Practical_Application_Effects_of_Advertising_on_Sales.ipynb

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   "source": [
    "# Effects of Advertising on Sales\n",
    "\n",
    "### LVC 1 - Introduction to Supervised Learning: Regression\n",
    "\n",
    "\n",
    "## Context and Problem\n",
    "\n",
    "- An interesting application of regression is to quantify the effect of advertisement on sales. Various channels of advertisement are newspaper, TV, radio, etc. \n",
    "- In this case study, we will have a look at the advertising data of a company and try to see its effect on sales.\n",
    "- We will also try to predict the sales given the different parameters of advertising. \n",
    "\n",
    "\n",
    "## Data Information\n",
    "\n",
    "The data at hand has three features about the spending on advertising and the target variable is the net sales. Attributes are:\n",
    "\n",
    "- TV    - Independent variable quantifying budget for TV ads\n",
    "- Radio - Independent variable quantifying budget for radio ads \n",
    "- News  - Independent variable quantifying budget for news ads\n",
    "- Sales - Dependent variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rzjQEUms29nL"
   },
   "source": [
    "### Let us start by importing necessary packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "Mbek6djw26sQ"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import numpy as np\n",
    "from sklearn import linear_model\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
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     "resources": {
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    "id": "eujy4X4H5Vgp",
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   "outputs": [],
   "source": [
    "# Let us import the files from our system. Note that you can also load the data from the drive. \n",
    "# The below code is applicable only if you are working on Google Colab, In case you are using Jupyter Notebook, you can directly use pd.read_csv(filename) to load data into dataframe\n",
    "\n",
    "#from google.colab import files\n",
    "#uploaded = files.upload()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 202
    },
    "id": "qIbGMZS36De1",
    "outputId": "403b1426-9d51-481c-c1ab-e5c93eb1fa4a"
   },
   "outputs": [
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
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       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
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       "    <tr>\n",
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       "      <td>17.2</td>\n",
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       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
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       "      <td>4</td>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
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       "   Unnamed: 0     TV  Radio  Newspaper  Sales\n",
       "0           1  230.1   37.8       69.2   22.1\n",
       "1           2   44.5   39.3       45.1   10.4\n",
       "2           3   17.2   45.9       69.3    9.3\n",
       "3           4  151.5   41.3       58.5   18.5\n",
       "4           5  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ad_df = pd.read_csv('Advertising.csv')\n",
    "\n",
    "# we have loaded the data into the Ad_df data frame. Let us now have a quick look.\n",
    "Ad_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "dQD08slX6tVt"
   },
   "outputs": [],
   "source": [
    "# we can drop the first column as it is just the index\n",
    "Ad_df.drop(columns = 'Unnamed: 0', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
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    "id": "PHN8-pYv7IAP",
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   "outputs": [
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       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
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       "  </thead>\n",
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       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
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       "    <tr>\n",
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       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
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       "      <td>9.3</td>\n",
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       "    <tr>\n",
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       "      <td>151.5</td>\n",
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       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
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       "      <td>10.8</td>\n",
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       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>38.2</td>\n",
       "      <td>3.7</td>\n",
       "      <td>13.8</td>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>94.2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>8.1</td>\n",
       "      <td>9.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>177.0</td>\n",
       "      <td>9.3</td>\n",
       "      <td>6.4</td>\n",
       "      <td>12.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>283.6</td>\n",
       "      <td>42.0</td>\n",
       "      <td>66.2</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>232.1</td>\n",
       "      <td>8.6</td>\n",
       "      <td>8.7</td>\n",
       "      <td>13.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        TV  Radio  Newspaper  Sales\n",
       "0    230.1   37.8       69.2   22.1\n",
       "1     44.5   39.3       45.1   10.4\n",
       "2     17.2   45.9       69.3    9.3\n",
       "3    151.5   41.3       58.5   18.5\n",
       "4    180.8   10.8       58.4   12.9\n",
       "..     ...    ...        ...    ...\n",
       "195   38.2    3.7       13.8    7.6\n",
