Regression-OLS method (124).ipynb

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   "id": "592c7e02",
   "metadata": {},
   "source": [
    "#### We're interested in how much money customers spend vs length of membership\n",
    "#### Can we predict how much they'll spend if we know how long they've been a member? \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d5a0730a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6878b90e",
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Email</th>\n",
       "      <th>Address</th>\n",
       "      <th>Avatar</th>\n",
       "      <th>Avg. Session Length</th>\n",
       "      <th>Time on App</th>\n",
       "      <th>Time on Website</th>\n",
       "      <th>Length of Membership</th>\n",
       "      <th>Yearly Amount Spent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>mstephenson@fernandez.com</td>\n",
       "      <td>835 Frank Tunnel\\nWrightmouth, MI 82180-9605</td>\n",
       "      <td>Violet</td>\n",
       "      <td>34.497268</td>\n",
       "      <td>12.655651</td>\n",
       "      <td>39.577668</td>\n",
       "      <td>4.082621</td>\n",
       "      <td>587.951054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>hduke@hotmail.com</td>\n",
       "      <td>4547 Archer Common\\nDiazchester, CA 06566-8576</td>\n",
       "      <td>DarkGreen</td>\n",
       "      <td>31.926272</td>\n",
       "      <td>11.109461</td>\n",
       "      <td>37.268959</td>\n",
       "      <td>2.664034</td>\n",
       "      <td>392.204933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>pallen@yahoo.com</td>\n",
       "      <td>24645 Valerie Unions Suite 582\\nCobbborough, D...</td>\n",
       "      <td>Bisque</td>\n",
       "      <td>33.000915</td>\n",
       "      <td>11.330278</td>\n",
       "      <td>37.110597</td>\n",
       "      <td>4.104543</td>\n",
       "      <td>487.547505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>riverarebecca@gmail.com</td>\n",
       "      <td>1414 David Throughway\\nPort Jason, OH 22070-1220</td>\n",
       "      <td>SaddleBrown</td>\n",
       "      <td>34.305557</td>\n",
       "      <td>13.717514</td>\n",
       "      <td>36.721283</td>\n",
       "      <td>3.120179</td>\n",
       "      <td>581.852344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>mstephens@davidson-herman.com</td>\n",
       "      <td>14023 Rodriguez Passage\\nPort Jacobville, PR 3...</td>\n",
       "      <td>MediumAquaMarine</td>\n",
       "      <td>33.330673</td>\n",
       "      <td>12.795189</td>\n",
       "      <td>37.536653</td>\n",
       "      <td>4.446308</td>\n",
       "      <td>599.406092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>lewisjessica@craig-evans.com</td>\n",
       "      <td>4483 Jones Motorway Suite 872\\nLake Jamiefurt,...</td>\n",
       "      <td>Tan</td>\n",
       "      <td>33.237660</td>\n",
       "      <td>13.566160</td>\n",
       "      <td>36.417985</td>\n",
       "      <td>3.746573</td>\n",
       "      <td>573.847438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>katrina56@gmail.com</td>\n",
       "      <td>172 Owen Divide Suite 497\\nWest Richard, CA 19320</td>\n",
       "      <td>PaleVioletRed</td>\n",
       "      <td>34.702529</td>\n",
       "      <td>11.695736</td>\n",
       "      <td>37.190268</td>\n",
       "      <td>3.576526</td>\n",
       "      <td>529.049004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>dale88@hotmail.com</td>\n",
