXLdf311+s73/mOnnnmGW3evFmzZs3S0aNHc369ZEGO4ziKRCI5Py+AYBHMADDGggULdPfdd+u9997T888/r/Hjx+uaa67RmDFjNGzYMP3v//5v7LHl5eWqrKzUSy+9FLvt+PHj2rhxY9LnP/3003X8+HG9/PLLsdv27dunt956S5/73Oe8eVMAPEcwA8AYtbW1OuOMM3THHXdo2LBh2rBhg55++mm99dZbuvXWW7V+/fq4x3//+9/XnXfeqRUrVujNN9/UNddco4MHDyZ9/uHDh+uSSy7RVVddpRdeeEF//etf9Q//8A/69Kc/rUsuucTjdwfAKwQzAIwyf/58/epXv9Kll16qqVOn6sorr9S5556rffv26Zprrol77A9+8ANNnz5dM2fO1Lhx41RaWqrLLrss5fMvWbJEZ511lr761a9q3LhxchxHTz31VGwVFQD7RJxkk8gAAAAWYGQGAABYjWAGAABYjWAGAABYjWAGAABYjWAGAABYjWAGAABYjWAGAABYjWAGAABYjWAGAABYjWAGAABYjWAGAABY7f8DuJoYtpFJ0Y8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(kind= 'scatter',x= 'TV', y = 'Sales')\n",
    "data.plot(kind= 'scatter',x= 'Radio', y = 'Sales')\n",
    "data.plot(kind= 'scatter',x= 'Newspaper', y = 'Sales')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7AZLI-EE-QsD"
   },
   "source": [
    "⏩ **6) Use data.corr() in order to plot the correlation coefficients.**\n",
    "\n",
    "**Comment about the coefficient on the diagonal.**\n",
    "\n",
    "**What feature is the most correlated to the sales?**\n",
    "\n",
    "**Plot the correlation matrix as a heatmap using sns.heatmap(...,annot=True)** "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation coefficient on the diagonals in one because the correlation of a variable with itself is just (1). \n",
    "As stated before, 'Tv' is the most correlated feature to sales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "Qk7P9Hq0-XPk"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.corr()\n",
    "sns.heatmap(data.corr(),annot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D77kYDB2dgkR"
   },
   "source": [
    "### Questions About the Advertising Data\n",
    "\n",
    "Let's pretend you work for the company that manufactures and markets this widget. The company might ask you the following: On the basis of this data, how should we spend our advertising money in the future?\n",
    "\n",
    "This general question might lead you to more specific questions:\n",
    "1. Is there a relationship between ads and sales?\n",
    "2. How strong is that relationship?\n",
    "3. Which ad types contribute to sales?\n",
    "4. What is the effect of each ad type of sales?\n",
    "5. Given ad spending in a particular market, can sales be predicted?\n",
    "\n",
    "We will explore these questions below!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6gO3207-dgkT"
   },
   "source": [
    "## II. Simple Linear Regression\n",
    "\n",
    "Simple linear regression is an approach for predicting a **quantitative response** using a **single feature** (or \"predictor\" or \"input variable\"). It takes the following form:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1x$\n",
    "\n",
    "What does each term represent?\n",
    "- $y$ is the response\n",
    "- $x$ is the feature\n",
    "- $\\beta_0$ is the intercept\n",
    "- $\\beta_1$ is the coefficient for x\n",
    "\n",
    "Together, $\\beta_0$ and $\\beta_1$ are called the **model coefficients**. To create your model, you must \"learn\" the values of these coefficients. And once we've learned these coefficients, we can use the model to predict Sales!\n",
    "\n",
    "Generally speaking, coefficients are estimated using the **least squares criterion**, which means we are find the line (mathematically) which minimizes the **sum of squared residuals** (or \"sum of squared errors\"):\n",
    "![image.png](data:image/png;base64,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)\n",
    "\n",
    "What elements are present in the diagram?\n",
    "- The black dots are the **observed values** of x and y.\n",
    "- The blue line is our **least squares line**.\n",
    "- The red lines are the **residuals**, which are the distances between the observed values and the least squares line.\n",
    "\n",
    "How do the model coefficients relate to the least squares line?\n",
    "- $\\beta_0$ is the **intercept** (the value of $y$ when $x$=0)\n",
    "- $\\beta_1$ is the **slope** (the change in $y$ divided by change in $x$)\n",
    "\n",
    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)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XaJYiEY_Kg9_"
   },
   "source": [
