regression_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pathlib import Path\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Analysis: Seasonal Effects with Sklearn Linear Regression\n",
    "In this notebook, you will build a SKLearn linear regression model to predict Yen futures (\"settle\") returns with *lagged* Yen futures returns. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Last</th>\n",
       "      <th>Change</th>\n",
       "      <th>Settle</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Previous Day Open Interest</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1976-08-02</th>\n",
       "      <td>3398.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3398.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1976-08-03</th>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1976-08-04</th>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1976-08-05</th>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1976-08-06</th>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3401.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "              Open    High     Low    Last  Change  Settle  Volume  \\\n",
       "Date                                                                 \n",
       "1976-08-02  3398.0  3401.0  3398.0  3401.0     NaN  3401.0     2.0   \n",
       "1976-08-03  3401.0  3401.0  3401.0  3401.0     NaN  3401.0     0.0   \n",
       "1976-08-04  3401.0  3401.0  3401.0  3401.0     NaN  3401.0     0.0   \n",
       "1976-08-05  3401.0  3401.0  3401.0  3401.0     NaN  3401.0     0.0   \n",
       "1976-08-06  3401.0  3401.0  3401.0  3401.0     NaN  3401.0     0.0   \n",
       "\n",
       "            Previous Day Open Interest  \n",
       "Date                                    \n",
       "1976-08-02                         1.0  \n",
       "1976-08-03                         1.0  \n",
       "1976-08-04                         1.0  \n",
       "1976-08-05                         1.0  \n",
       "1976-08-06                         1.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Futures contract on the Yen-dollar exchange rate:\n",
    "# This is the continuous chain of the futures contracts that are 1 month to expiration\n",
    "yen_futures = pd.read_csv(Path(\"yen.csv\"), index_col=\"Date\", infer_datetime_format=True, parse_dates=True)\n",
    "yen_futures.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Last</th>\n",
       "      <th>Change</th>\n",
       "      <th>Settle</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Previous Day Open Interest</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>6954.0</td>\n",
       "      <td>6954.0</td>\n",
       "      <td>6835.0</td>\n",
       "      <td>6847.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6847.0</td>\n",
       "      <td>48336.0</td>\n",
       "      <td>51473.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>6877.0</td>\n",
       "      <td>6910.0</td>\n",
       "      <td>6865.0</td>\n",
       "      <td>6887.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6887.0</td>\n",
       "      <td>38206.0</td>\n",
       "      <td>53860.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>6937.0</td>\n",
       "      <td>7030.0</td>\n",
       "      <td>6924.0</td>\n",
       "      <td>7008.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7008.0</td>\n",
       "      <td>49649.0</td>\n",
       "      <td>55699.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>6952.0</td>\n",
       "      <td>6985.0</td>\n",
       "      <td>6942.0</td>\n",
       "      <td>6950.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6950.0</td>\n",
       "      <td>29944.0</td>\n",
       "      <td>53111.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-08</th>\n",
       "      <td>6936.0</td>\n",
       "      <td>6972.0</td>\n",
       "      <td>6936.0</td>\n",
       "      <td>6959.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6959.0</td>\n",
       "      <td>19763.0</td>\n",
       "      <td>52072.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "              Open    High     Low    Last  Change  Settle   Volume  \\\n",
       "Date                                                                  \n",
       "1990-01-02  6954.0  6954.0  6835.0  6847.0     NaN  6847.0  48336.0   \n",
       "1990-01-03  6877.0  6910.0  6865.0  6887.0     NaN  6887.0  38206.0   \n",
       "1990-01-04  6937.0  7030.0  6924.0  7008.0     NaN  7008.0  49649.0   \n",
       "1990-01-05  6952.0  6985.0  6942.0  6950.0     NaN  6950.0  29944.0   \n",
       "1990-01-08  6936.0  6972.0  6936.0  6959.0     NaN  6959.0  19763.0   \n",
       "\n",
       "            Previous Day Open Interest  \n",
       "Date                                    \n",
       "1990-01-02                     51473.0  \n",
       "1990-01-03                     53860.0  \n",
       "1990-01-04                     55699.0  \n",
       "1990-01-05                     53111.0  \n",
       "1990-01-08                     52072.0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Trimming the dataset to begin on January 1st, 1990\n",
    "yen_futures = yen_futures.loc[\"1990-01-01\":, :]\n",
    "yen_futures.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Last</th>\n",
       "      <th>Change</th>\n",