       "196   94.2    4.9        8.1    9.7\n",
       "197  177.0    9.3        6.4   12.8\n",
       "198  283.6   42.0       66.2   25.5\n",
       "199  232.1    8.6        8.7   13.4\n",
       "\n",
       "[200 rows x 4 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ad_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lPtSvD8T-ALA",
    "outputId": "a18e28e4-458e-4708-941d-9eb423fd6653"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 200 entries, 0 to 199\n",
      "Data columns (total 4 columns):\n",
      " #   Column     Non-Null Count  Dtype  \n",
      "---  ------     --------------  -----  \n",
      " 0   TV         200 non-null    float64\n",
      " 1   Radio      200 non-null    float64\n",
      " 2   Newspaper  200 non-null    float64\n",
      " 3   Sales      200 non-null    float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 6.4 KB\n"
     ]
    }
   ],
   "source": [
    "Ad_df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TtclE25ghs4f"
   },
   "source": [
    "**Observations:** All the variables are of float data type."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vdPHnnpw_9oV"
   },
   "source": [
    "### Let us now start with the simple linear regression. We will use one feature at a time and have a look at the target variable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "q4UTFBGd9_Dr"
   },
   "outputs": [],
   "source": [
    "# Dataset is stored in a Pandas Dataframe. Let us take out all the variables in a numpy array.\n",
    "Sales = Ad_df.Sales.values.reshape(len(Ad_df['Sales']), 1)\n",
    "TV = Ad_df.TV.values.reshape(len(Ad_df['Sales']), 1)\n",
    "Radio = Ad_df.Radio.values.reshape(len(Ad_df['Sales']), 1)\n",
    "Newspaper = Ad_df.Newspaper.values.reshape(len(Ad_df['Sales']), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 107
    },
    "id": "Q4CKboT-CBgP",
    "outputId": "f8a42090-b219-41dd-db44-d5d42077480d"
   },
   "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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>7.032594</td>\n",
       "      <td>9.311638</td>\n",
       "      <td>12.351407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Coefficient</th>\n",
       "      <td>0.047537</td>\n",
       "      <td>0.202496</td>\n",
       "      <td>0.054693</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   TV     Radio  Newspaper\n",
       "Intercept    7.032594  9.311638  12.351407\n",
       "Coefficient  0.047537  0.202496   0.054693"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let us fit the simple linear regression model with the TV feature\n",
    "tv_model = linear_model.LinearRegression()\n",
    "tv_model.fit(TV, Sales)\n",
    "coeffs_tv = np.array(list(tv_model.intercept_.flatten()) + list(tv_model.coef_.flatten()))\n",
    "coeffs_tv = list(coeffs_tv)\n",
    "\n",
    "# let us fit the simple linear regression model with the Radio feature\n",
    "radio_model = linear_model.LinearRegression()\n",
    "radio_model.fit(Radio, Sales)\n",
    "coeffs_radio = np.array(list(radio_model.intercept_.flatten()) + list(radio_model.coef_.flatten()))\n",
    "coeffs_radio = list(coeffs_radio)\n",
    "\n",
    "# let us fit the simple linear regression model with the Newspaper feature\n",
    "newspaper_model = linear_model.LinearRegression()\n",
    "newspaper_model.fit(Newspaper, Sales)\n",
    "coeffs_newspaper = np.array(list(newspaper_model.intercept_.flatten()) + list(newspaper_model.coef_.flatten()))\n",
    "coeffs_newspaper = list(coeffs_newspaper)\n",
    "\n",
    "# let us store the above results in a dictionary and then display using a dataframe\n",
    "dict_Sales = {}\n",
    "dict_Sales[\"TV\"] = coeffs_tv\n",
    "dict_Sales[\"Radio\"] = coeffs_radio\n",
    "dict_Sales[\"Newspaper\"] = coeffs_newspaper\n",
    "\n",
    "metric_Df_SLR =  pd.DataFrame(dict_Sales)\n",
    "metric_Df_SLR.index = ['Intercept', 'Coefficient']\n",
    "metric_Df_SLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "IFjl_ZoW_njD",
    "outputId": "565cbed8-9980-4342-e3ae-a71f12a60f06"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TV simple linear regression R-Square : 0.611875050850071\n",
      "Radio simple linear regression R-Square : 0.33203245544529525\n",
      "Newspaper simple linear regression R-Square : 0.05212044544430516\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.611875050850071, 0.33203245544529525, 0.05212044544430516]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let us now calculate R^2\n",
    "tv_rsq = tv_model.score(TV, Sales)\n",
    "radio_rsq = radio_model.score(Radio, Sales)\n",
    "newspaper_rsq = newspaper_model.score(Newspaper, Sales)\n",
    "\n",
    "print(\"TV simple linear regression R-Square :\", tv_rsq)\n",
    "print(\"Radio simple linear regression R-Square :\", radio_rsq)\n",
    "print(\"Newspaper simple linear regression R-Square :\", newspaper_rsq)\n",
    "list_rsq = [tv_rsq, radio_rsq, newspaper_rsq]\n",
    "list_rsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 137
    },
    "id": "jMAZXp21AGsB",
    "outputId": "ed6b95e1-2bf4-4393-8fc6-4b6fb4f3e701"
   },
   "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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>7.032594</td>\n",
       "      <td>9.311638</td>\n",
       "      <td>12.351407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Coefficient</th>\n",
       "      <td>0.047537</td>\n",
       "      <td>0.202496</td>\n",
       "      <td>0.054693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R-Squared</th>\n",
       "      <td>0.611875</td>\n",
       "      <td>0.332032</td>\n",
       "      <td>0.052120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   TV     Radio  Newspaper\n",
       "Intercept    7.032594  9.311638  12.351407\n",
       "Coefficient  0.047537  0.202496   0.054693\n",
       "R-Squared    0.611875  0.332032   0.052120"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metric_Df_SLR.loc['R-Squared'] = list_rsq\n",