       "      <td>0787 Andrews Ranch Apt. 633\\nSouth Chadburgh, ...</td>\n",
       "      <td>Cornsilk</td>\n",
       "      <td>32.646777</td>\n",
       "      <td>11.499409</td>\n",
       "      <td>38.332576</td>\n",
       "      <td>4.958264</td>\n",
       "      <td>551.620145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>cwilson@hotmail.com</td>\n",
       "      <td>680 Jennifer Lodge Apt. 808\\nBrendachester, TX...</td>\n",
       "      <td>Teal</td>\n",
       "      <td>33.322501</td>\n",
       "      <td>12.391423</td>\n",
       "      <td>36.840086</td>\n",
       "      <td>2.336485</td>\n",
       "      <td>456.469510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>hannahwilson@davidson.com</td>\n",
       "      <td>49791 Rachel Heights Apt. 898\\nEast Drewboroug...</td>\n",
       "      <td>DarkMagenta</td>\n",
       "      <td>33.715981</td>\n",
       "      <td>12.418808</td>\n",
       "      <td>35.771016</td>\n",
       "      <td>2.735160</td>\n",
       "      <td>497.778642</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                             Email  \\\n",
       "0        mstephenson@fernandez.com   \n",
       "1                hduke@hotmail.com   \n",
       "2                 pallen@yahoo.com   \n",
       "3          riverarebecca@gmail.com   \n",
       "4    mstephens@davidson-herman.com   \n",
       "..                             ...   \n",
       "495   lewisjessica@craig-evans.com   \n",
       "496            katrina56@gmail.com   \n",
       "497             dale88@hotmail.com   \n",
       "498            cwilson@hotmail.com   \n",
       "499      hannahwilson@davidson.com   \n",
       "\n",
       "                                               Address            Avatar  \\\n",
       "0         835 Frank Tunnel\\nWrightmouth, MI 82180-9605            Violet   \n",
       "1       4547 Archer Common\\nDiazchester, CA 06566-8576         DarkGreen   \n",
       "2    24645 Valerie Unions Suite 582\\nCobbborough, D...            Bisque   \n",
       "3     1414 David Throughway\\nPort Jason, OH 22070-1220       SaddleBrown   \n",
       "4    14023 Rodriguez Passage\\nPort Jacobville, PR 3...  MediumAquaMarine   \n",
       "..                                                 ...               ...   \n",
       "495  4483 Jones Motorway Suite 872\\nLake Jamiefurt,...               Tan   \n",
       "496  172 Owen Divide Suite 497\\nWest Richard, CA 19320     PaleVioletRed   \n",
       "497  0787 Andrews Ranch Apt. 633\\nSouth Chadburgh, ...          Cornsilk   \n",
       "498  680 Jennifer Lodge Apt. 808\\nBrendachester, TX...              Teal   \n",
       "499  49791 Rachel Heights Apt. 898\\nEast Drewboroug...       DarkMagenta   \n",
       "\n",
       "     Avg. Session Length  Time on App  Time on Website  Length of Membership  \\\n",
       "0              34.497268    12.655651        39.577668              4.082621   \n",
       "1              31.926272    11.109461        37.268959              2.664034   \n",
       "2              33.000915    11.330278        37.110597              4.104543   \n",
       "3              34.305557    13.717514        36.721283              3.120179   \n",
       "4              33.330673    12.795189        37.536653              4.446308   \n",
       "..                   ...          ...              ...                   ...   \n",
