regression_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 69,
   "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": 71,
   "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",
       "    </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": 71,
     "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(\n",
    "    Path(\"yen.csv\"), index_col=\"Date\", infer_datetime_format=True, parse_dates=True\n",
    ")\n",
    "yen_futures.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "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",
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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": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Trim 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": 73,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <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",
       "      <th>Returns</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",
       "</div>"
      ],
      "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   Returns  \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": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create 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",
    "# YOUR CODE HERE!\n",
    "yen_futures['Returns'] = yen_futures.Settle.pct_change()*100\n",
    "yen_futures = yen_futures.replace(-np.inf, np.nan).dropna()\n",
    "yen_futures.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lagged Returns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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",
       "      <th>Returns</th>\n",
       "      <th>Lagged Returns</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",
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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   Returns  Lagged Returns  \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": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a lagged return using the shift function\n",
    "# YOUR CODE HERE!\n",
    "yen_futures[\"Lagged Returns\"] = yen_futures.Returns.shift()\n",
    "yen_futures = yen_futures.dropna()\n",
    "yen_futures.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a train/test split for the data using 2018-2019 for testing and the rest for training\n",
    "train = yen_futures.loc[:'2017']\n",
    "test = yen_futures.loc['2018':]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create 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",
    "# YOUR CODE HERE!\n",
    "X_train = train[\"Lagged Returns\"].to_frame()\n",
    "y_train = train[\"Returns\"]\n",
    "X_test = test[\"Lagged Returns\"].to_frame()\n",
    "y_test = test[\"Returns\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "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 Returns</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 Returns\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": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 78,
     "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",
    "# Fit a SKLearn linear regression using just the training set (X_train, Y_train):\n",
    "# YOUR CODE HERE!\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": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make a prediction of \"y\" values using just the test dataset\n",
    "# YOUR CODE HERE!\n",
    "predictions = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assemble actual y data (Y_test) with predicted y data (from just above) into two columns in a dataframe:\n",
    "# YOUR CODE HERE!\n",
    "sample_results = y_test.to_frame()\n",
    "sample_results[\"Out of Sample Predictions\"] = predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<AxesSubplot:xlabel='Date'>, <AxesSubplot:xlabel='Date'>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the first 20 predictions vs the true values\n",
    "# YOUR CODE HERE!\n",
    "sample_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": 82,
   "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",
    "# Calculate the mean_squared_error (MSE) on actual versus predicted test \"y\" \n",
    "# YOUR CODE HERE!\n",
    "mse = mean_squared_error(\n",
    "    sample_results[\"Returns\"],\n",
    "    sample_results[\"Out of Sample Predictions\"]\n",
    ")\n",
    "# Using that mean-squared-error, calculate the root-mean-squared error (RMSE):\n",
    "# YOUR CODE HERE!\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": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In-sample Root Mean Squared Error (RMSE): 0.5963660785073426\n"
     ]
    }
   ],
   "source": [
    "# Construct a dataframe using just the \"y\" training data:\n",
    "# YOUR CODE HERE!\n",
    "in_sample_results = y_train.to_frame()\n",
    "\n",
    "# Add a column of \"in-sample\" predictions to that dataframe:  \n",
    "# YOUR CODE HERE!\n",
    "in_sample_results[\"In-sample Predictions\"] = model.predict(X_train)\n",
    "\n",
    "# Calculate in-sample mean_squared_error (for comparison to out-of-sample)\n",
    "# YOUR CODE HERE!\n",
    "in_sample_mse = mean_squared_error(\n",
    "    in_sample_results[\"Returns\"],\n",
    "    in_sample_results[\"In-sample Predictions\"]\n",
    ")\n",
    "\n",
    "# Calculate in-sample root mean_squared_error (for comparison to out-of-sample)\n",
    "# YOUR CODE HERE!\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": [
    "The out-of-sample RMSE is lower than the in-sample RMSE, although, it should be lower for training data. It fits better for the out-of sample than in-sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
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