    "⏩ **7) We are going to do linear regression of the sales with respect to ONE variable amongst 'TV', 'Radio', 'Newspaper'. According to what you have seen from the dataset, which column would you like to keep? Write it down under the form:**\n",
    "\n",
    "`columns = ['Name of the column you want to keep']`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "0K_sYC3bKfGk"
   },
   "outputs": [],
   "source": [
    "columns = ['TV']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mvM49l2LMj2e"
   },
   "source": [
    "⏩ **8) Run the code below and try to understand it. What are the value of $\\beta_0$ and $\\beta_1$ of you model?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "TcIkF0aYHEHG"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7.0325935491276885, 0.04753664043301979)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "ls = LinearRegression()\n",
    "ls.fit(data[columns],data['Sales'])\n",
    "ls.intercept_,ls.coef_[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "y8qNPvcFTpCp"
   },
   "source": [
    "How do we interpret the TV coefficient ($\\beta_1$)?\n",
    "- A \"unit\" increase in TV ad spending is associated with a 0.047537 \"unit\" increase in Sales.\n",
    "- Or more clearly: An additional $1,000 spent on TV ads is associated with an increase in sales of 47.537 widgets.\n",
    "\n",
    "Note that if an increase in TV ad spending was associated with a decrease in sales, $\\beta_1$ would be negative.\n",
    "\n",
    "⏩ **9) Let's say that there was a new market where the spend in the advertising channel you considered was $50,000. What would we predict for the Sales in that market? Make the prediction \"by hand\" using sums and multiplication of numbers.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "CnElUKDpdgkY"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2383.8646152001174\n"
     ]
    }
   ],
   "source": [
    "# manually calculate the prediction\n",
    "x = 50_000\n",
    "b0 = 7.0325935491276885\n",
    "b1 = 0.04753664043301979\n",
    "y = b0+ b1*x\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gC4_CyBKdgkZ"
   },
   "source": [
    "⏩ **10) Use sklearn's predict method to recover the above result:**\n",
    "\n",
    "\n",
    "\n",
    "```\n",
    "New_data = pd.DataFrame({'Name of your column' : [the value]})\n",
    "ls.predict(New_data)[0]\n",
    "```\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "ECQ0jcgbtepR"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2383.8646152001174"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "the_value = 50_000\n",
    "New_data = pd.DataFrame({'TV' : [the_value]})\n",
    "ls.predict(New_data)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eW_mRs7Rdgka"
   },
   "source": [
    "⏩ **11) Using `ls.predict`, generate the predictions $\\hat y_i$ for the whole dataset. On the same graph, plot the scattered points $(x_i,y_i)$ and the line passing through the points $(x_i,\\hat y_i)$.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "5LvJx2c0tdp2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x174f6b7d0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = pd.DataFrame(data['TV'])\n",
    "plt.plot(dt,ls.predict(dt))\n",
    "plt.scatter(dt,data['Sales'],color = 'red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "R_qgyPcTnYQv"
   },
   "source": [
    "⏩ **12) Write your comments. How happy are you with the model?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BySGZuuXEQBq"
   },
   "source": [
    "The model has the same slope as the data and seems to be predicting the data well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TPTlSGExDLsI"
   },
   "source": [
    "## III. Multiple Linear Regression\n",
    "\n",
    "Simple linear regression can easily be extended to include multiple features. This is called **multiple linear regression**:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1x_1 + ... + \\beta_nx_n$\n",
    "\n",
    "Each $x$ represents a different feature, and each feature has its own coefficient. In this case:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1 \\times TV + \\beta_2 \\times Radio + \\beta_3 \\times Newspaper$\n",
    "\n",