       "495            33.237660    13.566160        36.417985              3.746573   \n",
       "496            34.702529    11.695736        37.190268              3.576526   \n",
       "497            32.646777    11.499409        38.332576              4.958264   \n",
       "498            33.322501    12.391423        36.840086              2.336485   \n",
       "499            33.715981    12.418808        35.771016              2.735160   \n",
       "\n",
       "     Yearly Amount Spent  \n",
       "0             587.951054  \n",
       "1             392.204933  \n",
       "2             487.547505  \n",
       "3             581.852344  \n",
       "4             599.406092  \n",
       "..                   ...  \n",
       "495           573.847438  \n",
       "496           529.049004  \n",
       "497           551.620145  \n",
       "498           456.469510  \n",
       "499           497.778642  \n",
       "\n",
       "[500 rows x 8 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "data_df = pd.read_csv('LSE_DA301_Week_1_files/Data/loyalty_club.csv')\n",
    "data_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "52af1a40",
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose our dep and ind vars:\n",
    "x = data_df['Length of Membership']\n",
    "y = data_df['Yearly Amount Spent']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "302a5713",
   "metadata": {},
   "outputs": [
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       "      <td>497.778642</td>\n",
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      "text/plain": [
       "            x           y\n",
       "0    4.082621  587.951054\n",
       "1    2.664034  392.204933\n",
       "2    4.104543  487.547505\n",
       "3    3.120179  581.852344\n",
       "4    4.446308  599.406092\n",
       "..        ...         ...\n",
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   "source": [
    "z = pd.concat([x, y], axis=1).reset_index()\n",
    "z = z.drop(['index'], axis=1)\n",
    "z = z.rename(columns={'Length of Membership': 'x', 'Yearly Amount Spent': 'y'})\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c089f24d",
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualise\n",
    "plt.scatter(z['x'], z['y'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ff774504",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.655</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.654</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   943.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 19 Jul 2022</td> <th>  Prob (F-statistic):</th> <td>4.81e-117</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:36:02</td>     <th>  Log-Likelihood:    </th> <td> -2629.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   500</td>      <th>  AIC:               </th> <td>   5264.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   498</td>      <th>  BIC:               </th> <td>   5272.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>  272.3998</td> <td>    7.675</td> <td>   35.492</td> <td> 0.000</td> <td>  257.320</td> <td>  287.479</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x</th>         <td>   64.2187</td> <td>    2.090</td> <td>   30.723</td> <td> 0.000</td> <td>   60.112</td> <td>   68.326</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.092</td> <th>  Durbin-Watson:     </th> <td>   2.065</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.579</td> <th>  Jarque-Bera (JB):  </th> <td>   1.122</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.037</td> <th>  Prob(JB):          </th> <td>   0.571</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.780</td> <th>  Cond. No.          </th> <td>    14.4</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.655\n",