       "      <th>Settle</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Previous Day Open Interest</th>\n",
       "      <th>Return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2019-10-09</th>\n",
       "      <td>9381.0</td>\n",
       "      <td>9391.5</td>\n",
       "      <td>9330.5</td>\n",
       "      <td>9343.5</td>\n",
       "      <td>38.5</td>\n",
       "      <td>9338.0</td>\n",
       "      <td>99153.0</td>\n",
       "      <td>145470.0</td>\n",
       "      <td>-0.410601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-10</th>\n",
       "      <td>9343.5</td>\n",
       "      <td>9380.5</td>\n",
       "      <td>9293.5</td>\n",
       "      <td>9301.0</td>\n",
       "      <td>34.5</td>\n",
       "      <td>9303.5</td>\n",
       "      <td>159397.0</td>\n",
       "      <td>144474.0</td>\n",
       "      <td>-0.369458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-11</th>\n",
       "      <td>9308.5</td>\n",
       "      <td>9309.0</td>\n",
       "      <td>9240.0</td>\n",
       "      <td>9267.0</td>\n",
       "      <td>52.5</td>\n",
       "      <td>9251.0</td>\n",
       "      <td>158810.0</td>\n",
       "      <td>147471.0</td>\n",
       "      <td>-0.564304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-14</th>\n",
       "      <td>9259.0</td>\n",
       "      <td>9292.0</td>\n",
       "      <td>9250.5</td>\n",
       "      <td>9261.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>9265.0</td>\n",
       "      <td>69457.0</td>\n",
       "      <td>153902.0</td>\n",
       "      <td>0.151335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-15</th>\n",
       "      <td>9264.5</td>\n",
       "      <td>9280.0</td>\n",
       "      <td>9216.5</td>\n",
       "      <td>9220.0</td>\n",
       "      <td>43.5</td>\n",
       "      <td>9221.5</td>\n",
       "      <td>108342.0</td>\n",
       "      <td>151564.0</td>\n",
       "      <td>-0.469509</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "              Open    High     Low    Last  Change  Settle    Volume  \\\n",
       "Date                                                                   \n",
       "2019-10-09  9381.0  9391.5  9330.5  9343.5    38.5  9338.0   99153.0   \n",
       "2019-10-10  9343.5  9380.5  9293.5  9301.0    34.5  9303.5  159397.0   \n",
       "2019-10-11  9308.5  9309.0  9240.0  9267.0    52.5  9251.0  158810.0   \n",
       "2019-10-14  9259.0  9292.0  9250.5  9261.0    14.0  9265.0   69457.0   \n",
       "2019-10-15  9264.5  9280.0  9216.5  9220.0    43.5  9221.5  108342.0   \n",
       "\n",
       "            Previous Day Open Interest    Return  \n",
       "Date                                              \n",
       "2019-10-09                    145470.0 -0.410601  \n",
       "2019-10-10                    144474.0 -0.369458  \n",
       "2019-10-11                    147471.0 -0.564304  \n",
       "2019-10-14                    153902.0  0.151335  \n",
       "2019-10-15                    151564.0 -0.469509  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating a series using \"Settle\" price percentage returns, drop any nan\"s, and check the results:\n",
    "# (Make sure to multiply the pct_change() results by 100)\n",
    "# In this case, you may have to replace inf, -inf values with np.nan\"s\n",
    "yen_futures['Return'] = yen_futures.Settle.pct_change() * 100\n",
    "yen_futures= yen_futures.replace(-np.inf, np.nan)\n",
    "yen_futures.dropna(inplace=True)\n",
    "yen_futures.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lagged Returns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Low</th>\n",
       "      <th>Last</th>\n",
       "      <th>Change</th>\n",
       "      <th>Settle</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Previous Day Open Interest</th>\n",
       "      <th>Return</th>\n",
       "      <th>Lagged_Return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2019-10-09</th>\n",
       "      <td>9381.0</td>\n",
       "      <td>9391.5</td>\n",
       "      <td>9330.5</td>\n",
       "      <td>9343.5</td>\n",
       "      <td>38.5</td>\n",
       "      <td>9338.0</td>\n",
       "      <td>99153.0</td>\n",
       "      <td>145470.0</td>\n",
       "      <td>-0.410601</td>\n",
       "      <td>0.170931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-10</th>\n",
       "      <td>9343.5</td>\n",
       "      <td>9380.5</td>\n",
       "      <td>9293.5</td>\n",
       "      <td>9301.0</td>\n",
       "      <td>34.5</td>\n",
       "      <td>9303.5</td>\n",
       "      <td>159397.0</td>\n",
       "      <td>144474.0</td>\n",
       "      <td>-0.369458</td>\n",
       "      <td>-0.410601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-11</th>\n",
       "      <td>9308.5</td>\n",
       "      <td>9309.0</td>\n",
       "      <td>9240.0</td>\n",
       "      <td>9267.0</td>\n",
       "      <td>52.5</td>\n",
       "      <td>9251.0</td>\n",
       "      <td>158810.0</td>\n",
       "      <td>147471.0</td>\n",
       "      <td>-0.564304</td>\n",
       "      <td>-0.369458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-14</th>\n",
       "      <td>9259.0</td>\n",
       "      <td>9292.0</td>\n",
       "      <td>9250.5</td>\n",
       "      <td>9261.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>9265.0</td>\n",
       "      <td>69457.0</td>\n",