    "⏩ **13) Include all the three columns in the model and re-train a least-square estimator using scikit-learn. Provide the values of the coefficients $\\beta_i$.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "cBkYmHAStYT_"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.9388893694593996, array([ 0.04576465,  0.18853002, -0.00103749]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns2 = ['TV','Radio','Newspaper']\n",
    "ls2 = LinearRegression()\n",
    "ls2.fit(data[columns2],data['Sales'])\n",
    "ls2.intercept_,ls2.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VaIVKUt9DMD1"
   },
   "source": [
    "⏩ **14) For a given amount of Radio and Newspaper ad spending, how much is the increase of sells resulting from a $1000 increase in TV ad spending?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iaqUCyuVDMXi"
   },
   "source": [
    "0.04576465*1000 = 45.7646"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pGHUb7egdgkc"
   },
   "source": [
    "### Linear Gaussian model and confidence intervals\n",
    "\n",
    "Our aim is now to compute confidence intervals on each of the coefficients $\\beta_i$ at the level 95%. A way to think of a confidence interval is the following: If the population from which this sample was drawn was **sampled 100 times**, approximately **95 of those confidence intervals** would contain the \"true\" coefficient. Keep in mind that we only have a **single sample of data**, and not the **entire population of data**. The \"true\" coefficient is either within this interval or it isn't, but there's no way to actually know. We estimate the coefficient with the data we do have, and we show uncertainty about that estimate by giving a range that the coefficient is **probably** within.\n",
    "\n",
    "Note that using 95% confidence intervals is just a convention. You can create 90% confidence intervals (which will be more narrow), 99% confidence intervals (which will be wider), or whatever intervals you like.\n",
    "\n",
    "To that end, we make the assumption that the model is homoscedastic, which means linear, Gaussian, and with a constant variance $\\sigma^2$:\n",
    "$$\n",
    "Y \\sim {\\mathcal N}(\\Phi \\beta,\\sigma^2 I_N)\n",
    "$$\n",
    "where $N$ is the number of sambles, $d=3$ is the number of regressors, $\\Phi$ is the $N\\times (d+1)$ design matrix containing the values of the regressors (TV, Radio, Newspaper), $\\beta=(\\beta_0,\\dots,\\beta_d)^T$ and $\\sigma^2$ are the unknown parameters, and $I_N$ is the $N\\times N$ identity matrix.\n",
    "\n",
    "A 95% confidence interval on $\\beta_k$ is given by:\n",
    "$$\n",
    "\\hat\\beta_k \\pm q \\sqrt{\\frac {\\hat\\sigma^2 s_k}N}\n",
    "$$\n",
    "where $s_k$ is the $k$th coefficient of the diagonal of $(\\Phi^T\\Phi)^{-1}$, $\\hat \\sigma^2$ is the estimated variance of the residuals, given by:\n",
    "$$\n",
    "\\hat \\sigma^2 = \\frac{\\|Y-\\hat Y\\|^2}{N-d-1}\n",
    "$$\n",
    "\n",
    "⏩ **15) What is $q$ in the above formula?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "U-p6L2NLrVVQ"
   },
   "source": [
    "q is the number we get from the table (z-score) for this confidence interval, if 95% it will be 1.96."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AeY2XiCkh2ju"
   },
   "source": [
    "⏩ **16) Draw the histogram of the residuals $e_i=\\hat y_i-y_i$, using 20 bins.**\n",
    "\n",
    "**Without calculating it numerically, what is APPROXIMATELY the mean and the standard deviation?**\n",
    "\n",
    "**Does it make sense to assume that the residuals are Gaussian?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean is nearly zero and the standard deviation is 1.5. Yes it makes sense to assume the residuals are gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "executionInfo": {
     "elapsed": 10,
     "status": "ok",
     "timestamp": 1675003593983,
     "user": {
      "displayName": "Pascal Bianchi",
      "userId": "14431080439002320783"
     },
     "user_tz": -60
    },
    "id": "A9RhCADJtEf5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = data['Sales']-ls2.predict(data[['TV','Radio','Newspaper']])\n",
    "e.hist(bins =20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QvzAmr1DolTE"
   },
   "source": [
    "The following function computes confidence intervals. The syntax is as follows:\n",