       "Model:                            OLS   Adj. R-squared:                  0.654\n",
       "Method:                 Least Squares   F-statistic:                     943.9\n",
       "Date:                Tue, 19 Jul 2022   Prob (F-statistic):          4.81e-117\n",
       "Time:                        19:36:02   Log-Likelihood:                -2629.9\n",
       "No. Observations:                 500   AIC:                             5264.\n",
       "Df Residuals:                     498   BIC:                             5272.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    272.3998      7.675     35.492      0.000     257.320     287.479\n",
       "x             64.2187      2.090     30.723      0.000      60.112      68.326\n",
       "==============================================================================\n",
       "Omnibus:                        1.092   Durbin-Watson:                   2.065\n",
       "Prob(Omnibus):                  0.579   Jarque-Bera (JB):                1.122\n",
       "Skew:                           0.037   Prob(JB):                        0.571\n",
       "Kurtosis:                       2.780   Cond. No.                         14.4\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ols test\n",
    "f = 'y ~ x'\n",
    "test = ols(f, data=data_df).fit()\n",
    "test.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "fbeb1af3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      534.580390\n",
       "1      443.480612\n",
       "2      535.988229\n",
       "3      472.773625\n",
       "4      557.935940\n",
       "          ...    \n",
       "495    512.999846\n",
       "496    502.079645\n",
       "497    590.813099\n",
       "498    422.445808\n",
       "499    448.048192\n",
       "Name: x, Length: 500, dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# look up the coefficients (m and c) and use in this equation:\n",
    "y_pred = 64.2187 * z['x'] + 272.3998\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b88d78ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x174a8aa14f0>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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T/d9PGK/94UNU9D+ox/FlAs6pNrfGXKtI5qt3675ISnE3xnwsIhtEZKQxZjXwVeC9+J9LgLr4z0XxlywGHhWRu+jeUD0ceDsXk1eUXBJGiPwaUVhZpqlCM8mEEXan2yWIK8cvbNLc3MzKO86lq6XZHjvkwjn0rf0Xz9e4TTU5MSpfvVv3VYJmqF4NPBJ3ynwEfI9uj/wCEbkMWA98B8AYs0pEFtAt/h3AVX5OGUXpTYIKdlAhSrVChm57Y3tHdv8LlAkM6l/l+jn8mnKAt+3RzQFz4BlT6XfkV3ocGxTnHUI2ywgrqQkk7saYRsDNbvNVj+NvA7SFitIrZFuwIZgQBVkhl0GgzNGwdBk8rYZ+IZdaj+/nhhtu4M4777QfH3zyd6k8/ruB5lIVKadvRZnr53TeIXhdAMMmdCnB0NoySlHjJ9iQ6Bdvae8IvHIMUs/ca4VcLkKXMfSvigQWdrfkpTLw3LD0q3HjVxfHuiBYF8TVf1vEp8/fax8zefJkFi5cyC1Pv8e8N9cHmrvlzU/VWtBr78GqfKlkFxV3pajxWmHPXLwqQSxTNWZOJkizDK8LQJcxrKmbyPi6pYHEPVImzDxzlP15nBcjt8SkVGWHTz1ioKvDpqm5lRHTn0UE9qxfycePztg7h/4HM/eZ/8v5J46kviHKwuXBSvomd3Hyu4Py2lQOutmshEPFXSlqvAQ2TCjEq6aK30q0viGKCLjpUnWf8lD1Y/arrHBNXjp0+rOux/uVHbaE2U0uDRDbtsnTAXPH0nX86tWo57yTk6KSV+apyjXU5rjSppKIirtS1Pi5VIKQTk2V+oYoU/+0wtUhArC7vZPd7cHn1OxRNqCmOuK6cvcTQ69QUdeeXUR/9wO6WrbbY4dc+HP61h5hP97WEvMtYWDi752ujTHVBVPJLiruSlHjJRiVkbKUtVa8NhctvFais55elZDmnynJdw71DVFmPb3Kdf6RcnEVQy/XjunqZPOCW9izrtEeS9cBk2m9mFRFyJTsouKuFDVeggHd9Vi8JNhNqIK6bsIU6ApCS3sHh05/1rOJtZN+fSp6zMnNtWOMYdvLD7Lz7/X2WP8TzqPmpAvTmmO2VtjZrrSpeKPirhQ9XoJxrU+xrWShynWCjZsbxsK6WESbW1M6VLa77CUkh2J2/c+LCQ6YqsOPY+CUGUhZYl32SBl0dHXfOexu6/Dcp0h1h5OMZqEWBiruSsnitYFXUxVJy9fufH2YDduqSDkzzxwVqk6MF34lBvasX8knj+11wFT0P5hB8RowblSUlzPnO6MTKlcmh7fCNijRLNTCQcVdKVgyWQHWN0Rpae/oMW4JbTJBfO0WM88cFbjuS01VhJlndpfXnbNkdUbC7lViILatiab7r0g4tvbKh6jYv2cNGCfOi1e24uGahVo4qLgrBUkmK0CvzFGn0CYTxNdunXvW06s8hb0qUsaeWFcPd006rfX85j5nyWp279ze0wFz0Z30HRw8Nu6cUzbi4V4XyWhzq72voGGa3kHFXSlIMlkBetkB+/XtuRlpEcSmZ1kg/ZwylZFybj/7i8xZsprr5jcyc/EqdrZ10BmiCFgy95w7JmHesViMd37zE/asW2GPpeuAKXNJDs3kjsnPmmrQME1vog2ylYIkVZjEr1l0qtVj8vGQuiG21SYvlQVyW0t3qdtocyuG7mSqTITdmQFqjOEnP/kJffr0sYW9/wnnM3zaM2kX90qemnXXY83fEuPk78sLt4bayVgXaSW36MpdKUj8wiSpQjZBVo/Xzm/kp0+tpKW907Ygvvz+FtfVapA2eU7Clvb1IlK219P+4IMPcvnll9vPVX3heAZOnt7DAZMpmcbMk2P3Xt+YtuHLPbpyVwoStxWgFSbxEyCv17qxu73TFvt5b673XK2mKqGbK/arrGDAjg8QEVvYK2oGMfS6JzjorJ9mRdhrqiIJj8NsLHsxZWwtr00/jTV1Ez2zabUNX+5RcVcKEr8wiV/YZXzdUgC+dUxm8dzWWCfXzm8MtRFaJu49JtMhtq2JxlsmcMopp9hjtVc+RO0PfkdZn+wIo7NgmYWX6KYrxn4XaSW3iCmAimzjxo0zy5Yty/c0lCIhleBGygVMuE5GfiQXzHJ7bkB1hF17OjJ+z849u2i6/wq6WnfYY6Ov/BU79h+R0XmT8UpMcnMaWZ8xbDKT85ya1JQbRGS5Mcat14aKu1J8BGmSkWuqIuV865haO04P3heAIJjODjY/8TP2rPsfe2zKT2bz1J03cuj0ZzM6txMB7k5y3yTjTI5KvrBFyoV+fSrY3hpToS4AVNyVkiNIe7ts41zBpqoBExRjDNuWPsDOZYvssf7jz6fmxAsoA/p7VIZMBwEuOG4Yt04ZHWg1HSQklU4Wq5I9VNyVkiXT5KB08eoqlEx1pIy2DuN67M7GF9i65Ff241w5YCysRCi3MghuIh30jiHTapFK+viJu1ohlV4nyKrRuTK3hNQt5uuWfBQ05l5bU8XH2/ek1Qko6GtaYl0kd5HbtfLPfPrcPfbjippBDPrevWltlFrfjd++gEVza8yzbEJrrJPrF3R7563vN2itfLU1FibqllF6lSBJMs5jYK+Quh1ruWoGVO+19PXrU8Gxhw7w7c1pOTZ6o8Wb9RZtTatZN3tSgrDXXvn7jBwwXcawtm4id587JlBHI78LXqcxCd/v1AkjA7l/1NZYmKi4K71KKo+61zFex1rsie1tJd3cGuO1D7cmCHekXKipivSwVfZGi7eOXVtZN3sSHz98vT028KybGD7tGSr2H5jRuS1htbzlmX4e5/c7ZWxtyrsBtTUWLiruSq8SJEkm1W2+5WcPk2QU6zT061vBmrqJvDb9NDv0EDThKR1MR4x1sycRve9ie6z/8ecyfNozVH/hhIRja6oi9Ouzdx5VkdT/Nd2ENRufx/n9+10skks0KIWFxtyVXiVI9UWv3qFOnCUHgsZ83Y5zK3Xb0t6RkUPFGEPTA1fSsXWjPdZ32GgOOf921+OtMsTJInlz/coeG5+pPOfOz5PuRrPz38KroJqKeuGj4q70KkGqLwYNg1shhKAbf26xYbfNXSAtH32kXNj8/H3saHguYXzY1EW+DpjWWCczF6/qIZa3ThnNuOEHhE4AcpbuHTPrxdCNRZz/Ftr3tHhRcVd6lSBi4dZKzoum5lbuPndMSjF2C2Ekl/CNNrcy9U8rmPPto7n97NH8ZEFjj6qJXnStXsoH9XcljA358WOUV30m0OubW2OMmfVi1pODwnyXfncDKubFh/rclbyTvHr26+eZTLkIXcbQP0Xru+Sa6PUNUa5b0Oh6lzCgOsItZ4zy7cFq0RZ9n4/n3ZAwNujf76PPwOGB5u+FlQGbnCjlTEQKQtA8gAHVERp+9vV0p6vkCfW5KwWLW/neSLkQKZMetr0y6Vl/3HLE+Am7sya68z291jXbWmIp64137PyU6K8vSRgbeNZPqf7C8b6vC0prrJPH3trQw6ppgEfeXM+44QcEWk1PnTAy5UUqUi7cckbP1oNKcaPivo9QqMWb3JwusU7DgOoI1X0qaGpupX9VBJFu0RUJHpOH7pWus+9o0I1Gz3rwHTHW33lWwlj/E86n5qQLgk8qIF4efAOh6qvPenqV5wZxmGJghfo7pLij4r4PUMgd6b2cLs0tMRp+9vUecfGwUUQDdh/ToE2tXc9jDE0P/JCOrXsTqPYbcTRDLqzLSwGzMFmht5wxKmPHSyH/DinuBBJ3EVkL7AQ6gQ5jzDgROQCYD4wA1gLnGGO2xY+fAVwWP/7HxpglWZ+5EphC7kifyho56+lVKVvb+WH5tGcu9m5qnYpPl9zHrsbnE8ZG3vQMVX2zV9QrLEGyQp0r7cpImR3WKhfhW8eE2yQt5N8hxZ0wSUynGmPGOIL304G/GGMOB/4Sf4yIHAmcB4wCvgH8WkRykyWiBCIb3XVyQX1DlJb2jh7jVZFyTj1iIOPrlmYsnrvbOqhviIayA1rs+p8XWTd7UoKwD7nmcY6euYS6b4+hOU/CHiQrNLnMQ2usy96v6DSGhcujgfuiQuH+DineZBKWmQycEv/7XOCvwLT4+OPGmDZgjYh8ABwLvJHBeykZECRxqLfxqsleUxVh0tGDQpfTFeCEww7gvU07Ey4Iza0xO3wQlLboP/h43tSEMacDRqQ7FNFbJYdrqiL061thx7pPPWIgc5as5rr5jZ6x71RZu5a3PmgMvRB/hxR/goq7AV4UEQP81hhzP3CwMWYTgDFmk4gcFD+2FnjT8dqN8bEEROQK4AqAYcOGpTl9JQhBEofSwSsByEswnMeXeZTM7de3gpff3xI6jm2AtZ+2Ut2nosdqvzXW6eq0SaZj5z+J/vrShDE3B8y2lljo5CAvLCunJdrJF7Xk