    "metric_Df_SLR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Es84uRdJhs4i"
   },
   "source": [
    "**Observations:** We can see that TV has the highest R^2 value i.e. 61% followed by Radio and Newspaper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6x63PBJxhs4i"
   },
   "source": [
    "Let's try to visualize the best fit line using the regression plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 803
    },
    "id": "_R45kkSNQxPx",
    "outputId": "a051ffa7-cf28-41ae-8fcd-32d0ee2ad30a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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j3DhgzZqx67u7gdWrRz9HdShm3ckVtP+RY7jaEZsRzz0H3HLLaIfsnXeG/37CBGCffUY7ZKdN8/7itsnq/w7qnG/shBeBnbsSfhEPs+DvGq+hqBs9LJomjWsxKlqng6iWjskhGmjVKuDWWz2RnzcPGBoK18Hx44G3vW1U6PfYw1uXGlkJdEFRMmUjtageAF0AXpN0u04WuXocIO6jdVS8ctB+zNJxx8TJsVOEOyAjl8dLL5E33UR+7WvkPvuQPT3hVe/u9kbRzp5N3nCDN1NVpmTlkknzfFa4Twed+PgBXALgNQAmArgPwDIAJ8TZNo1Fwu8AcW+0qBt9cDC4cWgWg7TSBAc1QnmSkgC++qqXW/7UU8l3vpNcb73oqu62m5cf59prvXw5bdFJWoys+lzSEOyK9wl1Kvx3+K8DAM4E0ANgYcQ2FwJYDmBRw7qTASwFcIe/zIhzfAm/I8S50eLcSHEEudMUAq5Z/G2O3FyzhlywgPzv/ybf9z4vYVnUA81OO5Gf/Sz5i1+QTz2VQtk7FUeXLeqKdxJ3Kvx3+2L/MwD7+evujNhmXwC7tRD+L8Y5ZuMi4W+Tom64qOPGeSrodCBVXJdSXucopsAMD5N3301+73vkoYeSkyZFC/3rXkfOnEledhn5v/9bXNlLiauZPFOiU+E/1rfUrwVgAPoB/CHGdlMl/DkzImQjF2+Rj7BhcfJBFmSUq6aTKRPNvAFaYb/J6hwFHGv44kE+9BB53nnk4YeTm20WLfRbYzGP6r6YF33qVi5Zkn5Rx1Blcaxyo8YOhb/lhsC4GL9pJfyPAFjou4I2jnMsCX9M4vi387qgo0S1sYEase77+4OzX7ZT/k6fPNLGL8+j2Io/6T2eH9/nIfb1RQv9pl3L+TFcwvPwST6E13I47/+yyuLooo8/xafQTi3+zQBcAOA6//OOAI6OsV2z8G8GoNuPDJoD4MKQbWcCGAIw1NfX13bFa0WciJa8rLQ4YhGnocryhoxryXZ4Iz7xBPnTn5Kf+hS53XbR1dx4Y/KQQ8jvfpdctIgcRsEWt4vimCZpu/s62V/K57pT4b8OwEdG/PoAxgG4K8Z2awl/3O+aF1n8MYkza1ReVlocUY3TUI0sI2mR4xLn5mu3cYq4EZ9+mrzqKvLYY8mdd46u2vrrkzNmkGec4XXkrl7dRjmzxuUOWpfoVLhT/q87Ff6/+q+3N6y7I8Z2zRb/lIb3nwNwWZzjS/hjEiWkeVppcS7gJNMbNvrmo4h788X5XYx6rFzphUqecAK5++7R1Vp3XfId7yDnzPFCM195JaX6iOLpVLhT7k/pVPhvAtALYIH/eU8AN0dscym8eP9XATwG4GgAFwO4y/fxX9PYEIQtEv6YBHVojlx4eXfstiuqnVo8SW6+KEu2xY24CuvyBhzA//gP8m1vI8eNCy/6uHHk3nuTX/2qN9gqcu7YVmWSxV0OOhVuxyz+3QDcCuA5//UBALvE2TaNRcKfABcEIqjjNo7FHbQksXjStJr6+/kKxvGPeBtPwWzujxu4Dl4MLWpXF7nHHuSXv0z+9rfk888nOF7cTnE1AG7SqXC75OP3tsc4ADsB2BlAT9zt0lgk/CUi6YXbLGRpzGnb4c23ejU5NESedhp54C5LORErI9ulXXYhjz+evOYa8tln4xc1Udnl8nGfNP6jHKJ6QpO0mdmhgV8CIHll2PdpoSRtJaLT5FlpTBeYcB/Dw8Ddd689peCzz4YfYvvt155ScJNN4hUtkrCkZn19SkxWBhyamrOt7Jxm9qOQfZLkv6ZRuCgk/CUijWyMadw4IfsggQcfHBX6G28EVqwI393UqaNCv//+wBZbJCtObMIaziVLOj+3olYoLbPIB0fT5S5ePCr08+YBS5eG/37KlLWFfptt8iln6NPK7NlOntvK4pDl3i4dp2UG8D4AXwLw1ZEl7radLrX28Tf6+3p7vcWVjr2g6BMH/NDLlpGXXEJ+8pPka18b7p8HvNP6oQ+R3/++N8F4rCkFs6KdVBciXSpyrtFhVM8PAfwEwKMAvgYvJPOCONumsdRW+KOiXoq8EKPy7eQcefLkk+TPf04ecwy5ww7RQv+a15AHHUSedRZ5551tTClYFK5G9bharnZxYdBcCnQq/AubXtcH8Ls426ax1Eb440a4uHAhFnVj+OfoOWzAX3Z9gJ/HGdy1ZxHNhkNP03rrke9+N/nNb5K33ebltRcpURHreC0qkpguSPjHxXQVvei/rjKzLQA8DSAvr2c9aPbtBs0b28ySJdmVqZ3jZlSeVauAP51yA+ad8Tjmrb4MQ5iONcP+5fvq2N+PHw+89a2jfvo3vznlKQXFKLNnr90nAXifZ88unU/8nwRFUPX15V+WLGjVGjQvAE4CsBGAQ+GNxl0G4JQ426ax1MLiTzKKNYmFndUjeMYW/8svk7f8x2958oZncl/cxPF4KfQ0dONV7jl+Pr/yFfL3vydfeCGVYiSjau6OuFTEOl6LijzFoB1XD4A9AGze8PlIAL8DcDaASWHbprk4K/xp3uhJ8taMLOPGhXf2ZnnxprzvV18l/+d/yG98g3zXu8j1xr8aWnXDGk7DfH4Bp/PXeC+fwwbFCk1FhKItKuIPH0MFGvJ2hX/BiMDDm1HrcQCHATgFwM/Dtk1zKVT484qwCLp5enuDZ6NqXiZM8JKZjZS301msoujgxlizhrz9dvLMM8n3vz/elII7YhH/HWfzShzMp7CxW0JTVfFrRfP/PmtWfRs9x2lX+O9seH8OgJMbPkdm50xrKUz4w8Q9amh9UkEMO1aSp4E4vy3AMh4eJu+5hzznHPKww+L1W2+LB/lvOJeX4qNchoipqYoWmiq6O1oRdJ02GhxKLOcM7Qr/IvgzbQG4D8C+jd+FbZvmUpjwh4l7mMB2Mkl4qxulXf9/0JKGFRpxUw8Pk3/7G3n++eS//Au5+ebRxdpqK/LII8kf/5hcvOVbW/+otzdeAri8qYvFH7eedXZ9OUS7wj8bXjbOqwHcjtGRvq8DcGvYtmkuhQl/mBUXdAMEuVe6utq/6MPSLSdd0rj5BgfJnp6199vTw8fOvoIXX0x+4hPx2qpNNiE/+lHy3HPJBx5oGjRVNuEoW3nbJe6TTV0aQsdpS/i97bAngEMATGxY93oAu0Vtm9bipMU/a1Zy0R0/vjPxj/KrBt2U3d3pPm77fprlmMzL8SF+Gt/n63FfZPU32og8+GDy7LPJu+6KMTq2bK6CspW3HeIKel1cX47TtvC7sDjl4x8/PtxBHdURm6bFk3Mn2zPPkFdfTR6Hs/hG3Bkp9BMnku99L3n66eT8+S2mFKw7ZWwo4j7ZyOJ3Agl/uzTenBMnhitdnCVriydFMVm5krzuOvJLXyKnT/e8VWFVWwcv8oAdl/HrXyf/9KcYUwpmUObSUGbXUJz/q8z1qxAS/riEhW/G8at3d3uzZye1+FtZ7zmL4YsvkvPmkSedRO61V4wpBfEK98IfeBL+kzdiP76IddqbdKIOApHFhDNplyntc17HBt0xJPxxCOpEHRHhuFZ9T09rl0+Qjz8qGVujiynFm+iVV8hbbyW//nXygAPIddYJL0JXl2f5f+n9i/ibce/jSgQ8AeU4W1YpiPP/5vVEGFamKja4ReJAwyfhj0OQCLUTQTOSQrnxc9Af3064Zhs36erVnq/99NM933scz9Ub30ged5zn23/mGYaPYWhHvOrQCZjk/82rwatDg1skjjSsEv44tBsimZX4dSgSw8Ne9MzZZ3vRNBttFL3L17+e/PSnycsvJ5cvb9phXMu1tzd+3dMUoMHB+I1tnsT9f/MUhjo0uEXiSMMq4Y9DFgOl4tzI7R636SYdHvbi4c8914uP33TT6F309Xlx9xdfTD72WErl7OmJL2BpWUaDg547rJOyZEVYOo6iXAGOCFNlcaRhlfDHIWl6hJGlleAkEbEkPuCmm3TxYm+k65FHeiNfozbZfHNvJO3553sjaxPNNJXk3CQRkDR8oWGNUtFi5shjv/NlqhKONKwS/rjMmpVM4EbcCWHCE8eyaxS/3t61HfDrr//PkbJ3YBd+AFdxoPtSbrvpPyKLN2mSlxvnnHPIe+/tcErBJE8mebsMwv4zF9wXDnT0jcHFMlUFRxpWCX8SGm+IsAFZzX9kGr7cpgvmQWzLI7ovia23G2zgZbs880zyjjtSnlIwSeqIKMsmbdFx2eIX8Yh7TbT6nYuNmANlkvC3S5AbplXHYQrRG0u33IOfwfdi72a99ch37fw4v7HRN/kXvJmv9r022wssjdHCWVhDLvv4RTRxr4lWv+vpGfvfy21FUsKfnGbXS5wY+jbitZ96ijzxxPjtxcjS10fefDP50o8uid8whdWxE4sk6X6y8n+6GtUjool7TbgYGuswEv4kBGSfjCUiESM0V2IiT8WJ7Eb4DFOtli9/mVyxoul4YTdCApdSZlZSq0bBkYgH4RBRfTRR146up5ZI+KNothZbLUni031emvlZfg+f4cZ4KrHQz8I5fBRbhgty1I0QZPXkEXUQ1Li4kK5AuEUcSz7s2tH11BIJfxitLPygJYLVq8mf/KS90PyBAfL++5nMddLuKNo8rO6w+HUHIh6EQyQZHCgff2xyF34AFwJY3jhTF4BJAK4H8KD/unGcfWUi/HEjdyKEf3iYvOoqL7VBUqE/6CBywYIU6hF2wxRp8Yc1Lg5EPGRCWJK/KtY3TRrPUZghU5aoHgcoQvj3BbBbk/CfBuBE//2JAL4VZ1+pC3+7A6Z8V8+8eV72yqSb74cbeTP2SV9gg9xUQXOhBp2DtK0kRwax5EbQOdVk5Mmp27WTEYW4egBMbRL++wFM8d9PAXB/nP2kLvwJ/TB/xe480H6TWOinTSN/9YV5HF4vp5s+aahlHml56yR4QddV0BOlRCyYul07GeGK8D/b9P0zcfaTuvBHdIjei+35UVyaWOi33Za85DN/4Oq+bTp7DE1LkMOspsbRxiPCFDdsNQl1egRPmu5DUSfh1OnayYjSCT+AmQCGAAz19fWlezaaBHExtua/4dzEQr/JJuQPf0i+/LK/3zSslDQtnTAhiuPqkoXVmiBBCmpog6Yuk8XfGgl+argi/MW6evwLajkm8ws4PbHQr7OOl8v+hRcC9p+GXzJN32ZS14PEKZqwhjlo9HB399ioMTWqrZGLJ1VcEf7Tmzp3T4uzn06F/9lnyZMPjZ4cvNVy0kn+BCRxSCNEMsk+oiyjoJsoyQmQO2JtohrmoDjzIlMwl4mydeo6/nRSRFTPpQCWAXgVwGMAjgbQC+AGP5zzBgCT4uyrXeH/4Q+TC/1xOIvLlrV1uHwt/iS5TZovTA17b5+ohrkuo5KzErwynb8SPJ3UbgDXokXxdO0TuIAPY+roiu7uxMf6J3n6+DtpZOKGszp2ETtB1Hkvm8XaDlkKXpnOXwnKWjvhf/jh1tp2GH7Gu7BTsNjNmpX4WGuRhiUUZx+dWkZ5RfVUjSjRK4EV2DFZCl6Zzl8Jnk5qJ/wcHOR9W+zP03AC/7z5wa1j2seNG/3zurs7F/08KYG1UVni9K047PcdQ9LyZi14ZTl/JbgH6yX8Qa6MiROLsWizSBdcJstIuEs711EJBC8x7TQ2JbgH6yX8YZ2Xef8xQSF+aUwQUhbLqE6U7T9pR8RLIHiJ6KQ+jv/f9RL+dlMVZ0FYI1SUheT4xVpayiiI7bptqnQNVfEJxidI+M37zm2mT5/OoaGh+BtMnQosXhz8vRkwPNxxuWLR1eVdRkWXY4S5c4GZM4FVq0bXTZgAnHceMDCQb1mqRtB1198PPPJI3qWJRxnLnDZB92gR92fKmNl8ktOb13cVUZjMmTPHE7Mg+vrGrps717sJurq817lz0ylLq2PF+S4rZs9eW/QB7/Ps2fmXpWosWZJsvQu0ulcmTPDW14Wg+7CI+zMnqin8AwOeBdvbO/a7Vhf1iBW8eLHX8i9e7H1OQ/znzAHGjx+7vqenmJurjOJUFsooICP3Sn+/Z+H292f/9JeVkdUudWz8Wvl/XFs6StkQxxeZtY8vi6iedqmwP7NwyujjzxtXz1GV+iwaQK18/EmpsI9vDPLxZ8vcuZ7bbMkSz9KfM0fntRH1KeRKvXz8SUn6iO7aowwrXFMAAAojSURBVGoSini0zwNX/pOBAU/Ahoe917Kf17SRq9EJJPxAMh9flv0BeVE1carCf1IXytgPUkEk/EAyK1hRMe6h/6Q81LEj1UHqLfyN7oHZs72LL8oKLuujqiuukCwo639SF5rvs6OOqp6rsVPyvj9b9fi6tqQ+5y7ZfnRBGaNiXI2kSIsy/id1oerXXhpkeI5Qq5QNcWhXLMp4IVddGDuZlEZkS9WvvTTI8BxJ+JsJy+cTRdkEpAR5wzum3WkoXf/vyk4drr1OyfAcBQl/fX38QVEEZtH+tbJFxYRFUlTF9x/1n6gDuBgUxRNNAeeovsI/Z44n8s2Q1RODoEiKGTOyD4N0pWFRB3AxtBPF48o1kxdFRDq1egxwbcnE1UMGu3qq+BiaZNL1NFNVuOJeka+5OJK4Rl26ZvIkI/cxlLKhBXUfPp51qgqXzq9SVZQDl66ZCqCUDa2o+2CSrH2LLrlXqpqqomq4dM1UmHoLf93FIOuGz7WOvbJ1ytcR166ZilJv4Qc6E4Oyd0Jl3fDV/YlKJEfXTD60cvy7tmTWudsJde2ESkrZxjyI4tE1kxpQ527KqBNKtIty9oucUOdu2qgTKh5ld4eljVJICweQ8LeLOqGikciNJWwEsRpJkRP1EP4sbih1QkWjNAljCXoiHGkU4zaSaiREJ7Ry/Lu2dDzZeladsOqECkcJusYSNIK4uzv+yGIFFoiYwKXOXTN7BMBKAGsArGaLzodGOurcVSdscejcjyVoBHHzk9EIrUZR67yKmLjYubs/yV2jRL9j1AlbHHKHjSVo7ER/f+vft+oz0jUtOqT6Pv4knbDym6ZL3UdGB9Fq0GCSRlKBBaJTWvl/sl4A/B3AAgDzAcwM+M1MAEMAhvr6+tp3ciWZnUl+U1EkcfuMdK2KmMClGbgAbOG/bgrgTgD7hv2+45G7cW4ope0VZUKBBSIGQcJf+MhdMzsZwPMkzwj6TS4jd7NOUSyEEDnjTOeumU00sw1G3gN4N4BFeZdjDPKbCiFqQhGdu5sB+KOZ3QngNgC/JvmbAsqxNopAEULUhHF5H5DkwwDelPdxIxmJNFHyLCFExcld+J1mYEBCL4SoPNWP4xdCCLEWEn4hhKgZEn4hhKgZEn4hhKgZEv46opxEQtQaRfXUjea0wCMTfgCKaBKiJsjirxuaFUuI2iPhrxvK5S5E7ZHw1w3lJBKi9kj464ZyEglReyT8dUOzYglRexTVU0eUk0iIWiOLXwghaoaEXwghaoaEXwghaoaEXwghaoaEXwghaoaEXwjhNkoqmDoK5xRCuIuSCmaCLH4hhLsoqWAmSPiFEO6ipIKZIOEXQriLkgpmgoRfCOEuSiqYCRJ+IYS7KKlgJiiqRwjhNkoqmDqy+IUQomZI+IUQomZI+IUQomZI+IUQomZI+IUQomYYyaLLEImZrQCwuM3NJwN4MsXilIU61lt1rg91rHc7de4nuUnzylIIfyeY2RDJ6UWXI2/qWG/VuT7Usd5p1lmuHiGEqBkSfiGEqBl1EP7zii5AQdSx3qpzfahjvVOrc+V9/EIIIdamDha/EEKIBiT8QghRMyot/GZ2oJndb2YPmdmJRZcnC8zsQjNbbmaLGtZNMrPrzexB/3XjIsuYNma2tZndaGb3mtndZnacv77q9V7XzG4zszv9ev+nv77S9QYAM+s2s9vN7Ff+50rX2cweMbO7zOwOMxvy16VW58oKv5l1AzgHwHsB7AjgcDPbsdhSZcKPARzYtO5EADeQ3A7ADf7nKrEawBdI7gBgTwDH+P9t1ev9MoADSL4JwK4ADjSzPVH9egPAcQDubfhchzrvT3LXhtj91OpcWeEH8GYAD5F8mOQrAC4D8MGCy5Q6JG8B8HTT6g8CuMh/fxGAg3MtVMaQXEZygf9+JTxB2BLVrzdJPu9/7PEXouL1NrOtALwPwPkNqytd5wBSq3OVhX9LAI82fH7MX1cHNiO5DPBEEsCmBZcnM8xsKoBpAP6CGtTbd3ncAWA5gOtJ1qHe3wbwJQDDDeuqXmcC+J2ZzTezmf661Opc5Rm4rMU6xa5WCDNbH8AVAI4n+Q+zVn95tSC5BsCuZrYRgF+Y2c5FlylLzOz9AJaTnG9mby+6PDmyF8nHzWxTANeb2X1p7rzKFv9jALZu+LwVgMcLKkvePGFmUwDAf11ecHlSx8x64In+XJJX+qsrX+8RSD4L4CZ4/TtVrvdeAD5gZo/Ac9ceYGaDqHadQfJx/3U5gF/Ac12nVucqC/9fAWxnZtuY2XgAHwNwTcFlyotrABzlvz8KwNUFliV1zDPtLwBwL8kzG76qer038S19mNl6AN4J4D5UuN4k/y/JrUhOhXcPzyN5BCpcZzObaGYbjLwH8G4Ai5BinSs9ctfMZsDzD3YDuJDknIKLlDpmdimAt8NL2foEgK8BuArA5QD6ACwB8GGSzR3ApcXM9gbwBwB3YdTv+xV4fv4q13sXeJ163fCMtstJ/peZ9aLC9R7Bd/V8keT7q1xnM3stPCsf8Nzxl5Cck2adKy38QgghxlJlV48QQogWSPiFEKJmSPiFEKJmSPiFEKJmSPiFEKJmSPhF5TGzNX6Ww0Vm9suRWPgE299kZtP999e2sf00M6OZvSfkNz82sw8l2a8Q7SLhF3XgRT/L4c7wEtod0+6OSM7wR80m4XAAf/RfhSgcCb+oG3+Gn6zPzN5sZn/y87z/ycy299evZ2aXmdlCM/spgPVGNvbzpE/233/ef4pYZGbHtzqYP8r4QwA+DuDdZrbuyHoz+56Z3WNmv0ZDwi0z+6a/fqGZnZHJWRC1pspJ2oRYC3+OhnfAS/cAeOkO9iW52szeCeBUAIcBmAVgFcld/NGyC1rsa3cAnwDwFngJAf9iZjeTvL3pp3sB+DvJv5nZTQBmALgSwCEAtgfwRgCbAbgHwIVmNsn/7g0kmdStJEQcZPGLOrCen8r4KQCTAFzvr98QwM/Mm73sLAA7+ev3BTAIACQXAljYYp97A/gFyRf8HPlXAtinxe8Oh5dcDP7riLtnXwCXklzjJ+Sa56//B4CXAJxvZocCWNVGfYUIRcIv6sCLJHcF0A9gPEZ9/KcAuNH3/R8EYN2GbaJymUTmgPafMA4D8FU/u+R3Abx3JAFXq2OQXA0vE+MV8Cba+E3UcYRIioRf1AaSzwE4FsAX/bTOGwJY6n/98Yaf3gJgAAD8fPe7tNjdLQAONrMJfgbFQ+AljmvknQDuJLk1yakk+zEq6LcA+Jg/scoUAPv7x1sfwIYkrwVwPLwpFoVIFfn4Ra0gebuZ3Qkvxe9pAC4ys89j1NUCAD8A8CMzWwjgDgC3tdjPAjP7ccN357fw7x+O0SyLI1wBrw9hBoAD4GUYfQDAzf73GwC42u8ENgCfa6eeQoSh7JxCCFEz5OoRQoiaIeEXQoiaIeEXQoiaIeEXQoiaIeEXQoiaIeEXQoiaIeEXQoia8f8B/8yNLxyiL/AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(TV, Sales,  color='red')\n",
    "plt.xlabel('TV Ads')\n",
    "plt.ylabel('Sales')\n",
    "plt.plot(TV, tv_model.predict(TV), color='blue', linewidth=3)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(Radio, Sales,  color='red')\n",
    "plt.xlabel('Radio Ads')\n",
    "plt.ylabel('Sales')\n",
    "plt.plot(Radio, radio_model.predict(Radio), color='blue', linewidth=3)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(Newspaper, Sales,  color='red')\n",
    "plt.xlabel('Newspaper Ads')\n",
    "plt.ylabel('Sales')\n",
    "plt.plot(Newspaper, newspaper_model.predict(Newspaper), color='blue', linewidth=3)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QxiuPBWPQnKm"
   },
   "source": [
    "## Multiple Linear Regression\n",
    "\n",
    "- Let us now build a multiple linear regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "p0XdOsasQ_uq",
    "outputId": "1e84b03f-b378-45d7-9dc5-eaf412a0d233"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr_model = linear_model.LinearRegression()\n",
    "mlr_model.fit(Ad_df[['TV', 'Radio', 'Newspaper']], Ad_df['Sales'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "f45Fynt_WSIr"
   },
   "outputs": [],
   "source": [
    "Ad_df['Sales_Predicted']  = mlr_model.predict(Ad_df[['TV', 'Radio', 'Newspaper']]) \n",
    "Ad_df['Error'] = (Ad_df['Sales_Predicted'] - Ad_df['Sales'])**2\n",
    "MSE_MLR = Ad_df['Error'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2IR7lKmrYCpl",
    "outputId": "6396556a-5894-4906-8813-df3812f74706"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.7841263145109365"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE_MLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yXJ6F7b5OqPI",