       "      <td>153902.0</td>\n",
       "      <td>0.151335</td>\n",
       "      <td>-0.564304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-10-15</th>\n",
       "      <td>9264.5</td>\n",
       "      <td>9280.0</td>\n",
       "      <td>9216.5</td>\n",
       "      <td>9220.0</td>\n",
       "      <td>43.5</td>\n",
       "      <td>9221.5</td>\n",
       "      <td>108342.0</td>\n",
       "      <td>151564.0</td>\n",
       "      <td>-0.469509</td>\n",
       "      <td>0.151335</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "              Open    High     Low    Last  Change  Settle    Volume  \\\n",
       "Date                                                                   \n",
       "2019-10-09  9381.0  9391.5  9330.5  9343.5    38.5  9338.0   99153.0   \n",
       "2019-10-10  9343.5  9380.5  9293.5  9301.0    34.5  9303.5  159397.0   \n",
       "2019-10-11  9308.5  9309.0  9240.0  9267.0    52.5  9251.0  158810.0   \n",
       "2019-10-14  9259.0  9292.0  9250.5  9261.0    14.0  9265.0   69457.0   \n",
       "2019-10-15  9264.5  9280.0  9216.5  9220.0    43.5  9221.5  108342.0   \n",
       "\n",
       "            Previous Day Open Interest    Return  Lagged_Return  \n",
       "Date                                                             \n",
       "2019-10-09                    145470.0 -0.410601       0.170931  \n",
       "2019-10-10                    144474.0 -0.369458      -0.410601  \n",
       "2019-10-11                    147471.0 -0.564304      -0.369458  \n",
       "2019-10-14                    153902.0  0.151335      -0.564304  \n",
       "2019-10-15                    151564.0 -0.469509       0.151335  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating a lagged return using the shift function\n",
    "yen_futures['Lagged_Return'] = yen_futures.Return.shift()\n",
    "yen_futures.dropna(inplace=True)\n",
    "yen_futures.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating a train/test split for the data using 2018-2019 for testing and the rest for training\n",
    "train = yen_futures[:'2017']\n",
    "test = yen_futures['2018':]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating four dataframes:\n",
    "# X_train (training set using just the independent variables), X_test (test set of of just the independent variables)\n",
    "# Y_train (training set using just the \"y\" variable, i.e., \"Futures Return\"), Y_test (test set of just the \"y\" variable):\n",
    "X_train = train[\"Lagged_Return\"].to_frame()\n",
    "X_test = test[\"Lagged_Return\"].to_frame()\n",
    "y_train = train[\"Return\"]\n",
    "y_test = test[\"Return\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Lagged_Return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-02-19</th>\n",
       "      <td>-0.427829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-02-20</th>\n",
       "      <td>-0.020460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-02-21</th>\n",
       "      <td>0.020465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-02-24</th>\n",
       "      <td>-0.204604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-02-25</th>\n",
       "      <td>0.020502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-22</th>\n",
       "      <td>0.084621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-26</th>\n",
       "      <td>0.118370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-27</th>\n",
       "      <td>0.118230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-28</th>\n",
       "      <td>-0.151830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-29</th>\n",
       "      <td>0.180221</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>966 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Lagged_Return\n",
       "Date                     \n",
       "2014-02-19      -0.427829\n",
       "2014-02-20      -0.020460\n",
       "2014-02-21       0.020465\n",
       "2014-02-24      -0.204604\n",
       "2014-02-25       0.020502\n",
       "...                   ...\n",
       "2017-12-22       0.084621\n",
       "2017-12-26       0.118370\n",
       "2017-12-27       0.118230\n",
       "2017-12-28      -0.151830\n",
       "2017-12-29       0.180221\n",
       "\n",
       "[966 rows x 1 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a Linear Regression model and fit it to the training data\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Fitting a SKLearn linear regression using just the training set (X_train, Y_train):\n",
    "model = LinearRegression()\n",
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make predictions using the Testing Data\n",
    "\n",
    "Note: We want to evaluate the model using data that it has never seen before, in this case: X_test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Making a prediction of \"y\" values using just the test dataset\n",
    "predictions = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assembling actual y data (Y_test) with predicted y data (from just above) into two columns in a dataframe:\n",
    "Results = y_test.to_frame()\n",