    "\n",
    "\n",
    "```\n",
    "confidence_interval(X,y,a,k)\n",
    "```\n",
    "\n",
    "where `X` is a $N\\times d$ pandas dataframe corresponding to the design matrix, `y` is a pandas series corresponding to the labels, $a$ is the confidence level between 0 and 1 (typically set to 0.95), and $k\\in\\{0,1,\\dots,d\\}$ represents the variable you would like to consider.\n",
    "\n",
    "⏩ **17) Compute the confidence intervals for the 3 variables.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "executionInfo": {
     "elapsed": 9,
     "status": "ok",
     "timestamp": 1675003593984,
     "user": {
      "displayName": "Pascal Bianchi",
      "userId": "14431080439002320783"
     },
     "user_tz": -60
    },
    "id": "oyhF0l-AWOv0"
   },
   "outputs": [],
   "source": [
    "def confidence_interval(X,y,a,k):\n",
    "  assert(a<1)\n",
    "  (N,d) = X.shape\n",
    "  lsf = LinearRegression()\n",
    "  lsf.fit(X,y)\n",
    "  variance = np.linalg.norm(y.values-lsf.predict(X))**2/(N-d-1)\n",
    "  Phi = np.concatenate((np.reshape(np.ones(N),(N,1)),X.to_numpy()),axis=1)\n",
    "  s = np.diag(np.linalg.inv(np.dot(Phi.T,Phi)))[k]\n",
    "  q = stats.t(df=N-d-1).ppf(1-(1-a)/2)\n",
    "  return (lsf.coef_[k-1]-q*np.sqrt(variance*s/N),lsf.coef_[k-1]+q*np.sqrt(variance*s/N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "executionInfo": {
     "elapsed": 9,
     "status": "ok",
     "timestamp": 1675003593985,
     "user": {
      "displayName": "Pascal Bianchi",
      "userId": "14431080439002320783"
     },
     "user_tz": -60
    },
    "id": "SbVj8sYTtHy8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval for TV is (0.04716145492062678, 0.0479118259454128)\n",
      "Confidence interval for Newspaper is ([0.05238174], [0.05700446])\n",
      "Confidence interval for Radio is ([0.19964958], [0.20534199])\n"
     ]
    }
   ],
   "source": [
    "confidence_interval_tv = confidence_interval(data[['TV']],data[['Sales']], 0.95, 1)\n",
    "confidence_interval_newspaper = confidence_interval(data[['Newspaper']],data[['Sales']], 0.95, 1)\n",
    "confidence_interval_radio = confidence_interval(data[['Radio']],data[['Sales']], 0.95, 1)\n",
    "\n",
    "# Print the intervals without array notation\n",
    "print(f\"Confidence interval for TV is ({float (confidence_interval_tv[0])}, {float (confidence_interval_tv[1])})\")\n",
    "print(f\"Confidence interval for Newspaper is ({confidence_interval_newspaper[0]}, {confidence_interval_newspaper[1]})\")\n",
    "print(f\"Confidence interval for Radio is ({confidence_interval_radio[0]}, {confidence_interval_radio[1]})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Hqoekl2MvLI-"
   },
   "source": [
    "⏩ **18) Compute confidence intervals at 99%. Based on this result, if you wanted to eliminate one feature from the model, which one would it be? Explain.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "executionInfo": {
     "elapsed": 9,
     "status": "ok",
     "timestamp": 1675003593986,
     "user": {
      "displayName": "Pascal Bianchi",
      "userId": "14431080439002320783"
     },
     "user_tz": -60
    },
    "id": "wyOlYICTtI4e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "confidence interval for TV is (array([0.04704181]), array([0.04803147]))\n",
      "confidence interval for Newspaper is (array([0.05164465]), array([0.05774155]))\n",
      "confidence interval for Newspaper is (array([0.19874193]), array([0.20624964])) \n"
     ]
    }
   ],
   "source": [
    "print(f\"confidence interval for TV is {confidence_interval(data[['TV']],data[['Sales']],0.99,1)}\")\n",
    "print (f\"confidence interval for Newspaper is {confidence_interval(data[['Newspaper']],data[['Sales']],0.99,1)}\")\n",
    "print (f\"confidence interval for Newspaper is {confidence_interval(data[['Radio']],data[['Sales']],0.99,1)} \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OCugmQla13Sr"
   },
   "source": [
    "## IV. Model selection by cross-validation\n",
    "\n",
    "Consider we seek to choose between two models:\n",
    "\n",
    "\n",
    "*   The first one includes all the columns `TV`, `Radio`, `Newspaper`\n",
    "*   The second one includes only `TV` and `Radio`\n",
    "\n",