    "outputId": "86c85dea-76e6-4860-e13f-f315c9407c2d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8972106381789522"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr_model.score(Ad_df[['TV', 'Radio', 'Newspaper']], Ad_df['Sales'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qsZJ-jimhs4k"
   },
   "source": [
    "**Observations:** The R^2 value for the multiple linear regression comes out to be 89.7% i.e. way better than simple linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UijVypbEhs4k"
   },
   "source": [
    "Let's now try to use statsmodel to get a more detailed model interpretation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qjFCh7tkWf0M",
    "outputId": "5dbf05c8-631e-4d00-9b19-743ba7e18954"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.897\n",
      "Model:                            OLS   Adj. R-squared:                  0.896\n",
      "Method:                 Least Squares   F-statistic:                     570.3\n",
      "Date:                Sat, 28 Aug 2021   Prob (F-statistic):           1.58e-96\n",
      "Time:                        15:28:21   Log-Likelihood:                -386.18\n",
      "No. Observations:                 200   AIC:                             780.4\n",
      "Df Residuals:                     196   BIC:                             793.6\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      2.9389      0.312      9.422      0.000       2.324       3.554\n",
      "TV             0.0458      0.001     32.809      0.000       0.043       0.049\n",
      "Radio          0.1885      0.009     21.893      0.000       0.172       0.206\n",
      "Newspaper     -0.0010      0.006     -0.177      0.860      -0.013       0.011\n",
      "==============================================================================\n",
      "Omnibus:                       60.414   Durbin-Watson:                   2.084\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.241\n",
      "Skew:                          -1.327   Prob(JB):                     1.44e-33\n",
      "Kurtosis:                       6.332   Cond. No.                         454.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# let us get a more detailed model through statsmodel.\n",
    "import statsmodels.formula.api as smf\n",
    "lm1 = smf.ols(formula= 'Sales ~ TV+Radio+Newspaper', data = Ad_df).fit()\n",
    "lm1.params\n",
    "print(lm1.summary())  #Inferential statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "w2aGVrtKnY7G",
    "outputId": "52b420f6-4dd9-427d-d7f6-b3768e289483"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*************Parameters**************\n",
      "Intercept    2.938889\n",
      "TV           0.045765\n",
      "Radio        0.188530\n",
      "Newspaper   -0.001037\n",
      "dtype: float64\n",
      "*************P-Values**************\n",
      "Intercept    1.267295e-17\n",
      "TV           1.509960e-81\n",
      "Radio        1.505339e-54\n",
      "Newspaper    8.599151e-01\n",
      "dtype: float64\n",
      "************Standard Errors***************\n",
      "Intercept    0.311908\n",
      "TV           0.001395\n",
      "Radio        0.008611\n",
      "Newspaper    0.005871\n",
      "dtype: float64\n",
      "*************Confidence Interval**************\n",
      "                  0         1\n",
      "Intercept  2.323762  3.554016\n",
      "TV         0.043014  0.048516\n",
      "Radio      0.171547  0.205513\n",
      "Newspaper -0.012616  0.010541\n",
      "*************Error Covariance Matrix**************\n",
      "           Intercept            TV         Radio     Newspaper\n",
      "Intercept   0.097287 -2.657273e-04 -1.115489e-03 -5.910212e-04\n",
      "TV         -0.000266  1.945737e-06 -4.470395e-07 -3.265950e-07\n",
      "Radio      -0.001115 -4.470395e-07  7.415335e-05 -1.780062e-05\n",
      "Newspaper  -0.000591 -3.265950e-07 -1.780062e-05  3.446875e-05\n"
     ]
    }
   ],
   "source": [
    "print(\"*************Parameters**************\")\n",
    "print(lm1.params)\n",
    "print(\"*************P-Values**************\")\n",
    "print(lm1.pvalues)\n",
    "print(\"************Standard Errors***************\")\n",
    "print(lm1.bse) \n",
    "print(\"*************Confidence Interval**************\")\n",
    "print(lm1.conf_int())\n",
    "print(\"*************Error Covariance Matrix**************\")\n",
    "print(lm1.cov_params())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "drlo5QI2h2oY"
   },
   "source": [
    "### Visualizing the confidence bands in Simple linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "daxXRhFiip3e",
    "outputId": "97113a83-dc13-4b6f-c95d-7158305f0016"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x22adbd435e0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7VnUlNjHzxbGL3Xy0tGb3W2d5Yl8f/aP2F5ACfmtjF/dtXUNPZ/nDPs0eJy0+F94Z/TjnopIx7ncB9wKvKqVeSh77U2zB/qZS6g+BfuDDFRyDINSceiiYVEl2HxnmT55+kWAsgdfpYGnAQ8DrynuN5dzEjCZMRqZjRPI0NCh089HSml8eO8fje3vpHTk/ju2XLOW+m9awtrOp6LHNhVKKgNdJq8+Fy1F8AnslXSW/Is80H3h3pV5XEOqNxVwYKjXTDsVMnIYiYWlOjUdY2WbPJHNdYzk2MROmxWgoxnRkdiGoTObbfNRa8+u3R3hsXy/HzwbTz/uNDUu4b9saLlraXPCYCsFhKFp9LgJeFw5jjt3HeZAiU4JQYRZzYajUasLjNEiYGsNQWGjOTkVxGCrnNZbSNLjYxryZbcEyNx83r2tn7zvneHxvH8eGp9OP37a+k/tvWsOGZYHibsQ8zNhwLPl8ItzCBUOtNghr1d28GtebWk0safZwaiJs50grTSRh5b3G7Ru7+BwUXW9lLj/2XGxZ35F2iWitOdA7yv/+jRd568xU+jE3ruvg/pvWcuny8gq2z+2g1Tdrw7FkpFaJcEFQKSdDMa9fzcJQ1breHTv3p1cTk+E456ajRBMWfreDL969qSyvFYnbdUXyxbELQWvN4f5xvvrrXt4Ymkwf37y2nY9vW8vlK1tKHmcKpRRNHluwPc7CNxzznS7XQZlxCxcEtd4gzNXdvJIz4mKvd6FjyVxNBLxOnA5Vti+IQuPY8/HSgC3Yr56cSB/b1NPGJ25ay5WrWks6dyYOQ9HidSXvQ2UrZotwCxcE9bZBWGmLYDHXW8pYFhr2mAutNT94ZYgv/+oEQxOFlVpNJdFkZkf63A6+ureXlwbG04+7enUrn7hpLdd0t+U9V7G4nQYtvvLFrwtBhFu4IKi3DcJKrwCKud5Sx5JrNbFQpqMJnntliC/87GjBndQzsyNbvE5OTYT47L++nu6aDnDlyhbuv2ktm3rayiaufrdt5/O5Sw6HFI10wBEuCOqtc8zAWCjLWwzlXQEUc72VHkshROImp8bDDE9G+Mbz/UV1Uk+VZlXAyfEIw1OxtGhftiLAX33oKh65+1quW9NesmgbStHic9Hd4