    "Results[\"Predicted Return\"] = predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<AxesSubplot:xlabel='Date'>, <AxesSubplot:xlabel='Date'>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3VmQwrX9brk66fL6DMyTHNCMiJIDVBhuQssoqXlm8n+teX82RohJem9abd29PISYs2GWf0SUm1BAX1qzl6Qx+cRnbj5z0+Gfby9r0AhKjmtKqmWP9KmyRGB1KtYSMfPtHIRszC+kRG0aTAPvDxolRobw6tTe7jp7it1/tbDRVFWqiDYjGJWQVnOWJL3bQIzaMP07s6rLt+vgIhiS0ZPWBAqqrjTkBtx0+wcTX1/DvpQeY0D2GJY8P5/qerRvki7dFl+hm5BWXUejBKsTvrMrkpYX7KDhTxq3vbGB9RqHHPtteyiqr+Plgkcv6w1gzsQ7YmYlVUl7JzuxTDLDDfXUpo5OjeGJMZ77bfoy3Vza+cifagNTDocKzPPHlDk6cLTdaitdSUl7J/R9uwddX8OatfVwS+6jJ0IRICs6UebxibUl5Jc//by+T31pHcWkl79+RwqtTexNeowyJK0mKsRT789D3/HD9Qf42P5UJPWJY/sQIWjcP5vb/bGJpaq5HPt9eth46SWlFtUviHwBxESH4+Qi7iypuOXSCymrJgHj7K0rX5MERHbmuRwz/WJjGsjTv2rcNRRuQeiitqGbelmw+WH/QaCleiZSSZ77exf68Yl6b2pvYFs6nWNbGUAPKmqw5UMDYV1fx3posfjmgPYseG8bIpCi3fmZStCUTywMG5MvNR/j9d3sY1aUVr97Si9bNg/n8voEkRYdy34db+H7HMbdrsJd1GQX4+giHWgLURYCfD/EtQ+yuibUxswhfH0GKHRNCbSGE4KWbetK1dTMe+XQ76XmNJ86lDUg9dI4OZVSXVsxdd5CzZZVGy/E6PtxwiG+3H+OxUYkMc6LAnT1ENQsiKTrUI3GQUyUVPDVvB798byN+Pj58PvMqnr+xG6FB/m7/7MjQQFo2dX9Jkx92HOO3X+1kaEJL3pje53ytsvCQAD6+ZwB92rfg0c+28cnGw27VYS9r0wvoERtGMxf+BolRoXZPJtyYVUi3NmG1lqKxh+AAX+bclkKQvw/3fNB4yp1oA2IHD4zoxMmSCj7d5B0nlLew9fAJnv/fXkYmteLhqzu59bOGJrRk08EiMh0IfDrKT7tzGPXKSr7aepQHRnRkwaNDnfJ7N4QuMaFurcq7ZG8uj32+nb7tWzD7tr6XuRtDg/z57139GZEYyTPf7GLOqgy3abGH4tIKdmSfYrCL4h9WEqKacuRECefK686OOldexY4jp7jKSfdVTVo3D2b2bX05evIcD3+6tVGUO9EGxA76tm/BgPhw3l2d5VQRtsZIwZkyHvxoKzFhwbxyc68Gp7HWxy392tE00I9Jb65jQ6ZrA715xaU88NEW7v9oK5FNA/nuocH8dlySy2M59pAUra6M3fHnsvpAPg9+vJWurZvx/h39as0oCvL3ZfZtKUzoEcML89P416J9hmUQbcxU8y8GdXKtIU+MCkVK6q2eu+3wCcqrql3mPuvbPpy/3did1QcKeGG++cudaANiJw9e3Ynjp0v5dttRo6UYTmVVNY98uo0TJeW89cs+hDVxv3unU6umfPvgYCJDA7ntvY18ubnhPcRVGZIjjPrXSpam5fHUuM589/BgurUJc4Fi50iKbkZ5ZbVTxf7qYlNWEff+dzMdIkP44K7+9brkAvx8eG1qb6b2a8vry9L58w97DcmCW5tRQJB/7fWnnOVCTay64xEbsorwETgd/7DFzf3acufgON5fm8UXLjiOjUQbEDsZltCSrq2b8fbKTKoMSif1Fv61eD/rMgr5643d6Nrac3+27SKa8NUDgxgQH8GT83by0sI0p//UjhSVMOP9TTw5byedo0NZ8OhQHhzRyaneJa7kfEkTFwbStx85yV1zf6ZN82A+umcAzZvYl0Xm6yP4v8nduWdIPHPXHeSpr3Z63O2yNr2AfnHhLh8NxkU0IcDXh/31BLQ3ZhbStbVr4y8Az47vwpBOLXnum91sOVTk0m1fyoJdOS6/ILGiDYidCCF4cEQnsgrOsmB3jtFyDMM6WXD6gHZMSWnr8c8PC/bnP3f2Y1r/dsxansHDn251aJZvVbXk/TVZjHllFVsPneD5G7vx+cyBdIxs6kbV9tOxlUoxTXNRIH3vsdPc/v4mS4D8Klo2DXRofSEEz07owmOjEpm3JZtffbrNY27cvOJS9ueecdn8j5r4+frQITJEFVWshdKKKrYdOel0+m59n//G9N7ENA/ivg+3cuzkOZd/BqgLpce/2ME/fnKPu0wbEAcY1y2aDi1DeHN5RqOcVVof1smCPWPD+OPEZMN0+Pv68MKkbjw7vgsLdh/nljkb7KqVdSC3mJveXsdf/reXAR3CWfT4cG67quFlSFxJoJ8vHSObumTOS3peMbe9t5EmAb58fM8AosOcm8UthODRUQn84bpkFuw+zj0fbKak3P0ZidZJjUNcNP/jUhLqycTaceQk5ZXVbkukaN4kgHdnpFBaUcXMDzfXG9B3FCklz327Gx8Bv7/OPeerNiAO4OsjuG94B/bmnGblfvO2WnUG62RBP1/Bm7/s26A+H65ACMG9wzrw9i/7sv94MZNmras1e6m8spp/LznA+NdWc7DgLK/e0ov/3NGPNs1dV4bElbiipEnu6VJufXcjQgg+vmcAbcMbPj/nriHx/OMXPVibXsCM9zZxutS9qahrDhQQFuxPcmvn2tfWR2Krphw9ea7W9PwNmUUIAf1dGP+4lISoUP49tRd7jp3mKReXO/l+xzFW7s/nibGdae2mY93UBkQIMU4IsU8IkS6EeNoTnzmpdyzRzYJ4c4Wx6Y2epKS8kifn7WR/XjH/ntrbq/54x3aN5sv7B1JZXc1Nb61nxb68i97ffuQkE19fwytL9nNtN1WG5MbebVxehsSVJMU0I+dUKSdLnK9+MG9LNrmny/jvXf3p4EL33M392vL6tD7syD7JtDkb3FZ2RUrJuoxCBnaIwNdNI8QEa0mTWjKxNmYVkhTdzO1JItd0ieLJsZ35Yccxl/2vnCwp5y8/7KVn2+bMGBjnkm3awrQGRAjhC8wCrgWSgWlCCLf7VQL8fLhnaDybsorcHvwymsqqaj7ZeJjhL63gx505PDU2yW2TBRtCtzZhfPvQYNqFN+GuuT/z3/UHOVdexV//t5fJb67l1LkK3p2RwmvTehPhYAzACJIsDaUa4sZatDeXnrFhbrl6n9AjhndmpJCRf4abZ68n55Tr/feHCks4evIcg93YSMzauMtWJlZ5ZTVbD5/gKhel79bHA8M7cn3P1vxz0T6W7G14uZMX5qdy6lwFL07u7jYDDCY2IEB/IF1KmSmlLAc+A27wxAdP69+O5k38eXN54xyFSClZtOc4Y19dxTPf7KJ9eBO+emAgD4zoaLS0WokJC+bL+wcyMqkVf/huD4P/vox312QxtX87Fj0+jFHJ7i1D4kqsmVjOBtJzT5ey48hJxnSNdqWsixjRuRX/vWsAuafLuOmt9Rx0cZaPtXz7YBeUb6+NduFNCPTzsVnSZGe2qr9lTwMpVyCE4B839aBb6zAe/Wybww2varIuo4AvNmdz77AO548ld2FmA9IGqJlEnW15ze2EBPpxx6A4lqbluXXWsBFsPXyCm2evZ+aHW5DA7Nv68uX9A+nb3jNXYg0hJNCP2belcN+wDsSEBfHZzKt4YVJ3l6dguptWoYGEhwSQ6mRvkCWWYoij3Ww0+8eH8+m9V1FSXsmU2etdWgRybXoBMWFBDWrSVR++PoKOkU1tBtI3ZinvQn83ZGDVRpC/L3Nm9CU4wI97PtjsVAHX0ooqnv1mN+0jmvDoNQluUHkxZjYgtsZlF0WghBAzhRCbhRCb8/NdG/S+Y1AcTQJ8eauRxEIy88/wwEdbmPzmOrIKSvjbpG4s+vUwxnaN9up4waX4+gh+N74LPz4y1K7ucd6IEIKkaOdLmizak0v7iCYktHJ/anL32DC+uG8gPgJumbPeJT1Fqqsl6zMKGdSxYe1r7SExqqnNq/0NmYV0jgp1W+Xl2ogJU+VOjp8q5aFPtlLh4LybN5alk1Vwlr/d2N0jlRTMbECygZoTEWKBi0qISinnSClTpJQpkZGu9d03bxLArQPa8cOOYxwuLHHptj1JfnEZv/92N2NeWcXK/fk8NiqRlU+O4NYB7Z3q7a1xDUnRzdiXW+zwpNUzZZWszyhkTHKUxwx/QlQo8+4fRLMgf5f0FNmbc5oTJRUMSXD/BUBCVCg5p0ovyiirqKpmy6ETLitf4ih927fghcndWZdRyN9+TLV7vX3Hi3l7ZQaT+7RhiBtjRzUx8z/Ez0CCECJeCBEATAW+96SAe4Z2wM/Hh9kGF5xzhrNllfx7yQFGvLScTzYdZmr/tqx88moeHZVASAOqjmpcQ1JMKKUV1RwsdCy2sHJfPuVV1YxOdl/8wxZtw5vw5f0DXdJTZG26tX2t+/8EbTWX2nX0FCXlVYaOYG/qG8vdlgoAn9lRxLW6WvL01ztpFuzPcxM8N0fLtAZESlkJPAwsBFKBL6SUezypIapZEL/o24Yvt2TbNZHNG6isqubjjYcY8c8VvLJkP0MTIln02DD+emN3IkO9P0PpSiH5fCDdsbjCor3HCQ8JoG9719aOsoeoZkEu6SmyNqOQTq2aEuWC9rX10fm8Abmwnzdmej7+YYvfXZvE0ISW/P673fx8sO6Mz483HmLb4ZP8/rouHnW7mdaAAEgp50spE6WUHaWUfzNCw33DOlJZVc17a7KM+Hi7qZlZ9ew3u89nVr19W1+vKeOhuUCnVk3xETgUB6moqmZZWh7XJLVya+pmXTS0p0h5ZTU/ZxW5bfb5pcS2CCbY3/eiQPrGLGXAHC374mr8fH14Y1ofYls04f4Pt3C0lnInx0+V8vef9jE0oSU39vJIHtF5TG1AvIG4liGM7x7DxxsOc+qcdzaJ2XLoBFPevpBZNcdEmVVXKkH+vnSIbOpQJtbGzCKKSyvdnn1VHw3pKbLt8AnOVVQxyI3puzXx8RF0atWUA5aiipVVyoC5o/6VM4Q18eedGSmUV1Zzby0lZP74/W4qq6v5243dPZ7wog2IC3hgREfOlFXyoZe1vc3MP8P9H27hF2+t41BRCS9M6s6iXw9jjMkyq65UusQ0c6ikyeK9xwny92FogvGTPZ3tKbI2vQAfgUcbeSVENT2fgrzn2GnOlld5vJFYXXRq1ZTXpvUm9fhpnvzy4nInP+0+zsI9ufx6VCLtIlzfTro+tAFxAV1bhzGicyTvrz3o8oJozpBfXMZz3+5i9CurWH1AZVateGIE0we005lVJiIpOpSjJ8/ZVXNKSsnivbkMTYgkOMDYOmVWnOkpsjajkB6xzQkL9tzcncSoUPKKyzhVUsHGLJVB5ooOhK7k6qRWPD0uiR935fDGsnQATpdW8Mfvd9Mlphl3D4k3RJdOt3ERD47oxM2z1/P5z4e5Y/CFH7O0oorjp0o5frqU