7NWgse8gK+rm1pj9GVLF0HP1O6TkjqDiPt4Y0xQX8JdE5H2fY90KyfX4bxW/QNwP3T73gPNQ0iAXWYZuIjP1TysSSu06BQMSsz69nCCZrIT9BK3LdFv+3OL3pqOd9XeenTBmNczwIoywjz/sAA4duF+gGuqpMlKDxr6DZu2mOo+FZqoWH6GTmERkJrAL+D5wSnzVPgj4qzFmZHwzFWPM7fHjlwAzjTGeYRlNYio+wjTJsDY1eyOE4dVEw7L8OROXjDE0/e4HdGxrso+rHH40B593W9bm40yecloxnXcSVhONZC++m5B6NdAQYE3dxITXp1NCIfk8SmGTURKTiPQDyowxO+N//zrwn8Bi4BKgLv7T6hO2GHhURO4CBgOHA29n/CmUgiLMRlpvbrq5CbsVPrArQf5pBR8/90t2Nb6QcFyqGjBhqamKJAi28/2ddxBWEw3rGL/Qi1dRtRpHPXvne1kXCGeugB8aQy8dgoRlDgaeku7GBxXAo8aYF0Tk78ACEbkMWA98B8AYs0pEFgDvAR3AVcaY/HUyVnJCmNv+wb24crdwdiaqjJfPrW+IcsOtd/Phk3cmHDvkmscpr9wv63PY3d7t1EkOq7iFhmJdxg6J+IVevG603cbdasL43XFpDL200NoySlq43fa7tbez4spAoFotuaJj0/tE/5hUA+ayX9PnwNxu5if3F/XrS2qFRPxCL+DdTk8gZSzcz6XkVnZYKWy0toySdbw22Jat22rXRElOlpm5eFVWHCZhcHXAnH0z1Ycf1yvvnxyS8rvjse5wUtkOPUsj0HMT22sDVDdGSx9duSu+hKkn4rYqdDpCwmzyha0hk4y7A+a71Jz43fRP6oOX1TLZoz7is1W89uHWnq8H7opvvvp9jxCs1vyA6gh7Yl3aZKPE0ZW7khZh64mksumFWcGnK+zdDpgr6Ni2yR6rHD6Gg8+7Nb0TBsTLQ7/TUb442tzqueruX7138zXI6tp6zutrcts41XIB+xYq7oonYeuJBElRt0T+5vqVzHtzfVbn++kLv2TXisQyRtl2wISlM2A9m+RSBn4NMpzPhbGkgpYL2JdQcS9BslWaNWw9ES+bngg9XCNWs4nkxJ502LliCVtf+GXCWK4cMODtpc+EdC2IXpmjfSvKXO+O1Oq476DiXmJkszRr2HoiXnrXZXCdg9Uj9PoFK1zFMjlendyhac/Gf/DJI0k1YHrBAfOZyoqsbgxnYkH0CuFAz9i8Wh33LVTcS4xslmYNW0/Er19na6yTWU+7F6patm5rjxBNpExcszZnPLmSnVs/cXHA/AfVh3851OdLl2wKe5hmGV74hXDUFbPvouJeYmSzNGtY21yqxKZtLTE7bGPdUTyxbL2re6QLWLZua8J7X3PKcN6/9fSE4/qfeAE1488P/dnyjQB3J/V1zTba2HrfRsW9xMh2aVY3gXDWSLHiz7UeVQ39aI11ugo7dG9EWvF4Ywxvz76Ac2d8bD9/9HEns/OUaVmPffcWVocoRckVYZp1KEXA1AkjqYokukOyGWt1NoGAvbVcos2tLFwe5VvH1FJTFfE7RWAM3Q6Y9XecQUdzXNhF6OjooPGN/0tXQGGPlAkXHucfh3crZZpLanVjU8kxKu4FTn1DlPF1Szl0+rOMr1uasnvOlLG13H72aGprqhC6RSSbiSt+TSBaY53Me3M9za0xqiJlDKiO2HMIK/g7G1/o7oLksDYOveZxRtz4NOXl3RevoHcj5x47lHHDD/A9Zk3dxFCCWxUpZ/xhB6R1UdCNTaU30LBMAZOu8yWXsdagsfvWWBdtHV12XNkt69JZ3MvCzQEz+LL/JnLg0O6/OwTYbcPXjXlvrvf11A+IV1ScOmFkj4qNTqz5OjdBnSEqP5zhK93YVHoDFfcCJtdNicOWFpizZHUoT3qX6W5w7bzYON/PGaPv2PFPov99acLra8+5hYpD/9V+LHRf4MbXLU2Yq5eVMgiRcmHiFwcxvm6pb8ZnuQh3nnN0Qm126zWD43cmfi6aTmN6lB5WlFyitWUKmKCNGdxIJdxe9Uu+dUwtL7+/JaVnOl2Sqw8uePNDzj3+8wnHDP3apZQf8+2EGuRuq/wB1RFuOWNURvO78LhhgTaBnd95uo0woGeVSEXJBK0tU6Sk63wJEs7xuitwZoxar+tbUeYpZGGzNa3GFMYYfjf7Zp5fMNd+7nNjTqDPpP+gNdaJiR9bFSmnX59ydrf3fP9tLd3Nr28/ezS3nz2a6+Y3hrqzEOCZFZsCibTzO0/VfNqPpubWrGUQK4ofuqFaAHhtmqbrfPEL51h4xc6TxbE11ukbbugyJvRm6dblz3L2MUP3CruUMWzqIrom3OQ6bzdhdz5vhamSuxGlwrqABOHUIwbaf8+kPkv/qojtNnKW6E21Ua4oYdGVe54Jusr2W+UlrwS9NvecopROA2U3wghk65oGNi/4D/txxQFDGHTJPZT1qbTPlQ7R+Go4ufhWNlm4PMq44QcwZWxt4O8uuSF3VaQcEXK6j6IoFhpzzzNeVf2CxmaDulCSz5lJ3DgssU830PTAlYlz+dEfqPjMgVl7j6pIOZWRspQ9QjPB+v6CfHeWKyb5wuwVOtLG1Eo6aMy9gPG6xbdcIanism4hGENPgU8O57g1UN7Z1hG4RG0QOlt3EP3NZZj2vZ/xkEvuoeqQz9Pfq4Ik6a3gW2Od9K0oI1ImCW3+snFuC+sOwfndRZtbPb9rN0uql21SqzUq2UZj7nnG6z+1ZftLFZf1i52nSmSaMraW16afxpq6ifTrW5E1YTedMT6edyMb7/2uLewHTpnB8GnP0Dcu7LecMcp1P+GC44alnb3Z3Bqjy+O5SJlwwXHDKBf3tKMB1ZEe83HD+newvru1dRO5+9wxgZPGcp1BrCgWGpbJM+mGVSz8mjWESZjxa9wcFGMMW1/6DbsanrXHak6+mP7Hn9PjWAHb6tjcEutxd1LfEA3tfvFz7ojA3eeMAdxL4Vot7LxW404ytTOqW0bJFn5hGV255xm3cgFeouK2SndbCVpEm1u5dn4jY2a9mNKN4RcWCJJiv7PhOdbfcYYt7NX/cjLDblzsKuywdyO2uSXm+nmnjK0NbWv0s2QaR015v/IMLe0d9vy8cP47hC0PAYl3TK9NP02FXckJunIvQLxW4+UidBnjuspNlQKfqjlyuhusyQ6YyGeHcsgld1MWqQx1HuiZ3h8krd/t9X54rbrrG6K+pQfczpGqIbii5BrdUC0yvGqmOCswOu2S1h+/0Eoqu13yJmEq3BwwGzdu5O+bE62bIz5bxesfbg20Ck9OnvrSsP6hxD3Ie1ir7uTQSEt7RyBhd8bHc1EeQkM2SrZQcS9Akp0sZS6xZDcRSeW/TpV8E+Qi0dmynehvL09wwNRe+gs2/v7H3X+vTSxqNr5uadrulzc/2pbGK/0ZXFPlmluQCom/1im22WyMAtltkagoKu4FitNGd+