    "Which one should one choose?\n",
    "\n",
    "**Cross-validation.** provides a reliable estimate of out-of-sample error, and thus is a better way to choose which of your models will best **generalize** to out-of-sample data. There is extensive functionality for cross-validation in scikit-learn, including automated methods for searching different sets of parameters and different models. Importantly, cross-validation can be applied to any model, whereas the methods described above only apply to linear models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8-_yYPT75hSB"
   },
   "source": [
    "⏩ **19) Use sklearn `train_test_split` method to spli the data into a train and a test set (see the doc [here](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html)). Then, fit two linear regressors on the train set only: one using all features, the other using only `TV` and`Radio`.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "id": "qJBcnWgrtNIG"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.04691087  0.18177172 -0.00704627]\n",
      "[0.0468662  0.17900829]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X = data[columns2]\n",
    "y = data['Sales']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33)\n",
    "ls.fit(X_train,y_train)\n",
    "print(ls.coef_)\n",
    "ls2.fit(X_train[['TV','Radio']],y_train)\n",
    "print(ls2.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OBfNIcKN6lFL"
   },
   "source": [
    "⏩ **20) Use sklearn `mean_squared_error` (doc [here](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html)) to compare the mean squared error of both models, on the test set.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "id": "rSHGNW5btO_2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of the 3 features together is : 2.940588798330039\n",
      "The mean square error of the 2 features without considering newspapaprs is: 2.839973879345958\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "y1_predict = ls.predict(X_test)\n",
    "y2_predict = ls2.predict(X_test[['TV','Radio']])\n",
    "ms1 = mean_squared_error(y_test, y1_predict)\n",
    "ms2 = mean_squared_error(y_test, y2_predict)\n",
    "print (f\"The mean square error of the 3 features together is : {ms1}\")\n",
    "print (f\"The mean square error of the 2 features without considering newspapaprs is: {ms2}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lbIal44v9fdj"
   },
   "source": [
    "⏩ **21) Observe that the mean square error vary, when you re-run the cells corresponding to Questions 21 and 22. How do you explain this?**\n",
    "\n",
    "⏩ **22) Between the two models, which one would you recommend? Justify.**\n",
    "\n",
    "⏩ **23) To choose between two models, your method seems to depend on the ratio of the test set versus the train set. Can you see a more rigorous method allowing to cross-validate the model?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hKjrbSWKApWw"
   },
   "source": [
    "21) as the data is splitted randomly, it takes different parts of the data as a training set.\n",
    "22) I'd choose the one having the Newspapers feature removed, as it is on average less mean square error and it seems that Newspapers are not correlated enough to be considered\n",
    "23) K-Fold Cross-Validation: In k-fold cross-validation, the dataset is divided into k subsets of approximately equal size. The model is trained and evaluated k times, each time using a different fold as the test set and the remaining folds as the training set. The performance metrics (such as accuracy, MSE, etc.) are then averaged across all "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mLzk-2iCdgkm"
   },
   "source": [
    "## Resources\n",
    "\n",
    "- To go much more in-depth on linear regression, read Chapter 3 of [An Introduction to Statistical Learning](https://www.statlearning.com/), from which this lesson was adapted. Alternatively, watch the [related videos](http://www.dataschool.io/15-hours-of-expert-machine-learning-videos/) or read [quick reference guide](http://www.dataschool.io/applying-and-interpreting-linear-regression/) to the key points in that chapter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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