46dKyTlVSu7pUnJOncPf14cHR3RyWbmJs2WVvLM6k3dWZVJWWc30/u145JoEHRw3KV1iVIB33/Fi+tVT0G/PsdMcO1XKY6MTPSHNbqw9RZoG+vHumizOlFXy4uTuNi9kiksr2H7kJPcP7+BRjYlRKga4P6+YjZlFdGgZQisPBPAdZeawDqQdL+Zfi/fTOTqU1QcKyCsuY85tKYb1sdEGxEX0jw8npX0L3liezsr9+ecNxYmSy68eQwP9iA4LIq+4jB935XBTn1h+M6az0+W2K6uq+XzzEV5ZfICCM2Vc2y2aJ8d2dmkRPY3nSYq2NJfKOV2vAVm0NxcfoQrzeRvWniKhQf68smQ/Z8sqeXVqr8sqOm/KUu1rXd3/vD4SWllqj+WcZtPBIq7rEePRz7cXIZQxzsw/w6Ofbae0soo7BsXRs21zwzRpA+JCfjOmM7/5Yjt5xWXEtgimb/sWxIQFER0WTHSzIKLD1K2pZZ7FqZIKZq1IZ+7ag/yw8xj3Du3AfcM7nn+/PqSULNqby99/SiMz/yz94low+7a+hqRwalxPTFgQYcH+dgXSF+05Tkr7cI/PnLYXa0+R0CA//vK/vZz5YDOzb+t7UV/2temFBPr50MfDx2+b5sGEBPjy/Y5jFJdWeqz+lTNYY0vXv7GGFj7+PDGms6F6tAFxIQM7RrDud9fYvXxYE3+eGd+F265qzz8W7uP1Zel8uukwj41O5JaUtnXGK7YcKuKF+WlsOXSCjpEhzLmtL6M9OPtY437sLWlypKiEtOPFPDehi4eUOc9dQ+JpGujH01/vZMZ7m3j/zn7na5Wty3BP+9r68PERdIoK5eeDJwAMm4FuL9FhQcx/dChSYvikXx1R9QLahjfh9Wm9+ebBQcS3DOHZb3Yz7t+rWZaWe1nmSsb5zKr1HLZkVi3UmVWNli4xzdh3vLjO4PPivZ4pnugqbPUUyS8uI+14MYM6GXP1n2ipG9Y+ogkxYd7T76Y2WjYN9IrYph6BeBG927Xgi/sGsmhvLi8uSOOuuZsZ2CGCZyd0IapZEP9eup9PNx0hyM+Hx0cncs/Q+ItcAJrGR5eYUErKqzhcVEJcLZVpF+09TueoUNpHuK9yrauZ0COGkEBf7v9oCzfPXs8t/VRZO0/HP6xYS5p4y/wPs6D/fbwMIQRju0YzMqkVn2w8zKtL9nPd62sI8vehskpy6wCVWWX0LFmNZ7AG0tOOn7ZpQE6cLefngyd4YLj39mqpDWtPkbvm/swL89NoFuRHtzZhhmhJjLYaEO+Nf3gj2oB4Kf6+Ptw+KI5JfdowZ2Um+cVl3De8g86susJIjApFCEjNKWZct8uzg5al5VFVLU3jvroUa0+RGe9v5OrOxpVgGdwxgr9N6sZ1Pb0zA8tb0QbEy2kW5M8TY43NtNAYR3CAL/ERIbXOSF+8N5foZkF0N+jK3RV0jw1j3dPXYGQIz8/Xh1sHtDdOgEnRQXSNxsvpEtPMZn/00ooqVh3IZ1RyK3wMunJ3FcEBvh7PvtI0HG1ANBovJyk6lMNFJZwpu7iQ3tr0AkrKqxjj4d4fGo0VbUA0Gi8nydIb5NKe44v35hIa6Gfa1r0a86MNiEbj5SRZMoRqxkGqqiVLUnMZ3jmSAD99GmuMQR95Go2XE9simNBAv4tmpG8/coKCM+WM6ardVxrj0AZEo/FyhBAkxYRe1N520d5c/H0FIzob3/tDc+WiDYhGYwKSolUmlrWkyeI9uVzVIeJ8HSmNxgi0AdFoTECXmGacKavk6MlzpOedIbPgLGNMOnlQ03jQEwk1GhOQFHMhkJ6efwaAUdqAaAxGGxCNxgR0thT7SztezPJ9efSIDTNF1VhN40a7sDQaExAS6Ef7iCas2p/P9iMnGe2FnQc1Vx7agGg0JqFLdDM2HzqBlOj0XY1XoA2IRmMSrHGQduFNSIzSVZk1xqMNiEZjEqy9QXTrYo23oA2IRmMS+seH06ttc25OaWu0FI0G0FlYGo1pCA8J4NuHBhstQ6M5jx6BaDQajcYptAHRaDQajVMIKaXRGjyCECIfOHTJyy2BAgPkWAkDTtm5rNFaHcVMeh3R6shv5i7csW/d9b284ThorOeZp7S2l1LarNp5xRgQWwghNkspUwz8/DlSypl2LmuoVkcxk15HtDrym7kLd+xbd30vbzgOGut55g1atQvLWH4wWoDGYRrrb9ZYvxc07u9mKNqAGIiUUh/YJqOx/maN9XtB4/5uRnOlG5A5RgtwADNpBXPpNZNWMJdeM2kFc+k1XOsVHQPRaDQajfNc6SMQjUaj0TiJNiAajUajcQptQDQajUbjFNqAaDQajcYptAHRaDQajVNoA6LRaDQap9AGRKPRaDROoQ2IRqPRaJxCGxCNRqPROIU2IBqNRqNxCm1ANBqNRuMU2oBoNBqNxin8jBbgKVq2bCnj4uKMlqHRaDSmYsuWLQW1dSS8YgxIXFwcmzdvNlqGRqPRmAohxKWtwM+jXVgajUajcQptQDSaxkhxLvzwayg7Y7QSTSNGGxCNpjGS9gNs+Q+k6m6uGvehDYhG0xjJ3aPu9/1orA5No0YbEI2mMXJ8t7pPXwoV54zVomm0aAOi0TQ2qqshby9EJEBFCWSuNFqRppGiDYhG09g4eQjKz8CA+yAgVLuxNG5DGxCNprFhjX+07gMJo2DfAqiuMlaTplHiNgMihAgXQiwWQhyw3LeoZblxQoh9Qoh0IcTT9qwvhOghhFgvhNgjhNglhAhy1/fQaExH7m5AQKskSLoOzuZDtp5Eq3E97hyBPA0slVImAEstzy9CCOELzAKuBZKBaUKI5LrWF0L4AR8B90spuwIjgAo3fg+Nxlzk7oaIjhAQAp1GgY8fpP3PaFWaRog7DcgNwAeWxx8AN9pYpj+QLqXMlFKWA59Z1qtr/THATinlDgApZaGUUo/PNRoruXsgqqt6HNwc4obCvvmGStI0TtxpQKKklDkAlvtWNpZpAxyp8Tzb8lpd6ycCUgixUAixVQjxlFvUazRmpOwMFGVBVLcLryVNgMJ0yN9vnC5No6RBBkQIsUQIsdvG7Yb611absPGarGcdP2AIcKvlfpIQ4ppa9M0UQmwWQmzOz8+3U5JGY2LyUgF5YQQC0Plada/dWBoX0yADIqUcJaXsZuP2HZArhIgBsNzn2dhENtC2xvNY4JjlcW3rZwMrpZQFUsoSYD7QpxZ9c6SUKVLKlMhIm9WINZrGRa5lAmHNEUhYLMT00m4sjctxpwvre+B2y+Pbge9sLPMzkCCEiBdCBABTLevVtf5CoIcQookloD4c2OsG/RqN+cjdo+Z+NG938etJEyD7Zyg+bowuTaPEnQbkRWC0EOIAMNryHCFEayHEfAApZSXwMMoopAJfSCn31LW+lPIE8DLK+GwHtkop9UwpjQbUCCSqK4hLvMNJE9T9vgWe16RptLitoZSUshC4LDYhpTwGjK/xfD7KDWXX+pb3PkKl8mo0GitSqhFIj5svf69VMjRvr9xYKXd6XpumUaJnomtqp7IccnbC9k9g8R8hf5/RijR1ceoIlJ2+OIBuRQg1qTBzBZQVe1yay6iqhLeHwKZ3DNRQoSZmyvryfRo/V0xLW009nC2E3F2qiuvxXcoVkr8PqmvM0cxYBvcuB1992Hgl1hImNQPoNUkaDxtmqQq9XW/0mCyXkrVCHZ+75kH/e43RsOcb+PpeuP516DPDGA1egv4nuNKoroKiTDi+UxmLXIvBKM65sEzTaIjuBgmj1Z9RdHe1zFd3w+b3VJE+jfdhLeHeqovt99teBcHhkPajeQ3Izi/V/dHNas5LYFPPa8jZoe7nPwWx/Wrf31cA2oA0ZsqK1VXp8V0XRhW5e6HS0h/Cxw9adob4YRcMRXR3CGl5+bZaJipX1rK/QvINEBrt2e+iqZ/c3dAiHgJDbb/v6weJ41R13qoK8PX3rL6GUl6i5rJEdFITIw+tg8QxnteRn6biSRXn4Ms71Kg8oInndXgB2oA0BqRU/u/jFheU1RV1IuvCMkHNlXFIudNiLLpBZBL4Bdr3GULA+JfgzYGw8Bm46X23fBVNA6hZwqQ2ksbDjk/Un2+H4Z7R5Sr2L1Bl6se9CJ/dquI5RhiQvDRoPwh6TYcPJ8GCp+CGNzyvw16KMiGsrVsuGLQBMYqDa2Hd69A0Epq1gWatIbS1um8Wo/7wL03FBKgohfzUi91Pubuh9JRlAQHhHSCmB/S6VRmK6O7qM2xtzxEiOsLQx2HF/0Hv26Dj1Q3bnsZ1lJdAUQZ0+0Xdy3UcCX5Byo1lNgOy80t1jnQcCe0GQJYBjbJKT8PpbFXpuOPVMPQ3sPqfED8cekzxvB57+HCy+g+45UOXb1obECOQEn56WtUs8g9W5bYvreDi38RiVGLUn7+sUkajYL96DOAfAlHJ0HXyBfdTq2T3+oUH/xp2fg7zn4AH1tk/gtG4l/xUkNXqgqEuAkKgw9Uqnffavzf8osJTlBRB+mIYcD/4+Ko/7GXPw5l8dRHmKayZiJGWuMeI38GhtfC/X0ObPuoiy5soylSeiKsedMvmtQExgoylKohtzeKoLIczx+H0sYtvxZb7Q2uV0YnupiaERXeD6B7K3+3j4Uxs/yAY/0/4aDKsfQ2GP+nZz9fY5nwGVj0uLFDH0P4F6hiM6eleXa5i77dQXXlhjkuHq5UBObiq/lGXK8mzFL1olaTuff3gF+/B24NVPOSeJd51UZWxXN13HOmWzWsDYgSrX1FD8R5T1XO/AFV64tLyE95Kp2sg+UY1dO9+E4THG61Ik7tHjUibx9W/bOI4QEDafPMYkJ1fqoSP6B7qeeteEBim4iCeNCD5aeAXfPF+DmsDN74Fn06FRb+H8f/wnJ76yFgGYe3cNjLSEwk9zZFNcGgNDHpYGQ6zMu7/VBbXgqf0hCpv4Phu5c60Z0TaNBLaXWWeXuknj8DhddB9ygWXm48vxA2BTA/HQfJSITLx8v3c+Vq46iHYNBtSf/CsptqoqoSsVSpW4yZXpTYgnmb1yyoXv8/t9S/rzTRrDVc/AwcWec8Jc6UipaUGVj3xj5p0Hq8SME4ccp8uV7F7nrrvftPFr3cYDicPqViip8hPuxD/uJRRf4LWveG7h+DkYc9pqo1jW1VlAje5r0AbEM+Su1f5ngfcb8wEKFfT/z71p/XT02pSl8YYTh+D0pP2xT+smKm44s4vIbb/5a7SDiPUvaeysc6dVBNua5s46BcAN/1HGfR5d6m5NkaSsQyEj5rn5Sa0AfEka16BgKbGlWBwNb5+MOFlOH0UVr5otJorF1s9QOojoqOaB+TtTaZy90DeHuW+upSWiapqgqfcWPlp6r6umefh8XD9a6p0/rK/ekZXbWQsUyOiJuFu+whtQDzFiYOw+yvoe4dbf1CP026AyiRb/6YaYWk8z3kDkuzYep3HqwmFJUWu1+Qqdn0Jwhe6Trr8PSGUGytrFVRXu1+LNQMrMqnu5bpOgpS7YO2rcGCJ22XZ5NxJVfDRje4r0AbEc6x9TQX+Bj5stBLXM+rPEBQGPz7umRNZczG5e1QGX1CYY+slXafmFB1Y7B5dDaW6WhVN7Diy9rkeHUZASYEapbibvDSV6RbWtv5lx76gRoTfzITTOfUv72oOrla/rVkNiBAiXAixWAhxwHLfopblxgkh9gkh0oUQT9e3vhDCXwjxgRBilxAiVQjxO3d9B5dRnAvbPoKe09Qs88ZGk3AY/Rc4vB52fGq0miuP3D2Oua+stO6tXEDe6sY6slGV6LHlvrISb5lN7wk3Vn4qRHa2L9PNP1jFQyrOqcq91VXu11eTjGXKXR7bz60f484RyNPAUillArDU8vwihBC+wCzgWiAZmCaESK5n/SlAoJSyO9AXuE8IEefG79FwNrypyqIPftRoJe6j163QdgAs/r13u0S8hbMFsH8hLH9B1XU6usW57VSUQsEBxwLoVnx8VG2s9KVqO97Gri9URQZrwN8WYW1UcUVPBNLz0hyrvBuZCBP+pUYDq15yny5bZCxTwXM3F8x0pwG5AfjA8vgD4EYby/QH0qWUmVLKcuAzy3p1rS+BEEs/9GCgHDjtavEu49xJ+Pk9NfHO28ocuBIfHxVQP3cSlvzJaDXeRcU5OLwR1s9S2Tmv9oCXOsInN6s/lv0LYdU/ndt2fppyVTgzAgHoPAEqzhpTV6ouKstV343O4+vPWOwwQtWWc2fWU0kRnM2rP/5xKb2mK8/Dyr9D1mr3aLuUokwVc3Wz+wrcOxM9SkqZAyClzBFCtLKxTBvgSI3n2cCAetafhzIuOUAT4DEppfde8v78LpQXw5DHjFbifqK7wVUPwPo3oOdUVbH0SqO6WtUrO7pF9aw4ukW5mKor1fthbVXNpH73QJu+akb1yn+owprFxx0vk19fE6n6iB8KAaGquGLiWOe24Q4ylsG5E3W7r6zED1fnWfZmaD/QPXryUtV9KwcTFUCV/sneDF/dAw+std0uwZVkLFP33m5AhBBLAFtH/LP2bsLGa/VNa+4PVAGtgRbAaiHEEillpg19M4GZAO3aGVAmpLwENrwFnUar6rhXAiOeVn9G8+6CmSshNMpoRe7ldM7FxuLoNnXBABDYTBmLwY9CmxT12JaB6H2bytjZ8anjFxq5u1VpDWfLyfgFQsIoFQfpPN5SrdcLKiTs+kJNuO10Tf3Lxg0BhBpFucuA5FsNiIMjEFAjqClz4Z2R8M19MP1L99awy1iukirCO7jvMyw0yIBIKUfV9p4QIlcIEWMZPcQAeTYWywZqpjTEAscsj2tbfzrwk5SyAsgTQqwFUoDLDIiUcg4wByAlJcXz9Ta2faQyRIY+7vGPNozAULjlI3h3lDIiM75rPC1wy87AsW01DMZWNQcGVFmXqG7Q8xY1smiTonzz9vxRtOwE7Qaq42Xwrx0rO5FrLWHi69RXAmDAA+pP59NbILiFahjW7SY1gmzIdp2lrFjV6eo13T4ffpNwVdMrc6W6gHEHeanqgqBZG+fWj+6myv/8+Disf9198dCqCpXW3G2yRyotu/PM/h64HXjRcv+djWV+BhKEEPHAUWAqykDUtf5hYKQQ4iOUC+sq4FX3fIUGUFUB615TbUSvNFdOdDeY+Kq62lr6Jxhj8IQqZ6iqVHn/NY1FfpoqmQ6qEnL7QReMRXR3VanYWXrfBt89CIc32H8VLaWqgdXlOuc/F9RcnicOKNfH7nlq5veWuaqVQNfJ0P0X0LqP50q/p81XXTPtcV9Z6TBCuU7d1eY2L01lYDVkH6TcpUZJS/8C7QZBWzdkSB3dosqXdPBMrx53GpAXgS+EEHej/vSnAAghWgPvSinHSykrhRAPAwsBX+B9KeWeutZHZW39B9iNcoH9R0q5043fwzl2falSECf8y2glxtBzqpqNu+51lUqYfEP96xiFtaNjttUNtQWObb/Q+jc4XBmK5BssBqOv6yeDdr0RFvwWtn1ovwE5kwvnipyPf9TELwA6j1O38rOw/yc1B2PTHNgwS7lDuv1CjUycceM4wq4vVAXZtgPqX9ZKh+HKDXh4PSSMdr2m/FTl4msIQsDE19SxNe8uuH+VGvG5kozlbi9fUhO3GRApZSFwmQNTSnkMGF/j+XxgvgPrn+GCMfFOqqthzavqxE4woOWmtzD2BXWyfPuQCj62TDBakeLcSVVoLnvLBYNx1uIh9Q1U7pC+d0CsJW7RIt79V98BIcrtsOtL1bI1qFn96xy3zkB3IoW3Xi2/ULdzJ1SxzF3zYPW/VNZYVDdV2LDbL1zfguBMvvoTHPyoY3GCtleBb4Aq7+5qA3ImH0oKHUvhrY3g5mp+yPtj4LuHlbvXlcdWxjI1WvRQtYtG4px2I9ZS5Y78yPt+hIJ9qtGMWTq+uQO/QLj5A5g9DD7/Jdyz1PNFJCvLVY/488ZiMxSmX3i/ZWfoNEoZitgUaNXVuCBynxmw9QPY87UyYPWR6yYDUpPgFkpXnxlqQuyeb5Sba8mf1K3tADUq6XojNLWVaOkge75RacmOuK8AApooLe6YUHg+gO4CAwIQ21dVb1j0rMoec1VtvHMn1fE99AnXbM8OtAGpj8IM+GiS+pPpNFoNDev6E5RSlWxvEa/mflzphMXCTe/Dh5Pg+1+px+42qkWZsOFtZTCO74SqcvV60ygVr+g5TRmL1r0dL//hTtr0VaXCt35opwHZA81iXe8GqY3QKLjqfnWz1nbb9RUseBJ++q1Kp+1+E3SZ6Px+3fWFGuE4WtcLlBtr2V/VJE1XpsrmWYoo1lbG3RkGPqQmGC58Btr2d01jr6xVKkbngfRdK7oWVn1UlUFUd9jxOXw2Df4RDx9cr3z7eWmXN1PKWqncI4MfbTzZRw2lwwgY+Zy6st74tvs/b+U/YPN7agQ04H6Y8gE8tgd+sw+mfQLDnlCavMl4gDKsvX+priKt8w7qIne3e0cfddEiDob+Bh5cBw+sV+nHJ7JUL4yXOqnZ9Xu+UZMo7aUoU8XNHB19WIkfoe6zVjm3fm3k7VXHiqNzdOpCCLjhTWjSUrXCLStu+DYzlqk5PbEpDd+WnWgDUh9RXdWfzm8PwozvYcB9cCYPFj0Hbw6AV7vDD49C6v/UQbD6ZVVfqNf0ejd9RTH4MRWEXPScyjRyF1KqEyn5BrhzPox5XrlXwmLN4U7sORV8/FVKb11UlqkJi9EuCKA3lKhkuOYP8Mh25aZMuVsZgi/vUMbk65mwf1H9M8V3faXunW1R27q3SrV19ax6axMpVx8/IRFw03tqNPe/xxrW2VNKyFjqkfIlNdEGxF78AtQQecxf4aEN8OvdcN2raui5ax58fiv8PV4dvAMfUle/mgv4+Ki+0c3bwRe3K3+6O8jbq7KTPDiMdykhLVV71B2fqvhNbRTsV7PbjRqB2EIIdfV77YvweKq64Oo2WZVq+WQK/DMRfvg1HFxzedVmKZX7qv1gaG5HtVtb+PpZ2tyuaOg3uVhXXqr7Ms/aD4IRz6jkifouGuqiKFN1QezomfRdK9qAOEvztpByJ0z9GJ7Kgtt/gIEPWnoB3Gm0Ou8kuDnc/CGUnrJ0bKt0/WdYyzh4KA/eLfSZobJ+9tfRLbChJUzcjY+vuuC6/nU1x2TaZ8qo7/wc5k6AV7rCwmfVxEwpIWeHMorOuq+sxA9XV/SuatV7Jld1e3Rl/ONShj6udM9/8kK8xVE8WL6kJtqAuAK/ADV0HP0XVbIgMNRoRd5LdDeY+G84tEZNMnQ1GctUwbswJ2cMewMdR0JoaxVMr43ju1TKcbgJCnT6BahR1U3vwZPpKjuxdS/YOBvmjIDX+6o/Tx//hs8XcnWb2/M1sNw498XHFya/o5JzvrxDlUByFA+WL6mJNiAaz9PzFlVMcN3rsOdb12234pzqsGdW95UVH18VQ8tYCqeO2l4md49KKzVbokZAiMrUmvYpPHlATawLa6NiJknjGz5/IbKzpc3tCpfIvdDG1omsMEcIjYLJc9Tn/fRbx9a1li/pONLjcT5tQDTGMPYFlVL73UO1/0k6yqF1UFlqfgMCKhtLVsOOT2y/72wTKW8iuAX0vV25f5/MgEmzG75NIZQ3IGtVw4LSVvJSVSWCkFo6IrqSjiOVO2vrf1Vc1V6yN6sCngYc99qAaIzBL1BdcZWfURPTXEHGMjUbuTHUHguPh7ihKrB6acD5TJ6aOe9NAfSGEhKhuvi5gg7D4Wz+hR7mDSEvVY30PHVlP+IZNav+h0fVHDR7yFjm0fIlNdEGRGMcER0hphfstVVn0wkylkO7q5SbpDHQZ4YKCB9ac/Hr1hno3pDC6424qs2tlJYUXjfX/qqJr5+KFfn6w7w7Vbp2fWQuV5NQPTWhtAbagGiMpeuNasb4ycMN207xccjb0zjcV1a6TITAsMuD6dYMrFaNaATiSpq3VckFDY2DnD6mKtu6qoSJvYTFqkmGOTtg8R/qXvbcCXX+GHTcawOiMZYu16v7vd83bDsZy9V9YzIg/sEq4Jz6vapzZCV3jyq1HhJhmDSvp8NwONTANrfWGlieHIFYSRoPVz2oKjek/q/25QwoX1ITbUA0xhLRUfXSaKgbK2OZKgsR1d01uryFPrepxICacaLjBpYwMQsdRqj42tGtzm/DOifD0yMQK6P+pFy83z1Y+wg9Y5ml82VfTyo7j9sMiBAiXAixWAhxwHJv00EnhBgnhNgnhEgXQjxd4/UpQog9QohqIUTKJev8zrL8PiGEFzVy1jhF8g2Qvcn5bKzqauUH7ni1e1uFGkFML2UUrW6sqgrllzd7Bpa7iRsKiIa5sfJTVfaVu3uY14ZfIEz5jzq+5919+WhKSkhf5vHyJTVx59n2NLBUSpkALLU8vwghhC+qQdS1QDIwTQhhTbjeDUwGVl2yTjKqc2FXYBzwpmU7GrNirVqc+oNz6+fuVlk3He3on202hFCjkJztavJgwQGortAGpD6ahENMj4ZNKMzzcADdFuEd4PrX1AXW8r9d/F5RJpw6fGHypAG404DcAHxgefwBcKONZfoD6VLKTCllOfCZZT2klKlSyn21bPczKWWZlDILSLdsR2NWWiaogLCzbqzzZRxMXL6kLrpPUenJWz/0TA+QxkKHEXBkk+qw6CjWDCyj3Fc16TZZlfdf8wqkL7nwukHlS2riTgMSJaXMAbDc2+o20wY4UuN5tuW1unBmHY23k3yDakdafNzxdTOWKQPkynLb3kSTcEi6TtWROrpFGRNv6e7ozcQPV6O1Q+scX/fUERVDMXoEYmXci2o2/Nf3XThHMpZB8/YeL19SkwYZECHEEiHEbhs3ewva2JqdU