j0Z12PSRaRVFUSg9rt3C4SpjPGJ4/9lLboe/bYwCk3UT3yBN9zZZLNmU4xsL4VZbR1uHtmrFV32PIBXqGcbDdGyXWhOGXfQjdUiwAvsUgetzZnB7ik4Yex2zk3aY0xfPrir1n/87NsYa85+WKGT3vGFvZyEc8Nxf4+pQly0SDDS9jLRexYeJgLTqRMPL+3bNsas30noOzb6Mq9CAjaqNqK1za3xKjxsRm6cXP9Sh57awOdxlAuwnGfG8AbzzzOmsX32sdU/8tXOPCM6xFJXBM49wKund/IE8vW88j3jwe6LYhuWBUdw26apkunMfbn9wtfOYuUJVewTCZsj9lU8fRs3wko+zYq7kVAEBFJjtdaFRWDNGG+uX5lQjOLXR8t59G6n9mPjzzySH72u0Xc+7f1CX1TvXzlr324lZvrV3LrlNGe9V6aW2L2vKY+scIzq9QNyzUU1gNv4VcGoKa6D6v+M7iHPWhjlCDx9KAXcUUJgop7kZBKRLzitdcvWGG/3ovH3toAQOyfG2h6MNEBM27GfP7Z1Y97/7a+xwXFay/AOuetU0Z7rkatcM2cJatDCbuA3TRjhM/7J+O8CE0ZW8u18xtdj8tVCCRIPD3snYCi+BFY3EWkHFgGRI0xk0TkAGA+MAJYC5xjjNkWP3YGcBnQCfzYGLPE9aRKaLxu7b1EqdOYlI6L9t3N3TVgYnvssUMuuYe+h3yeLfEQtttK0y+8YYnp1AkjXVfmu9s7qG+IhhZT43j/AR71adxILmlQ28shkKDx9Fy2SFT2LcJsqF4D/MPxeDrwF2PM4cBf4o8RkSOB84BRwDeAX8cvDEqGWLf2bjVn/EQpuZa7RXt7OyeccAIbf3mBLewDz7rJrgHjdp5ZT6+yMzKtbE6/+U4ZW8t+lT3XELFOw5wlq0OLqVOkbzljFJHyxKB+mdBjzC204azPHmQ8U4JuiitKtggk7iIyBJgIPOAYngxYbXTmAlMc448bY9qMMWuAD4BjszLbfRy/W3u/MgSQuEI0xnDllVfSt29f3njjDQBqvnJJtwPmC/7Wxm0tMfvisq0lRpmP5cW68HjF3ZuaW5k6YSQRv5M4EOhR2XLOt49OKCVw1zljeoy5ZYy+/P4W1/fwGs8ULRim9DZBV+73ADdCQtG9g40xmwDiPw+Kj9cCGxzHbYyPJSAiV4jIMhFZtmVLbv5DlRp+t/aWDdKr6qG1QrzvvvsoKyvjN7/5DQDnn38+nZ2dXHXt9fZry0Xo1yfYzVaXwfNY68LjtToti7/fnO8cnbKbkwAXHDfMNWSxu63DvpOZ9fQqgITaLUCP+i9+pZYPm/EcI0LUigmCWw0hLVOg5JKUMXcRmQRsNsYsF5FTApzTTV167JgZY+4H7ofu2jIBzrvPk8oqZwmFm+Pi3/b/GHEI/6hRo3j77beprq4G4NYpo7l1ymj7+TC1ZlraOz3rujQ1t3L3uWM8yylYPVAbb/l6wnPJ1szzvzw0YX7WHJPj+dtaYkz9095NZC+XSo1PvN6rzEOmaDxd6U2CrNzHA2eKyFrgceA0EZkHfCIigwDiPzfHj98IDHW8fgjQlLUZ78MEubVPXiEOaN/M+7eezqyrLrCPiUajvPvuu7awu+G20vRaXZeJeNoS+1dFfDNC3fYD6huiLFwetUW20xgWLo/2WEV7OW2seL51jFsoyxgC1W/32q9QlEIn5crdGDMDmAEQX7nfYIy5UETmAJcAdfGfi+IvWQw8KiJ3AYOBw4G3sz7zAicXBaCCWuWmjK3lxKF9GTFiBGt377bH33nnHcaOHRtqvn5eeguvMgGRMmF3e0fKHqvJIZKZi1cFSsMPUkfHK/yyvTXG3eeOCZREpRmiSjGSic+9DlggIpcB64HvABhjVonIAuA9oAO4yhiT+0adBUQuC0ClurVva2vj1FNPtTdKAZ588knOOuusUPO9bn4j185vTGj4EaSgmUVtvNJiEKuis0RBfUPU82KQLLJ+zTmsUJVfKMv6TH4NT5znUpRiIlRtGWPMX40xk+J//9QY81VjzOHxn1sdx91mjDnMGDPSGPN8tidd6Pi5WnKFMYYf/vCHVFZW2sJ+++23Y4zxFXav+SaX37VCIs5GE11eXY/o3tD0csn0ON6xS+P3HSWLrF9hMStUFSSU5ec0UkeLUqxohmoOyFYBqKChnV/96ldcffXV9uPvfve7PPzww5SVBbt2p5pXa6yTa+c32pbLVElMqVbNyTgvAn5zmTphZMJ34rVyr6mKhMr6TK5lb503TJtCRSk0VNxzQDYKQAUJ7bz44otMmDDBfk3kwOF86epfc+gXh3LSHX8NHO8PKsLJc0hVCyVVCWKLMhE74clrLlalS+f53IS9KlLOzDNHJYwFcamok0UpNbTkbw7IRsKKX2jnvffeQ0QShL32R3MZfNl9fNximPfmetcs1jDz9cIZXkrl3e7h3KmOuCYsWZbI+oao53dnVZB0u1CUi6h3XFGS0B6qOcIZPqipjmBMt0MjqHPGrRtSZ8t2ov/975iONnvsi1f/hu3VQ1LOx6vhRPJ8g3YlWlM3MeVxXu9z/YIVrqtuZ29StzCKV4eoTOajKMWM9lDNA9ZtfrrOGWd4wnTE+Pix6bQ37d1sfOqpp5gyZYpvZUYnQVvsAYyZ9aKvfTET98iUsbVcl6Iio1eIROudK0pwNCyTY9J1zkydMJLKijI+feFXrL/zLFvYL/7xTRhjmDJlChCudV5QZp45KqfukXSLaGl9FkUJjop7jknXObPh1SdZfds32bXiBQAGjvkaC5etZ+4vbks4Lki8PKwAOmPlsLfRRbZi2umKtNZnUZTgaFgmx4QNJbzwwgucfvrp9uPRo0fz1ltvUVXlfryb1e/UIwby8vtbMsqOzaV7JJOmFOpqUZRgqLhngJ8P3blBmVxUS+hZN/y9995j1KhEC19TUxODBg1KOY9iEDy378pvg9fvdYX+WRWlEFBxTxO/jVJI9GMnOzwMsHB5lHHDD2D8kD4MHz6c1ta9q/uGhgbGjBmT40/Qe6S7qZzLMg6KUupozD1N/DZK/aogWrS07uGiyf/GQQcdZAv7U089hTHGFvb6hmiPOuTFSLqbyvko46AopYKu3NMk3Y1SYwxbl9xnb5QCzJ49mxtvvBHwDucU86o13e8qW2UcFGVfRMU9TVJtlLo9t2P502z782/txwPHfI2Ply+xa8AkhyGSwzluZW/9KJR4dbr+dPW1K0r6aFgmTfzsfMnPtX60nHWzJ9nCHhk4gi9Mq+f+h/6QUNwrSDgn6KrVr5l2b5Ou9VF97YqSPrpyT5Mgdr5Zf1xC4z2XJbxuyFV/ZNiQWtdVdBDhDrpq9YtX9/bqPV3rYyaWSUXZ19HaMjlgy5YtDBs2jD179thjQRwwqZpGVEXKAyfteNVhAbSUraKUCH61ZTQsk0Xa2tr48pe/zEEHHWQL+6JFixIcMH64hSGsGophszH9Vvj5DNEoitI7qLhnAWMM3//+96msrOTtt7vbxc6ePRtjDGeeeWbg87il19997hjW1k3ktemnhVpppypLoJZCRSltNCyTIffeey/XXHON/fiiiy5i7ty5iPSsW97bBCnjqyEaRSletORvDnj++ef55je/aT8++uijeeONNzxrwOQKP7tjkAbQxeyfVxTFGw3LhGTVqlWIiC3sIsKmTZtobGzMi7AHsTtqiEZR9j1U3AOyZcsWKisrOeqoo+yxhoYGurq6OOSQQ/Iyp6Dp+cklfN3QrE9FKS1U3FPQ1tbGsccey0EHHURbW3d7uzAOmFwSJj1/ythaXpt+mqfA11RHSqKOjaIo3ai4e2CM4fLLL6eyspK///3vANxxxx2hHTC5JJ2ORm4hmki5sGtPR0FksyqKkh2KWtxzVTXx3nvvpaysjAcffBCAiy++mK6uLqZOnZqV82eLdNLz3eyW/fpUEOtKdE1pHF5RipuidcvkotZ3oThggpJJWr/zGK8m2xqHV5TipWjFPZu1U959911Gjx5tPxYRmpqa8rZRGoZsdGHS6ouKUnoUbVgmG7W+N2/eTN++fROEvbGxMa8OmHyQKrxTKk1DFGVfomhX7pmsNvfs2cNJJ52EMyt20aJFgTdKC6VOerbwC+9oqztFKU6KVtynThiZIDqQejPRqgFjbZQCzJkzhxtuuCHw+xaL2IW9AHmFdwqpdLCiKMFJGZYRkUoReVtEVojIKhGZFR8/QEReEpH/jf8c4HjNDBH5QERWi8iEXEzczfXhVzXxnnvuSXDAXHLJJXR1dYUSdiiOvp7ZbNShre4UpTgJsnJvA04zxuwSkQjwqog8D5wN/MUYUyci04HpwDQRORI4DxgFDAb+LCJfMMb4txhKgyCbickOmLFjx/L6669TWVmZ8vxuq99iELtsrrZ1s1VRipOUK3fTza74w0j8jwEmA3Pj43OBKfG/TwYeN8a0GWPWAB8Ax2Zz0kF49913E2rAlJWVsWnTJt55553Awu62+q2pjrgeX0hil80LkLa6U5TiJJBbRkTKRaQR2Ay8ZIx5CzjYGLMJIP7zoPjhtcAGx8s3xseSz3mFiCwTkWVbtmzJ4CMksnnzZvr06ZPggFmxYgWdnZ2hHDBeq19jKHixSydz1Yuw4S9FUQqDQOJujOk0xowBhgDHishRPoe7FTLvUTTeGHO/MWacMWbcwIEDA03Wjz179jBu3DgOPvhgYrEYAIsXL8YYwxe/+MXQ5/Na5W5vjRW82GV7tW3VpVmTRtMQRVHyQyi3jDGmWUT+CnwD+EREBhljNonIILpX9dC9Uh/qeNkQoCkbk/WYE5dffjkPPfSQPfbzn/+c66+/PqPz+sWas5E4lEu0sbSiKCnFXUQGArG4sFcBXwNmA4uBS4C6+M9F8ZcsBh4Vkbvo3lA9HHg7B3Onra0tIX5+6aWX8tBDD2WlC1I6VstCotAvQIqi5JYgK/dBwFwRKac7jLPAGPOMiLwBLBCRy4D1wHcAjDGrRGQB8B7QAVyVC6cMQHt7OwMHDmTIkCGBHTBByffqt9QSpRRF6V20h2oBkpwoBd13DYUW21cUJb/49VAt2toypUp9Q5TrF6wo+EQpRVEKGxX3AsJasXd63E0VUqKUoiiFjYp7AeHmrXdSSIlSiqIUNiruBYTfyryYnDqKouSfoq0KWahk4nLx8taXi+hmqqIoodCVexbJtBqjV2bpneccrcKuKEooVNyzSKblgLWOi6Io2ULDMlkkG9UYNbNUUZRsoOLuQTqxc619rihKoaBhGRfSjZ1r7XNFUQoFFXcX0o2da8xcUZRCQcMyLmQSO9eYuaIohYCu3F3IZicjRVGUfKDi7oLGzhVFKXY0LONCvmu5K4qiZIqKuwcaO1cUpZjRsIyiKEoJouKuKIpSgqi4K4qilCAq7oqiKCWIiruiKEoJIsajX2evTkJkC7Au/vBA4J95nE666Lx7j2KcM+i8e5tinHfYOQ83xgx0e6IgxN2JiCwzxozL9zzCovPuPYpxzqDz7m2Kcd7ZnLOGZRRFUUoQFXdFUZQSpBDF/f58TyBNdN69RzHOGXTevU0xzjtrcy64mLuiKIqSOYW4clcURVEyRMVdURSlBCkocReRb4jIahH5QESm53s+QRCRh0Rks4i8m++5BEVEhorIyyLyDxFZJSLX5HtOQRCRShF5W0RWxOc9K99zCoqIlItIg4g8k++5hEFE1orIShFpFJFl+Z5PEESkRkT+JCLvx3/Hj8/3nFIhIiPj37H1Z4eIXJvROQsl5i4i5cD/A/4N2Aj8HTjfGPNeXieWAhE5GdgF/NEYc1S+5xMEERkEDDLGvCMinwGWA1OK4LsWoJ8xZpeIRIBXgWuMMW/meWopEZGfAOOA/Y0xk/I9n6CIyFpgnDGmaJKBRGQu8Iox5gER6QNUG2Oa8zytwMS1MAp82RizLtXxXhTSyv1Y4ANjzEfGmHbgcWBynueUEmPM34Ct+Z5HGIwxm4wx78T/vhP4B1DwxetNN7viDyPxP4WxOvFBRIYAE4EH8j2XUkdE9gdOBh4EMMa0F5Owx/kq8GEmwg6FJe61wAbH440UgeAUOyIyAhgLvJXnqQQiHt5oBDYDLxljimHe9wA3Al15nkc6GOBFEVkuIlfkezIB+BywBfh9PAz2gIj0y/ekQnIe8FimJykkcReXsYJflRUzIrIfsBC41hizI9/zCYIxptMYMwYYAhwrIgUdChORScBmY8zyfM8lTcYbY74EnA5cFQ9DFjIVwJeA/zbGjAV2A0WxfwcQDyOdCTyR6bkKSdw3AkMdj4cATXmaS8kTj1kvBB4xxjyZ7/mEJX6r/VfgG/mdSUrGA2fGY9ePA6eJyLz8Tik4xpim+M/NwFN0h08LmY3ARscd3Z/oFvti4XTgHWPMJ5meqJDE/e/A4SJyaPzqdR6wOM9zKkniG5MPAv8wxtyV7/kERUQGikhN/O9VwNeA9/M6qRQYY2YYY4YYY0bQ/Tu91BhzYZ6nFQgR6RffcCce2vg6UNCuMGPMx8AGERkZH/oqUNBGgSTOJwshGSigBtnGmA4R+T/AEqAceMgYsyrP00qJiDwGnAIcKCIbgVuMMQ/md1YpGQ9cBKyMx68BbjLGPJe/KQViEDA37iYoAxYYY4rKWlhkHAw81b0WoAJ41BjzQn6nFIirgUfii8SPgO/leT6BEJFqut2CP8jK+QrFCqkoiqJkj0IKyyiKoihZQsVdURSlBFFxVxRFKUFU3BVFUUoQFXdFUZQSRMVdURSlBFFxVxRFKUH+fzofpzIeGi1iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(z['x'], z['y'])\n",
    "plt.plot(x, y_pred, color='black')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}