9/0UbvXEULMFEJsFkJszs/Pt1OSxhCSbwCk426s8hJleBrr6MNKn9tUUb+t/1XlOgzyeZuK9oNUH4+t/3V8XaMD6JfiH6zq7FWUwFf3QEWpYeVLatIgAyKlHCWl7Gbj9h2QK4SIAbDc59nYRDZQs3ZzLHCsno+1ex0p5RwpZYqUMiUy0gOlCDTO0ypJtZd11I11aJ3qONiY0ndtET8CwtqpPxAd/7AP/2DVmyT1B/tndVsxMoW3NiI7w/h/qk6GX8xQIySDj3t3urC+B263PL4dsPXP8DOQIISIF0IEoILj9U0I+B6YKoQIFELEAwnAJhdp1hhJ1xtV7v4ZW9catZCxTFWlbQzlS+rCxwd636oe6/iH/Qy4T43WNrzp2Hp5aaooY0OLO7qaXtOhxy1wYKFh5Utq4k4D8iIwWghxABhteY4QorUQYj6AlLISeBhYCKQCX0gp91iWmySEyAYGAj8KIRZa1tkDfAHsBX4CHpJSVrnxe2g8RfINalJUWh0Tpy4lY6kyHq6qo+TN9JmhGph1Gm20EvMQGq3+cLd9DGcL7V8v341NpBqCEDDhXxCRAO0GqR47RsqRrqhYaQJSUlLk5s2bjZahqQsp4Y0UaNYGbrdjZvqpo/BKMox+HgY/4n59GnOSvw9m9YcRv4MRl80muJzqavi/NtDndtVd0RspPQ1IFeNxM0KILVJKm43WTdZMwLVUVFSQnZ1NaWmp0VI0Voa8AaXFsGe36otRF+VnYOwX6iozNfWit4KCgoiNjcXfXwebr3giO0PiONg0BwY9AgFN6l7+5CEVa/LGEYiVoGZGKwCucAOSnZ1NaGgocXFxCAMzGTQ1KC+Bgn0QFl3/DOCig1AepILKNX4/KSWFhYVkZ2cTHx/vXr0aczDoEZg7XvWa73d33ctam0i5s41tI6GR1X1wjNLSUiIiIrTx8Cb8g9U8h9KTdS8npaqUGtjssjRGIQQRERF6ZKm5QPtBql7U+jegup6QqbWNbWRn9+syOVe0AQG08fA2hFCBwbIzUFVZ+3IV50BW1dp/Xv+umosQQo1CijIh7ce6l81PU3E4gwPUZuCKNyBG4+vrS69evejWrRtTpkyhpKTE6W3dcccdzJunqrbec8897N1be0e2FStWsG6d4zN04+LiKCgosPl69+7d6dGjB8OHD+fQoUN1bqfOzw9qDkgoO1X7BspOq/taDIhGcxldJkKLOFj3Wt3tbvNSvWv+hxejDYjBBAcHs337dnbv3k1AQABvv/32Re9XVTmXofzuu++SnJxc6/vOGpC6WL58OTt37mTEiBH89a9/rXPZOj/fv4lyY9XsgcEl+6KsGPyC9Yxsjf34+MLAhyH7Zzi8wfYy1VVQsN97ZqB7OdqAeBFDhw4lPT2dFStWcPXVVzN9+nS6d+9OVVUVTz75JP369aNHjx7Mnj0bUMHihx9+mOTkZCZMmEBe3oUJeCNGjMCatvzTTz/Rp08fevbsyTXXXMPBgwd5++23eeWVV+jVqxerV68mPz+fX/ziF/Tr149+/fqxdu1aAAoLCxkzZgy9e/fmvvvuw56074EDB3L0qCrNbmu7tj6/5ugJIWjasT+UFbNi2dKL9sWKFSsYMWI4N93+AElDruPWW2+1S5NGA0CvWyE4HNa9bvv9EwdV/xU9ArGLKzoLy5uorKxkwYIFjBs3DoBNmzaxe/du4uPjmTNnDmFhYfz888+UlZUxePBgxowZw7Zt29i3bx+7du0iNzeX5ORk7rrrrou2m5+fz7333suqVauIj4+nqKiI8PBw7r//fpo2bcoTTzwBwPTp03nssccYMmQIhw8fZuzYsaSmpvLnP/+ZIUOG8Ic//IEff/yROXPm1PtdfvrpJ2688UYAHn30UZvbvfTz33vvvUu2IgAJ5Wcv2hcrVqxg27bt7Fn6Oa27DmTwyHGsXbuWIUOGNGj/a64QAppA/3th5T9UafxLi1JaA+h6BGIX2oBYWfC06rfgSqK71zsR6dy5c/Tq1QtQI5C7776bdevW0b9///MpqIsWLWLnzp3nr9BPnTrFgQMHWLVqFdOmTcPX15fWrVszcuTldXE2bNjAsGHDzm8rPNx2aYYlS5ZcFDM5ffo0xcXFrFq1iq+//hqACRMm0KKFzb5gAFx99dXk5ubSqlWr8y6s2rZrFz7+UHbmon0B0L9PT2Jbx0BgKL169eLgwYPagGjsp9+9sPbfahRy/WsXv5evM7AcQRsQg7HGQC4lJCTk/GMpJa+//jpjx17cfHH+/Pn1ZhtJKe3KSKqurmb9+vUEB19eEsTejKbly5cTEhLCHXfcwR/+8AdefvnlOrdbEz8/P6qrq89rLi8vV1kwFSWENLl44legnw8EhoCPD76+vlRW1pGtpdFcStNI6DkNtn8CI5+DpjU6TeSlQVhbnZxhJ9qAWPHWkgXA2LFjeeuttxg5ciT+/v7s37+fNm3aMGzYMGbPns2MGTPIy8tj+fLlTJ8+/aJ1Bw4cyEMPPURWVtZFLqzQ0FBOnz59frkxY8bwxhtv8OSTTwKwfft2evXqxbBhw/j444957rnnWLBgASdOnKhTa3BwMK+++irdu3fnueeeq3W7l35+XFwcW7Zs4eabb+a7776joqLiQjZWdQ0DUVVhSd/1jpm4GpMy6FewZa6anT7yuQuve0sTKZOgg+gm4J577iE5OZk+ffrQrVs37rvvPiorK5k0aRIJCQl0796dBx54gOHDh1+2bmRkJHPmzGHy5Mn07NmTW265BYCJEyfyzTffnA9iv/baa2zevJkePXqQnJx8Phvsj3/8I6tWraJPnz4sWrSIdu3a1as3JiaGadOmMWvWrFq3e+nn33vvvaxcuZL+/fuzceNGNQILCAEfP9UUyEq5Jc1ZXyFqGkJER0iaAD+/e6FjYVWlysDSAXS7uaKLKaamptKli77a8GpOZcPZAhVP8vGFoix1wkd1rbeRjv59NXVyZBO8Nxqu/Ycq+56/H2b1gxvfUmXTNUDdxRT1CETj3ZyfVHjaUr6kWI0+9ExzTUNp2x/aDlDlTaoqvbOJlJejDYjGu7G6sc6dVBVS6yhfotE4zKBH4ORhSP3+QhtbnYFlN24zIEKIcCHEYiHEAcu9zfxPIcQ4IcQ+IUS6EOLpGq9PEULsEUJUCyFSarw+WgixRQixy3LfyHuZXuEIoUYhZaeh1FLaRBsQjavoPB4iOqnyJvmp0Ly9umjR2IU7RyBPA0ullAnAUsvzixBC+AKzgGuBZGCaEMJaf2M3MBlYdclqBcBEKWV3VKvcDxsi8kqJAZma4OaqU+GZfEu13vrLl+jfVWMXPj6qvMmxbbB/IbSqvfyP5nLcaUBuAD6wPP4AuNHGMv2BdCllppSyHPjMsh5SylQp5b5LV5BSbpNSHrM83QMECSECnREYFBREYWGh/rPxdgKaKjcW1Xal71r7gQQFBblfm8b89JwKTVp6fxMpL8Sd80CipJQ5AFLKHCFEKxvLtAGO1HieDQxw4DN+AWyTUpY5IzA2Npbs7Gzy8/OdWV3jSUpOqw6ETQG/Oqr0WrB2JNRo6sU/WGVhLf+bbiLlIA0yIEKIJUC0jbeetXcTNl6zazgghOgK/B0YU8cyM4GZgM35C/7+/rpjnVnI3w8bv4L+f9cVeDWuZ8B9KlEjsda/E40NGmRApJSjantPCJErhIixjD5igDwbi2UDbWs8jwWO2Vju0m3HAt8AM6SUGXXomwPMATUPpL7taryYyES47mWjVWgaK0FhMO4Fo1WYDnfGQL5HBbmx3H9nY5mfgQQhRLwQIgCYalmvVoQQzYEfgd9JKde6Tq5Go9FoHMGdBuRFYLQQ4gAw2vIcIURrIcR8ACllJfAwsBBIBb6QUu6xLDdJCJENDAR+FEIstGz3YaAT8HshxHbLzVZ8RaPRaDRu5IopZSKEyAcu7bPaEpUWbBRhQP0RYYXRWh3FTHod0erIb+Yu3LFv3fW9vOE4aKznmae0tpdSRtp644oxILYQQmyurcaLhz5/jpRypp3LGqrVUcyk1xGtjvxm7sId+9Zd38sbjoPGep55g1ZdysRYfjBagMZhGutv1li/FzTu72Yo2oAYiJRSH9gmo7H+Zo31e0Hj/m5Gc6UbkPobfHsPZtIK5tJrJq1gLr1m0grm0mu41is6BqLRaDQa57nSRyAajUajcRJtQLwMIXSnJA0IIXS9FjeizzPX0KgNiKVcvNcfLELxmBAiVprEpyiESBBCmKLcrRCihxCiqdE67MFyLPwJ+LX1uaGC6sEs5xiY7zwzwznWKA2IEOIOIcQ24FGjtdSHEGIGsBzoDZz29hNRCHGDECID+AvwrhAi3GhNtSGEuFUIsRP4M/C5pVyO1yKE+CXqWJgB/BLAW//ozHSOgbnOMzOdY43OgAghkoAHgf8Bw4QQHaSUUgjhdd9VCDEYmAs8IaWcIaU8bf3D8MYD3HIg3wNMl1JOQxXIfFYIkWissssRQlwL3Ac8IKWcBHQEJlre86p9K4TwFULcDdwLPCWl7AActVSc9jrMdI6Buc4zM51j0EgMiBDifI9TKWUa6gruFWAvqnYWUspqY9RdzCVa16IKSnaxvPe0EGKiEKKpt1x51tRrfQmw7svPUD1ZxnvD1b3VnWJhhZRymJRyrRAiDMi0LCO8aN/6Akgpq4DvpJTDpZSbhBBdgGJstzswhJouQG8/x+AyvV59ntlwr3rtOXYppjcgQvVR3yaE+LsQ4g7Ly/uklEWoku8dhRDDLMsa+n0v0Xq35eUHgQ+EENuB5sCvgJcsV3mGUkPvP4QQ0y37dBdwu1A97lOAzaieMG0MlIoQ4i/AH4QQ1po9ZZbXo4D5wEnUiegt+9aqtxWAlLLA8rqQUqYCcUAvy2tGH7dPASssx8EMUEbEG88xi4aaeu+0vOyV51kNrS8JIaYCJ/DSc8wmUkrT3oCRqJ7p8cDVQA7Qo8b7TVHByI9rvObrRVr7WN57CEixPI4EvgXGeuG+TQTaAy+jSup/DHQFVgBxBukMBH6HKpT5DTDGxjJhlvtwVLuA8Qbu1zr1Wo9P4BHgbYOPgQiU6+cLlDG7CdgItKmxjDedY7XpbW95/yGgr+WxoeeZDa1TLFojgA7edI7VdXNnS1tP4I9qaZsFZAkh/g38HzDB8v5ZYB7QRQjxPOrknQ3U2oTKw1pfAMZJKWdZF5JS5gshilB/dkZyqd7XgX9JKScCjwshoqWUxwGEKrsfDhw0QGcFyhf/GsqVcrUQ4oBFNwBSylOW+yIhRB7QwgCdVurUK5U7C9QI6pTFRy+kMe6hs8AiKeUnAEKIQ8A4VOO3ozWW8ZZzrDa9bYBDXnae1aa1g5TyZ7zrHKsVw4ebDaQJEGFNdZNSvgjECCGmWJ5LoBToDjwA5Ms6OhgaoLWVVSuoAJoQ4l9AD5TP1kgu1fsC0EYIcYvl+XEhRFshxCzUCbrPCJGWP9b9UsqzwOeoP7f+QohAuBAktezbf6Ku9gzbt3botcZx0oA7pcKQ2IKUspSLCxFWovZfDlwUT/KKc6wOvdk1l/OG86wWrT2B3BrLeMU5VhemMCC1ZUpIKb9BZddcV+PlfwCP13j+f8AeoJ2U8iW3ibTgrFYhRDzwKerKf7iUMt3NUrF8rqN6f13j+RuALzDB8ofoVurQWma5PwisAYYDSTXW64FyFVj37X53a7V8rsN6a4xA1gEvCCH8PJEpVIfW4hpPI4A8KeVhy3vWAPTf8eA5Bs7ptazXARWY9th55qxWC7Pw4DnmMEb70Oq6ATcAHwC9LnldAIGWx1NRvvo4y/N2qJ0eankeZAKtAUAQEG6SfdvU8ryJF2j1sTy2xg6aAa8D04HbgOssr0d6yb6tS+8vgUme0umE1iFYYh3AWCzxGyDYJHpHWB5HmECrdd+GePJ4cPTmdTEQ67BYCHE18DzKZzxQCHFISnmixrC5zHI18TmQDDwn1MSmicBBabHuUg0VvV1ruWWTbtPqYr1nAKSUJV6gVVq0FgEnpZSnhWqjPAsoRAWjkVLmu0urO/R6o1ZgGBAghHgL5bJ6BkBKec4EensAT1v0FppIq/eNOmpitAWrecNSHdjyOA6IQWUDzUUNN63v+aB2cD4wFNWycjDK2j+ptZpbrxNac4BrUVd2Sag5H8948b41TK+TWidYXvsYOAw86uX71hC9ZtLqqpvXjECEEA8D1wghVgGfSuUfBsgRQowFhgsh0qWUR1E50aeARCnlCctya4UQG+QFH7LWakK9TmpNtmoVQhwEuksPXbmZSW9DtaJidA9JKU+6W6vZ9JpJq0sx2oJZrO8kVDbE1cB/UMHZnjXe7wl8hA3/MCrAJDyh02xazaa3gVr9PLlfzaa3gVr9TbZvParXTFpdffOWLKwBwFtSyuXAn4AsahRpk1LuQP1A3YUQI4WaIW31N1ZJyy+htZpeb0O0VnpQpxn1NkRrhYe1mk2vmbS6FKNLJFjT2zJRWShIKQ+hZmCGCCGur7H4p6giY5+jUt48ipm0grn0mkkrmEuvmbSCufSaSau78KgBEaqonfVxzaJ284ASIcQNluc5qKn7yULRFPg3qkZMDynlk+DeUtdm0mo2vWbSaja9ZtJqNr1m0uopPGJAhBADhBDfAe8IIe4SQgRKKaW4MOv2BKou0AOWH+YUqsZOkGUnl6KyEyZIKXO0VnPqNZNWs+k1k1az6TWTVk/jdgMi1CzgWSgrPQ+V1tYJLpp1GwwsRFnuOUKI1qjGLxWW5SqllHlaq3n1mkmr2fSaSavZ9JpJqxF4YgTSF0iXUn4ILEbNuD4sxPkaRc+jrHcU8BtULZhPUJNrXvSAPrNqNZteM2k1m14zaTWbXjNp9TzS9Sltw4EBNZ63QlUW/RuqqNkG4H3gCdSP8QnQ6ZJteKpEhmm0mk2vmbSaTa+ZtJpNr5m0esPNlTs+FPgaNTX/faBFjfeSUAXXZtT4keZj6Ydhec3HY1/aRFrNptdMWs2m10xazabXTFq96eZKF1Y5sAxVEO4YqkEKcL4FZhIXyipvsSxjHQb6SM+WrDaTVjCXXjNpBXPpNZNWMJdeM2n1GhpkQIQQM4QQw4UQzaUqUf0usATYD6SIixvBLwL+aPEdTgW6AQXgmV7KZtJqNr1m0mo2vWbSaja9ZtLqrQjL8Mv+FdQOjEb5/qpRncdCUGlq1r7OCcDtQJmU8nnLa8HAHJRP0Rd4REq510Xfw/RazabXTFrNptdMWs2m10xaTYEj/i4u1K5PBD6yPPZD9TP46pJlJwFvAglYgkqWZaM94Zszk1az6TWTVrPpNZNWs+k1k1az3OyqxiuE8AP+AvgKIeajmuBUgcpxFkI8AhwTQgyXUq60vP6NEKILsABoKoS4WkqZChy35zOdxUxazabXTFrNptdMWs2m10xaTYcdVns4sAN4C7gX1aFuHKp2ff8ayz0ALK/xfAqqcfw7QCtPWEMzaTWbXjNpNZteM2k1m14zaTXjzZ4fYChwW43nb1p29h3AFstrPii/4hdAfI31hnr0y5hIq9n0mkmr2fSaSavZ9JpJqxlv9mRhbQG+EBfqvqwF2kkp56KGhL+SKgshFqiSUmYBSClXSylX27F9V2ImrWbTayatZtNrJq1m02smraajXgMipSyRUpbJC3VfRqPanQLcCXQRQvwPVa54q3tk2oeZtIK59JpJK5hLr5m0grn0mkmrGbG7pa3FgktUzZfvLS8XA8+gcqKzpGrXaDhm0grm0msmrWAuvWbSCubSayatZsKRiYTVgD9q8kwPi9X+PVAtpVzjZTvfTFrBXHrNpBXMpddMWsFces2k1Tw4EjABrkL9EGuAu90RlHHVzUxazabXTFrNptdMWs2m10xazXJzaCa6ECIWuA14Waqp/16LmbSCufSaSSuYS6+ZtIK59JpJq1lwuJSJRqPRaDTg4Z7oGo1Go2k8aAOi0Wg0GqfQBkSj0Wg0TqENiEaj0WicQhsQjUaj0TiFNiAajZsQQlQJIbYLIfYIIXYIIR4XQtR5zgkh4oQQ0z2lUaNpCNqAaDTu45yUspeUsiuqBtN44I/1rBMHaAOiMQV6HohG4yaEEGeklE1rPO8A/Ay0BNoDH6LaqQI8LKVcJ4TYAHQBsoAPgNeAF4ERQCAwS0o522NfQqOpA21ANBo3cakBsbx2AkhCFfKrllKWWnpwfyqlTBFCjACekFJeZ1l+Jqqh0V+FEIGocuRTpKXsuEZjJHZX49VoNC5BWO79gTeEEL1Q7VUTa1l+DKr4302W52GoPt3agGgMRxsQjcZDWFxYVUAeKhaSC/RExSJLa1sN+JWUcqFHRGo0DqCD6BqNBxBCRAJvA29I5TcOA3Kk6oZ3G2DtmFcMhNZYdSHwgBDC37KdRCFECBqNF6BHIBqN+wgWQmxHuasqUUHzly3vvQl8JYSYAiwHzlpe3wlUCiF2AHOBf6Mys7YKIQSqm96NnpGv0dSNDqJrNBqNxim0C0uj0Wg0TqENiEaj0WicQhsQjUaj0TiFNiAajUajcQptQDQajUbjFNqAaDQajcYptAHRaDQajVNoA6LRaDQap/h/sJrN/vDT6+8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the first 20 predictions vs the true values\n",
    "Results[:20].plot(subplots=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Out-of-Sample Performance\n",
    "\n",
    "Evaluate the model using \"out-of-sample\" data (X_test and y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out-of-Sample Root Mean Squared Error (RMSE): 0.4154832784856737\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "# Calculating the mean_squared_error (MSE) on actual versus predicted test \"y\" \n",
    "mse = mean_squared_error( Results[\"Return\"], Results[\"Predicted Return\"])\n",
    "# Using that mean-squared-error, calculate the root-mean-squared error (RMSE):\n",
    "rmse = np.sqrt(mse)\n",
    "print(f\"Out-of-Sample Root Mean Squared Error (RMSE): {rmse}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In-Sample Performance\n",
    "\n",
    "Evaluate the model using in-sample data (X_train and y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In-sample Root Mean Squared Error (RMSE): 0.5963660785073426\n"
     ]
    }
   ],
   "source": [
    "# Constructing a dataframe using just the \"y\" training data:\n",
    "in_sample_results = y_train.to_frame()\n",
    "# Adding a column of \"in-sample\" predictions to that dataframe:  \n",
    "in_sample_results[\"In-sample Predictions\"] = model.predict(X_train)\n",
    "# Calculating in-sample mean_squared_error (for comparison to out-of-sample)\n",
    "in_sample_mse = mean_squared_error(in_sample_results[\"Return\"], in_sample_results[\"In-sample Predictions\"])\n",
    "# Calculating in-sample root mean_squared_error (for comparison to out-of-sample)\n",
    "in_sample_rmse = np.sqrt(in_sample_mse)\n",
    "print(f\"In-sample Root Mean Squared Error (RMSE): {in_sample_rmse}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "YOUR CONCLUSIONS HERE!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Out-of-Sample Performance Root Mean Squared Error (RMSE): 0.4154832784856737 is lower than the In-of-Sample Performance Root Mean Squared Error (RMSE): 0.5962037920929946 so the Out-of-Sample data are more significant"
   ]
  }
 ],
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