Wd5q7cmog0y4xYuECqxpC+FSq8AirneWq5GcsWxi8127B8LEo1bWZmaHqeB32Xwdzs2lWWG7XIY6fi1UYL/ulyIcAsXDOVc0pdKNSyChV5vLeyKlqUZD8dz9ngsNNvxneFpHtvby2gwnj7mcRp0NrkxFCxp9pYs2h6X7Q5p9tSXVNbXaAShDqmE+6OeVgDVHstkJM5YMIZpLayT+olzQR7f28ueY+fSz3EmMxLb/U6iCT1n5/VC8LudtPmLqx9STcTHLQhzUGv/dz1Qri+uUCzByHRhCTS5Sq0ua/XwxL4+dr91lpRqren08/Fta/E6Db55aDBnadZCUUrR7LE3HN3Outn+k2bBglAsmQkmKUKxBF0BL089sLWGI1s4xQhxOb64ogmTsWCcUGxhfuyB0RBf29/Hz98cTgv26nYfH9+2lu2XLi2p5gec33BsqYL/egFIAo4gFEu9+b9LpVjPdilWwZmNeYvl5HiYr+/v46dvnCEVVVnV5uO+bWu4dWNXyYLtNIxkwaf62HAsBhFuQZiDevN/l0qxQryQL65iC0HN5PREhK/v7+NHr59OC/aKVi/3bl3Dey9fVrJgl7vgUy0Q4RaEOahVgahKUawQF/vFNRWJMxaMk7CKKwQFcGYywpPP9/PD106nNy67Ah7u3bqG37liWclhDG/SIdJUZw6RhdD4VyAISerJ/VGvrcqKFeJCv7h+8tpp/mHPO5wcLyxFPZOzU1GefL6fH7w6RCIp2EubPdxzYw+/e9XyBTUayKQpueFYrw6RhSCbk8KioJ7cH/U0lnKMba7KhnHT4vsvn+KvfvzWnA15czEajPHkgX7+9eVTxE1bhzqb3NxzYw+3XbWiJGdHnTpEFoJsTgqLl1pX/6vXscxkISuIXIk8lqUZC8WYjCR4fG9fOkUdSH8hPH1wIKdwj4ViPH1ggGdfPkU0mZre7ndxz409/N5VK/CUMDNOVehr8ZXWYabeEeEWFgX15P6op7HkotQM0pkJNIWmqE+E4jxzaIB/efEkkaRgt/lc3LW5m9uvXVlSKMPlMNKWvkbdcCwGEW5hUVBP7o96Gks5CcdMRoLRrKp7MH+K+mQ4zrdeGOS7h08STjZDaPE6uWtzN79/7aqSCjXNt+FYr3sNpdLQwR9BSFFP1f/qaSzlIG5anJmMMDQRniXaYKeoJyxNOG6isX8mLM0Hr1nJV399gnu+/DzfeL6fcNyk2ePk371rLU/+0Y3s2NKzYNFu9jhZ2eZjZZtvTtH+7LOvMzwVyfKs7z4yvKDXrCdkc1JYNFS7PVijjGWhmJZmPBnHnqkTMxsXbOpu5cWBCU5Phlna7GVZq4d9x0cIRu0ZdpPbwZ3Xr+ZD169ecMEmQykCXictPldBTpOFZL3W4QxdUt4FQZgfrTWT4QTj4dyFoDIbF2S6SP74N9bTPx7im4cGmUqWafW7HXzoulXcef1qAl7XrHMVwkIzHG/+/C7afK6smHcqOeiXn7511uPr1A0krhJBKJY6nIHNSanjLaSTeqpxQSqm7XEaTE5H+dwP30wLvddlcMemVXzkhm5afQsTbLfToM3vpsntWNCGY7F7DfXsBpqJCLewqClFyCrdF7LclDLeSNxkJBgjWkAn9ZSLxErOXkeDcczkyt3jNLj92pXctbmbdr97Qdfhczto87lL7i5TbNZrvbuBMhHhFhYtpQpvrWZgC/2yWch446bFWDDGdLTwyn3LAl7eOTtFMJY9K1/a7OFLH7uOjqbiBVspRZPHdoh4nOXJcCzWs95IbiARbmHRUqrw1mIGVsqXTTHjnWvjMR+xhMWXdr/Da6cmyAx9p4IYv3fV8qJFWyU3HFsL3HAslmI8641Ul0aEW1i0lCq8pczAqjlrLma882085iJuWvzotdP80697mQjPLtHqcihafU5eHJjg3oLOWJ8ZjvXUlWg+RLiFRUupS9+FzsCqNWsudryFbDxmkjAtfvLGGb62v48zk9H0cQU4DTAMA0trHIaize/O28w3k3rPcKynvqRzIcItVJ1qOTVKXfoudAZW6VlzseO9cX0ng2OhnMkzuTAtzc/ePMMT+/oYmogAYCjb5bG8xcOZySiJZFEopewZea5mvpnUa9PdRkXuolBVqunUKMfSdyEzsErOmosZbyxhMRqMMTQx/0wYbMH+t7eGeWJfH4Nj9nMMBe++bBn3bV3DX//kKCPBKO1+N8NTEeyS2xpDqbzNeRdjSdV6QIRbqCrVdmrUYulbiVlzMddgJiv3Tc3YeJyZ7ZgS2qcO9NM7GiQSt9LV+hTw7su6+NjWNfR02ONOdV93GoqugIdzwRgJE9Z2+HngN9anKwFWesNREOEWqkwjeWUXSjlnzcUwV8uwzGzHFq+TkWCUh3/0JnFTE01Y6QYGAFevauU/vncDazubss6xZX0HD7Eh3X398uWtWQ0T6nHDcbEiwi1UlUbyyi6UWrgTpqMJRqdjeVuGZWY7aq0xLc1EOEGmvDd7HDR5nBhKzRLtFFvWd8yqsb0Yejg2GiLcQlVpJK9sKVQrRFNoxuPQZJiAx8F0NGE/PmOjssntoLPJjdflQKMLcoeAneHY6nNlfQkL1UHuuFBVGskrW8/ETXvjMVhAxqPWmiaXk77RULpFGNhxbIcDVrWdd4PM5w6pRIajUDwi3ELVaRSvbD1STMaj1poX+sZ4bG8fx0eC6eN+t4NmjzPt5w7Hzawqf7ncIQ5DEfDa/utSu60vdqphdxXhFoQGoNiMxxf7x3hsby+vnpxMH7t4aROgmI7GWZ7hKkltNi7P0Z09lTAT8BRXUvVCpVp2VxFuoeo0WqnUWhOMJhgtMOPxlcFxHtvby0sDE+ljV69u5RM3reWa7racz8nV0NfjctA2R0swITfVsrvKuyJUlXLNSC4E8Y/ETUaDMSIFlFp9/dQEj/26lxf6x9PHrlzZwv3vWsum7raC3R4zE2bq4T7XwxgKJZ/d9diZSXbs3F+2a5AOOEJVWUg7qZnUaaeSshFLWIyFCtt4fHNoksf39nKgdyx97PIVAe6/aS3Xr2kvSLCVUjQnBdvtPB+/rof7XA9jKIZcf99npyKMheKsbvct5BqkA45Qe8qRgNNInUqKIV/GYy6Onpnisb297D8+mj526fIA99+0hi1rOwoS7NSGY2uehJl6uM8PP/cmw1MRTEvjdhgsafbgcqi6fa9z2V3HQnE6mlxlvY8i3EJVKUcCzmLLvpwr43Em7wxP89i+Xn799kj62MpWLx6ng7FglGcODKK0yhm3TlFoD8da3+fdR4Y5dnYah1I4lCJhak5NhFnZ6q3b9zqX3XUiHKezyZP1uFLvowi3UFXKkYBTDvGvl7jpZCTOeDCeN+MxxYlzQR7f18ueo+fSx5yGotPvIhRL4DAUrT4XI8Eoj+w6xkNsyJnh2Oa3K/QVMiOvRJZrMff90T3HcRkGGjucoxRgwZmpKJu62xc8hkoz0+6aK3xS6n0UQ6ZQVbZv7OJzH7yCroCXiXCcroC36Hjlg7esJ25qQjE7pBCKJYoS/1TcdHgqkrVBuvvI8EIvq2iC0QQDoyHOTUXnFO2+kSB/+f03+OTjh9Ki7TQUnU1u1nb6GIvEmYoksLRGYceBnYbi6YMD6XN4XQ6Wt3rp7vAT8LoK3qgs9T7PpNj7PjAWYlmLB63B0prU/xot07bc9xFkxi3UgFITcErNvqxl7LbQFPWB0RBf29/Hz98cTtcT6W73YSiFaVnpsVuWxlAwGozRlDzmdRmcngyXXFK13Fmuxd731Ix/ZZuXs1NRYqaFQykuWtpUl/HtfFQiW1iEWyiYegkvQGniX4vYbaFOkZPjYb6+v4+fvnEm3ddxVZuPe7et4d0bu/jYV56nxXv+Y+tyGCRM67zHW9mvtaaziWUt3pLHXc4s12Lveyqs5nIo1i1pSofVPv2+jWUZTzUpd7awCLdQENVsgDDXGMrxxVHNCoWFOkVOT0T4+v4+fvT66bRgr2j1cu/WNbz38mVp18eKFh8jwSi+5Cy63e/mzGQEh6EwFMRMC60V77qos6y+4XJQ7H2Xujb5ER+3UBDl8F+XQjn9vNXyBttOkblT1M9MRvjG8/0899rp9OO6Ah7u3bqG37li2ay6IJl1tb0ug2jCYjqaoKvZQzBmi+C29R18+/DJuvM+N5onu04oj49bKWUAzVrryXke90/A7wHDWusrk8f+Avgj4GzyYX+qtf5hsWMQqk+trWHljEtnzuSODU8RS1hpb3Dq96VQSIr62akoTz7fzw9eHUo3MVjS7OajN67hd69anrdzTKqZwTOHBhiejNDd4eePf/OiWS6GWvuvc3GhzqArEWIsSLiVUk8CfwyYwAtAq1LqC1rr/zHH0x4D/g54Ysbxv9Fa/88FjFWoIbVugFDuL47UB+ezz75Oq8+eAZYa/ilk43FkOspTBwb411dOpUusdja5uefGHrqaPXzn8EmePtifbi2Wy9L3u9es4K4t3Wl3yO4jw1lhkaNnJlnRml2atV587hdaZchKhRgLnXFfrrWeVEp9FPgh8GlsAc8r3FrrPUqptQsemVBX1LoBQiW+OMo1i48mTMaCcUKx/BuPo8EYTx/s59mXh9Ld1tv9LnZs6eEDV6/g5YGJWa3FMv3Y+Yo+5RKG6ajJuekoSwPnNyfroctQPW1uV4qZ1zgeilVk9VOocLuUUi7g94G/01rHlVILDY7/e6XUfcAh4FNa67FcD1JKPQA8ANDT07PAl7qwKecHpdbL3Ep8cZQ6i4+bFmPBGNNzOEXGQzGeOTjAv7x0Kt11ptXnYseWbj54zcq0VS+ztVhqHOG4yTdfGOD2TavwuXNb+h7dc5y4aTIynSBmWrgdBk1uB2OhOE0eZ910GaqHze1Kk+sae0dCrG7LdveUY/VTqHA/CvQCLwN7lFJrgDlj3Hn4EvCXgE7+/Gvg3+V6oNZ6J7AT7M3JBbzWBU0lPii1XOZW4otjobP4QpwiE+E43zo0wHdfPEkkbpaDMdAAACAASURBVAt2i9fJR27o5o4cQjw0GT5v81NgJDuln52K5hVtgGPDU0yE4hiGwmEoEpYmFkngczvoCnjrJpZcD3VPKk2ua3Q5FGcmo7T43OnHlWP1U5Bwa62/CHwx41CfUuq3in0xrfWZ1L+VUv8IfL/YcwiFMfOPKGFqhqciPPj1F7iup73mH+SFUO4vjnyz+G3rO3Ja6SzLrikyEc5fU2QqEufbLwzyncMnCcXsWHezx8mHb1jNH2xalbe+9YoWH6OhKE1uJw5DoZQiFEvM+wGPJay00AMoBVZyMVwNt0+h1HpzuxrkusZlAQ+D4+GyhxgLSnlXSi1TSn1FKfVc8r8vBz5e7IsppVZk/OcdwGvFnkMojIGxUHrZPRmOc2oijGVpTMuqSYp3PZIr/f7O61bx7cMnZ6Vl//CVUwyOhRkLxXKK9nQ0wRP7ernny8/ztf39hGImHqfB8hYvPrfBi33jvH4y9yLV5TD4o99Yh9a2DxsoOC3a5bAF27I0WmuspEPF7aivbjXd7X7CMzZt6yHuXk5yXaPTYbBhaXNJJR5yUWio5DHgq8D/k/zvo8AzwFfyPUEp9RSwHViilBoE/guwXSl1LXaopBd4cCGDFuYnMwxwbjqKgQIFHoexKJepCyVXQaDMlYrX6SBuxtm55wRfuOuaWc8PxRL884sn+eahQaYidqzb73awdV0nrw9N4HIoAq7cxZ/cToNXByd4fG8vg+NhAh5nulJgoeGNS5a1cOLcNFOR8zHugNfFuiXN5bpFZaHWm9vVIN81/vltl9es5+QSrfU3lVL/N4DWOqGUmrPYgtZ6R47DeYVeKC+Zf0Qx07Jd/FqxNGCXl1xsy9RykVruWlqTMO1ZrMdp1/7IJBw3+d6LJ3n64ACTScH2ugzu2LSKj9zQzX999g3cDmPWZuPTBwe45dKltPldHDg+yn9/7kh6HyL1Qf/L268s+IOeep+Xt9bPRmQuar25XQ2qeY2FCndQKdWJPVNGKbUVmJj7KUItyf4jCqOA5a1eAl47Btcoy9RqW8hWtfk4PRHG4zy/IRiJWyxv8SX/bfLsy6d4+sAA4+E4AB6nwe9fu5K7NnfT5rc3obI2G5P43Q7OTkdY2Wafqxwbdo0kiBeCh7ta11iocP9n4FngIqXUr4GlwJ0VG5VQFlJ/RCmHicNQaK3rdlY2k2payKykU+SOTat45OfHsLSJ12UQiVskLM2HrlvFdw4P8uTz/YyFbMF2Ow0+eM0K7t7cQ0eTO+t8mTVFUo6PSNykp6Mp/Zhcm1kJ0+Jw/xg3f35XwV9UF4IgCtkUXKtEKeUELsXOnX9Lax2v5MAykVolpZOaudb7rCyTatRH0VozGUlk1RQ5cHyUpw8OcHoyTFfAy7olTfzqnXOMTMcAe0PwA1evZMeWbjqbPTnPe+DEKH+76208TntGnasux8zrm4rEGRwL43QoLl7aLLU8BFhIrRKl1B/k+dUlSim01t8teVhCVajmrKxc4Y1KW8hCsQQj07NrimxZ38GmNW386LXTfH1/P6+ctKOCTkNx21UruOfGnvRewUxU0n/9oetXs7zFO+eX5czNrNMTEQCWBbwopWQTWcjLfKGSD8zxOw2IcAtZlDO8Uan6KLGExWgwljNFPWFa/OSNM3xtfx9nJqOA3VT3/Vcu56M39uStcW0oRYsvu/HufF+WM+PTGljV5qUl48tKNpGFXMwp3FrrT1RrIMLioJwZcuW2kM2V8Whamp8mBXsoOfM1FPzOFcv52NaeWUWbUhTaeDcfmeKeCp1k0iibyEJ1Kbisq1LqNuAKID3l0Fp/rhKDEhqXcoY3yuWYmKuLumlpdh0Z5ol9fZwcty1/hoL3XLaMe7euYVX7HILtd9HiLazxbiFcCF5noTwUWtb1HwA/8FvAl7EdJQcqOC6hQOqt4lq5wxulxuanInHGcnRRNy3NL46e5fG9vQyM2YKtgFs3dnHvtjX0dOQer8th0OIrr2CnaCRrn1BbCnKVKKVe0VpfnfGzGfiu1vq3Kz9EcZXkox47itTLmMIxk5FgNF1CNYWlNXuOnuPxfb30jdirAAVsv3Qp925bw9rOptknw7b+tfndNOepNSIIFaKkDjiptLGQUmolMAqsK8eohIVTjxXXaj1rzNeUV2vNr94e4Uu73+H05Pk48hUrW/hP79nA+qW5U8R9bgdtPvecFfqE+cm3Mqy3FWOjUKhwf18p1Qb8FXYDBbBDJkINqdeKa7VICEmYFuPh+KyNR601+46P8NjePt4enk4fb3I7aPY4GQ3GODcVY/3S7PM1e5y0+l1ZGZTCwsjnNLpzcDzdG3Ox1uiuFPP5uDcDA1rrv0z+dzPwKnAE+JvKD0+Yi3LHkxtx9mNamvFQjMkcgn2gd5THft3HW2em0se9LoOuZk+6gUGqfsiW9R1pD3arz5W356NQPPlWhl/+1QmWBjx1tWJsFOabcT8KvAdAKXUL8DDwH4BrsZscSNp7DSmnC6FeO5Tk+zKxLM14OM7kjNrYWmte6Bvjsb19vDF0voxqwOO0O9VojZnxeK/LLiDV5ndnebCF8pFvZRiMmfS4HLOOz1wxNuKEotLMJ9wOrfVo8t93ATu11t8BvqOUeqmyQxPmo5zx5HqMl+f6Mvnz773GZ6IbuXJ1azpFPcWL/WM8treXVzPqXl+8tJmxUAy/20HCsoibFsOTUbpaoMnjJJ7QrO1smlVrRCgf+VaGTW57sjHXirFeJxS1Zl7hVko5tdYJ4N0ke0AW+FyhCpQrnlyP8fKZXyYep4O4afGPv8yujf3K4DiP7e3lpYHzBSuvWd3K/e9ay+O/7iOaMPG5HLT73QxPRdBoRqejeJwGloY//s2Lqn5tFxL5VoafvHkd3z58cs4VYz1OKOqB+cT3KeAXSqlz2M6SXwIopS5GyrouKjJnRVOROGenokQSJk1uJ7uPDNfkQ5KujW1pEtbs2tivnbSbELzQP55+ztpOPw6lOD0Z4fFf99E7Mp2uKxLwunAoxUgwStTULGvxNcSyu9qhgnK/3lwrw6tXt825YqzHCUU9MK+PO1l7ewXwE611MHnsEqBZa3248kMUH3c1SC1J46bJualY2j3a2eTG7XTUxBt+1z/s4/Rkdm3scNzE63TQ1uTiYO9Y+vjlKwJsW9/JD14dwuUw0iVZT09GaPW56Ap4MRTpXo7lrDBYbjKFM+BxcnY6SqvPVRVffL348FNUo0JkrSjwCzLnpsu8W+da6/1a639OiXby2NFqibZQHVL9F4NREw24HQYrW30sDXhxORSP7jletbFEEyZnJiPcsWkVMdOuH66x09aHp6IcOzudFu1Llwd4+A+u4m93bOKFvnFcya4zCnt53dHkYiqSIJqwGzYV2suxVqSEM9Xz8sS5IOOhOAlTpysGVvL9yAxNVOP15uPBW9YTNzWhmO0aqvf3r1Bmvs/F9oGVOLWQZvvGLlp8Lno6/Fnp3NVamsZNO3lmOtkKbMv6Dh5iA//06xP0jYaIZmRBXtzVzP03rWHb+s70WFNdZwxD4VAKw1AsbfZiWhG6At6GSCOfGdM1tcZQcG46mq4aWMn3o95CE9VO6KpWWKrU2L0I9yJmIX+ElSqlOhf5vNjHz07zw9eGOJqROLN+SRMfv2ktN1/cOatWyOo2P6OhKF7X+YVkOG6yoStQ02V1Me/DTOF0OwzippXu/g6VfT9q8f7PR7USuqrpYCn1C1KyDBqY3UeG2bFzPzd/fhc7du7PWmYtdClWzaWp1pqJUJzBsRAT4XhatHtHgnzuX9/gk0+8wJ5j5wBY0+nnv3zgcnbedz2/sWFJlmg3e5ysbvfzH269GNOirpbVxb4P3e1+wvHzfbiXBjxYmnTbuUpfU72EJub6264U1QwTzXyfobgvSBHuBmU+QVjoH2Eq1t0V8DIRjtMV8JZ9Y+rf3jzDh7+0l23//ed8/J8OsO/tEQD6R0P8tx+8yR8+dojdR88C0N3u489uu4wv33cDv3nJUoykYNtZji5Wt/vpavHidhpVGXuxFPs+zBROh6Fo97tY2+GvyjXVwz0sNf67UAbGQvgKSAgqB6V+QUqopEGZL0ZWylKsUktTrTXPvTrE//uDN3EYdnr5SDDKX//0Lbrb/bw0OE4qp2ZVm4/7tq3h1o1dWdmMRkZaujNHWnq9Nc4t9n3IFdP989sur+o11foezvzbTpia4akID379Ba7raa9Y3LmaYaJSY/ci3A3KfIJQb7HKqYjdyGDnnhM4DNtqFjctJsJxJiMJziYb8a5o9fKxrWv47cuXZQm2w1C0eF20lJiWXm1P9ELeh1oL50LuUTnva+bf9mQ4zqmJMAq7JG8l487VbmRRyvssoZIGZb4YWb3EKqejCQZGQ5ydihI3LYYmwzgMODMZ4cRIiMmkg8RQ8Kn3XsLjn9jM+69cnhZnp2HQ2eShu91Pe5O7ZNGu9hK8Xt6HQlnIPSr3fc382z43HcVAoZTC43RUNO5cD2GiQpEZd4My3+yg1nWxQ7EEo8FYViODs1NRTFPTOxlOH3MmQybd7X5uu3pFxvHytwarRfp0rd+HYlnIPSr3fc38246Zlp2BolU6A7aS9sRar3YKRYS7QSlEEFL/Ti1hU7OUSv5hhmMmo6EY0YzVwMh0lCcPDPD9V04RN+0gtqHsrEyP08DUcM+WHqAygp2iVh7lRhEDWNg9Kvd9zf7btsMky1u9BLz2a5Q75NeI1QdFuBuY+QShmr7USNxkLBQjHDsv2KPBGE8f7OfZl4fSM+92v4t3XbSE/tEQw1MR3E4HaM3/+vlRug/7ufniTvafGKvIh6je4v71yELuUbnuay4BBfjss6+n7ZDljjs3avXBgnpO1poLqVZJOb/9U3UeTEtzdipKzLRwKMW6JU089x9vKct4I3GT8VCcUOx8q7DxUIxnDg7wLy+dSmc7tvlc7NjSzQeuWZluYnDg+CiP7DqGx2nQ5HYwEoxxdjpGV8BNZ5On7HUy6q0ORz2ykHtUjvs61zmgcqGmUmuhVGG2nnPZKcJdR5RbWG7+/C4cCoYmoigFSoFlaUwNX7nvhpL+wKIJW7AzeztOhON869AA333xJJG4LdgtXid3b+7m9k2rsjyyDkPxqW++zGgwSpPHXgIfPztNzLRwO4x0D8hyFxRKfdBqFW9Ovf7RM5PETY3babChK1CVcRQqMgu5RzOfs219B/uOjxYsaLUqJnXz53fR5nNlheW0tuvi/PLTt8753CpNBEpqFiyUSCEfmnJv8nS3+3mxfwylOJ+4ArgcLPicsYTFeChmd5NJMhWJ8+0XBvnO4ZOEkqGSgNfJR25YzR2bVmV9GB2Gos3nJuB1cnoykhUbjZkWhiIrvdvncnBseIodO/eXZVZTy3hz6oMeS5hpN004ZtI7Ml3x5XkxIYGF3KPM52S+lkPBiwNj/OETh7ikq5lPv29jznPXav+hlDBPLWuFix2wChRqlyp35taDt6wnbllobdeytiyNhWZZwFP0OROmxdmpKINjobRoT0cTPL63l3u+/Dxf299PKGbS5HFw/01r+MYnb+SjN65J/1EfOjHKp7/9Cvf8437++OsvsOfo2VmWRrfDbmzgzkisGQlGmYokqp5FVwlSH/SpSAIDhdMwMAzFZDhR8Qp81UznfnTPcWIJk8GxMH2jYaJxC7TmxLlg3veu1BTwhVKKXbOamZYzEeGuAoV+aMr9x7t9YxcbljZjGApTa5wOxcpWH06HUfA5TUszMh1lYCzMVCQO2EvYh587wh1/v5fH9/URjJp4nAYf29rDk5+8kfu2raXZYwu2w1C8cWqSv/23txkNxdJdaD777OtsW9+R9aEJeJ1YGlp8zvSHaDQYp93vqpsyo6WQ+qDHTIvUylwlVxiV/sDPFJmpSJyh8TAHekfLXgvk6JlJRjKsoBowtX2d+d67WvndS/Fu1+rLBkS4q0Kh38yV+OP9zPsvoyvgpafDz7olTTgdqqBzpgS7f/R8AahwzOSpA/185B/285M3zmBqjVJ2WKTN5+LKFa1py5ahFG1+N93tfr7xfD9upzFLfPcdH8360Kxb0sxDt17M2s7m9Ieo2eNgSbNn3nvXCKQ+6G6HQWprSSdXGJX+wGeKzFQkzqnxCHFL43UaZV/FpCyfYIfmMl2d+d67Wia/bN/YxVMPbOWXn76Vpx7YWvBr1jK5SmLcVaDQONpCkzXyxc9Tx0OxBLGEhduh2LCsZc5z5uqeHombfO+lUzxzcIDxsD3rVkCb30W7343TUITjJk8fHGDrRZ22kPvPZznOFb/MFU/9k4x/59q0alQLXyqxxK7REsOyNGhoaXJV/AOfmdQyPGn33QRY0uwpe2zW7TRsW6jCnm4ndVwpNed710h+d6htcpUIdxUopgZCsX+8+Tad7hwc59uHT+JyKJa3eLNeM9f5LUszmawnkhLsaNzkX18Z4qkD/YyFbMF2Ow2chmJZiweXcX7B5nU5GJ6K0N3hn5WWXsoGUCn1I+otsSLzg54wJ4klXSVrO5srPrbM1+4dCeF1Gixp9lSkOcOGrgC9I9OMBeNEEnbmo9Og4NVeI1GrLxuxA1aJStnQ8tmozk5FWRrwzGuvSgn2RDiOmSzNF0tY/ODVIZ58vp+RoF38yeVQ/N7VK7lnSzf/7QdHGAlG7fCPAodSRBMmy1p8Oa1bpdqmFmpPE892biptvcu89wnT4sxklLhlsWFpM595/2UX/P0vErED1pJKfTPnC0MEYyY9c8TVcwl23LR47rXTfGN/P2eno4BdS+S2q1Zwz4096VoRd2/u5pFdx4iZFk1uB5GERcIi70yq0CVlvhlyIfdu5nPHQ7GaWbXqnUpXwZv5fm+qYCnWCxUR7hKoh6V4rjDEuaToHjk9hSdjSRyOm6xq8zEWjDGREcNOmBY/eeMMX9vfx5lJ+7kOQ/H+K5fz0Rt7WNbiTZ/bYSjed9Vyulo8/OMvTxQ8C65ken6u5/aOhFjd5s16XKNuapabasRmGy1e3WhIqGSBfPFnR/n73e+QsCwcAEphauZMMqgEM0MC56ajnJ2O0ep1MhVJpBdaHX4XToeDP7n1Yjav6wBs58hPk4I9NBEB7OJP77tiOR/d2sOKVl/6dQylaPW5aPW5MEoorZqPUpbvuZ57bHgKNGxYFij6fIJQR0iopFzsPjLM3+9+B0trDCBmAWicBukkg2oVqZk5ewrFTLoCbpY0e5mKxBmejBBJWASjJn9226VsXteBaWl2HRnma/v7GByzS6waCt5z2TLu3baGVW3nBVslO860+0urhT0fpWTO5XrusoCHwfFw1YriC0I1EeFeAI/uOY5paZyGIpaMD9sdOsDUOp1kUK1Zd+ayNFV7QWuNz+VgdYcfrTVTkQTXr21n15FhHt/by0BSsBXw7su6uHfrGro7sl0ezUnBduVoETaTUsNGpThPcj3X6TDYsLSZ9iZPQ9TBFoRiEOFeAANjITxOg4Sp04kUKFu4fQ6jprHUVW0+Tk+G8Tgdaf9sOGbidTr45BOH6BsJpYbL9kuXct+2NazpbEo//8DxUb71wiCnJ8O0eO0vgOmYOW9RolJLY5ayYZbvudXu1dhI1MP+jLBwRLgXQHe7n4Rppa1yAGhbDJcGPDVJEPnp66f5h18c552zUwRjJm0+u6HuWCjBRDhOwjq/l3HLJUv4+La1rFvSlHWOl/vH+fvdb6e92seGpwFY1eadU4zLUWynlA2zWiVCNKr4NWoNauE8sjm5ADKrvI0FY0STKb5dzW4CPjsL7s7rVhVV1nKhROImz70yxF/95C2chsLrMhidjjIeSYC2a0SkeNfFndy/bS0XdTVnncPvdtLmd/GJrx5MhxyOn522xV7biRPrlzbn3dzLVxrz9ESYDctaGk7YCqGRfeK1KqEqLAjZnCwXmTM8lyNEk9uBUorpqP3Hv219RzprsVIzmlAswXgoTiRu8vi+Plu0nQahqMl0zCKjMipb13dw/01ruSTDYQHgczto97vTjQ0yN/lippXejEyVWc0XAspnSZyKmrOq+tXDrO6LPzvKl391gmDMpMnt4JM3r+NP3nNJUeeoZUnPUqlVCVWhfIhwL5C5fKo7du6v2Id6OppgPJTdhPfURAinoRgYixLJOO52KP7mrmu5bEVL1jm8LgcdTecFO0WmALsdRnrGnSqzmi8ElCvGPBaK09Hkqjth++LPjvLIrrcxlJ2GHY6bPLLrbYCixLuRxU9auDU+Uh2wAhw9M8ngaIjXTk7w2skJjp6ZImFaC/5Qa21nOQ6MhhiejGSJ9uH+MYJRk1MT50Xb73LQFXBz+YrWLNH2uBysaPWxss03S7Qhu9rZkmY3pqUxtWZJs3vOyme5KrsFvE46m+qvqt+Xf3UiKdoGhjKSP+3judh9ZJgdO/dz8+d3ZZU/rWVJz1KpZVU7oTxUbMatlPon4PeAYa31lcljHcAzwFqgF/iI1nqsUmOoBbuPDCc3A88fiyYsBsfCbJgRW54PrTWT4dTmopX1u5cHx3ns1728PDiRPuZxGixtdqOUImFp7t7cDYDLYdDR5KbJM/fbPXOTb0NXM1prgjGTroB3zhj1zBVIvVb1C8ZMnDOmK4ayj89krk28SqeNV5JaVrUTykMlQyWPAX8HPJFx7DPAz7XWDyulPpP8709XcAxV59E9x5NtwrS9q5AsbWlqsjbv5iJXHZEUr52c4LG9vRzuH08fu2pVC1vXdXKwd4zTk2GWt3i5e3M3N128hPYmV7pGdiGUK1W5XoWtyW2PJTOXyNL28ZnMFcd+6oGtDS1+kpLe2FRMuLXWe5RSa2ccvh3Ynvz348BuFplwD4yF0IAr2XVGa7uQvAFZfRpzkTAtJsJxpiKJdB2RFG8OTfLY3l4O9p5foFy+IsD9N63l+jXtKKXYcWMPkGpiYKen/+KtszWxrNXrrO6TN6/jkV1vk7Ds/paWtv//yZvXzXrsfHFsET+hVlR7c3KZ1noIQGs9pJRadH/13e1+zk1H0ZadvQdgaXv2nS9MEEtYjIdjBKMmM+2ZR89M8djeXvYfH00fu3R5gE/ctJbNa9uzZvEqo56Iw1A19+vWo7ClNiALcZXIJp5Qr9Stq0Qp9QDwAEBPT0+NR1M4D96ynv/z2y8zHoqjk2EOS0O73zUrTJCrY3qKfzl8ksf29aa7gYNdYrW73c/9W9eAhk998xWGJsOsaPXxiZvWctvVK9JfFlAZy1pm0knA4ywos7Le+JP3XFKQg6Rewz2CUNEEnGSo5PsZm5NvAduTs+0VwG6t9aXznafeEnDm44s/O8qXfvEO4biVnGn7+Mvbr0yLWjhmMhGOE4rNFuwT54L8zU+P8tqpyazjBrCsxY3T4UgLfbPHid/tIG7a9bBnJn/kS4yZCMf55advLfq6ZhbIHxwLY2p7c8/tNGj2OPmfd17TEOJdKJVqgCEIBVIXCTjPAh8HHk7+/F6VXz8v8/VtLDRGvPvIMN8+fJKVbb6sWVrK0jcRihM3rVnP6xsJ8sS+Pna/dTZVYiTpn9bJUItiPJygu93NmakISsPKNh+GUridjpwz6XIv9VMzeNPSDIyFSe2bag3agvFQnIefe3NRCVs9hnsEoZJ2wKewNyKXKKUGgf+CLdjfVEr9IdAPfLhSr18MhfRtLDRGPDM84XM5MK0EX9z1Nn/9kWtmPb5/NMTX9vWx68hwWrAdhmJps5uAx8mJkaBd/1rbHWoMQ9lNZiHpXiH9Orm6xn/22dc5Nx1hIhQnalo4DYPbr1m5oPs0MBbCoWBoIkqm2UVjx/ENBSdG6j8BRRAanUq6Snbk+dW7K/WaCyVfLPjLvzqR1bexkBhxyolgaY1p2bNll0MxNBHOetzJsTBf29/Hz948kxbB1e0+7tu2hh+8PMRoKIZSClcyg1ElMxhdDsOOY8+IcOXrGn/n4Dh/v/sdTEvjdToIeJ18+/BJrl7dVvRMsrvdz4v9Y+RyNZpa4yzQ7igIQmnU7eZkOZkv3LHQvo25WNnq40yqrGqSSNxieYvdnGBoIszX9/fz49dPpwV7RauX+7at4T2XLcNhKFo8Lh7ZdYxw3KTD7+L0ZBSlFEsDHkKxBM0eJwrSm2bnpqOMhWzf946d+7Oub9/xUVa3+2YVFFrIBuWDt6znD584iCOHQKdsdRuWNuV4piAI5WTRC/d8lrjdR4aZDMcZmgjjdTpYGvAQ8Nr9GVPJGoXEiIPRBOPhOH+waRWP7DqGpU28LoNI3CJhaX7nimV84adHee610+mkmuUtXu7d2sN7L1+W5QbZsr6D/2xcwjdfGOD0RIRLlgWyMhj//LbLAXulcOzMJFNRk44mF51NnlnXV86aGts3drFhaTO9oyEc2k4USk38DWU7Zz79vo1Fn1cQhOJY9MI9lyUO4LPPvo4/KdAx0+LkWJglAROXw/b3fvvwybx2MK01U9FE1objlvUdPMQGnj44wOnJMB1+Dy0+J3/906PpmthdAQ8f29rD71yxfFZ3GYehaPO5ufOG1Xw4mbKej+0bu2alls8M55R7g/Iz778sy1lyZjJK3LLYsLSZz7z/MtnIE4QqsOiFe64ZZ0rUW31ePE475BBN9mf84t1Xs31jF1evbptlB7vlkqWMh2I5U9LBFu/1XU08dWCA779yiniyKHZns5t7tvRw21UrcM8omJFKnmkrshnvfDPqcnuRZ2ZEbuppF4ucIFSZRS/cc804M0WvxeeiJdmrcSIcTwtRph0slZLePxqalZKeYjQY4+mD/Tz78lC6il+738U9N/bwe1etwDMjZq6UotnjpN3vygqXlOP6UuMvd+q5WOQEobYs+g44c3UqeXTP8SzRmwzHOTMVQWu4LmMmOVdKeorxUIxnDg7wLy+dIpoU7Dafix1buvnANStzllFt8tjNeGfOvst1ffnEtVFbbgnCBUjO5feiF27In/02MxPw5HgEsHssOh0G0YTFp95zCdf04FyUcAAAEP9JREFUtOU990Q4zrcODfDdF08SiduC3eJ1ctfmbn7/2lX4clSdy9fIoNzXl++xjdpySxAuQC5M4Z5vdpn6/eH+MRSwvNWL3+3EtOwC851NHr5w1+zEmalInG+/MMh3Dp8klKzlHPA6+cgNq7lj06qs0EUKt9Oui53rd4WMtRwU229QZueCUFPqIuW9qhRSHS8Vr33Xwz+nxevC0nYsG8DrMjg9mZ04Mx1N8N3Dg3zrhUGCUVuwmzwOPnz9av7gutU052hW4DSMeetiF1PJrxQxLcYeWOvqgoIg5GZRC3ch1fFMS/PcK0NMhOIMTUTwJGfFTW5nVuJMKJbgu4dP8q0XBplKVuzzux3ced1q7rx+Nc3e2bcyZe1r8TnnbaJQaCW/UsW0GHtgIzfEFYTFzKIW7rlmlymHyM/eOMP/+vkxO1kmYRI3Lc5MRGhvcuF0OLhj00qeOtDPMwcH0iVWvS6DD123mg9fv5oW3+xZtFKKFq+TNr873Sk9Rb7ZcqEz4VLFtBh7YCM3xBWExcyiFu5cs8tUPHdgLIzWmqcODOA0FIEmD26ng7FkB/Vg1GT7pZ38zc+OMR6OA+B1Gtx+7Uru2txNm9+d8zWbvU46/O6c1r65ZsuFzoRLFdNi7IHSSEAQ6pNFLdyZs0uP0yAYTRAzNQ9cvzpt6xuaDNOSDHOk6luPh+OMBmP88LXTgL2pePs1tmB3NOUW7EKsfXPNlgudCZdDTAv1YUsjAUGoTxa1cG/f2MWfxk12/vI4p8bDLG/xcffmbras70g/ZkWLj5FgFI/TYCIcZzR0PhvS5VB84OqV7NjSTWezJ+drFGPtyzVbTpgWh/vH+LPvvUaz24FSiolwPO9MuJpiWq99IwXhQmdR2gEty64hMhnO3bQgk71vn+OvfvwWwaiJmXEvtq7r4D+99xKWBnILtsuR3MTM4SLJx0wr3lQkzuBYGKdDcfHS5oI91dKVRRAuGBa/HTBhWkxGEkxFsmuIHDg+ytMHB+z+jMlZ93Vr2vjx62f42v6+rL6OnU1u/ujmdfz2lctzvobTMGhrctEyh7UvHzNny6cn7ISfZQEvSqmCNxol5VwQLmwWhXBHE3YPx1wp6QeOj/LIrmM4DdvpcW46wn//0Zs4lGI0ZG86Ggred8VyPrq1hxWtvpyvYShFm98W7GKKQGUyM/SgsbM0M50p4toQBGE+Glq4wzGT8XCMcDJzMRdPH7RdI16nwVQkwUgwlq7WZyh47+XL+NjWNaxqyy3Yc1n7FkLmbDkVOsm6JnFtCIIwDw0n3Kka2JPheLr63lycmghhKMXpyUhasMH2Yj/6sevp7sgvkk0eJx1N7lk1s8uFuDYEQVgIDSPcpqWZDMeZjOSugT0TS2t+eewck+EEkQyBdyi7K7lDKYbGIzmF2+006Gzy5CwQlUmpdTzEtSEIwkJoCFfJtdddr//5J3vyllTNRGvNr94e4fF9vRw/G0wfdzsUpqXtRreadGbkQ7duSNsDHYaivcld0MajVNkTBKEKNK6rxLT0vKKttWbf8REe29vH28PT6ePvuriT63va+cqvTpCwTNyO87VIwnGTpw8OcONFnbR47QSaQjcepY6HIAi1oiGEey601jx/YpTH9/Xx1ump9PGt6zu4/6a1XLIsAMAzhwZY2eZFZXyBeV0Gw1MRVrf7io5jSx0PQRBqRcMKt9aaQ31jPLa3lzeHzgt2wOPE5VREYhbjwXj6eCpD0pfMcFRKETct1nQ2zRLtQmLXUsdDEIRa0XDCrbXmxf5xHtvby2unJtPHnYZCo/G6FG1+NyPBKI/sOsZD2DHsuzd388iuY0QSJk1uJzHTwrRsZ0emUAc8Ts5OR9ONe/OVTRVHiCAItaKhhPvlgXG+ureXVwYn0sfcDoM2n5OpaIK4qRkPJXA7HVkx7C3rO9h6USfNHidff76Pk+PhtIMDyKrY9/bwNAlL0+R2otz5sxnFESIIQq1oCOEOx0w+9a2XebF/PH3sqlUthKImMdPC53IwGophKIXG7rTe5HamO9i0+Fy80j/ONw70Mzgezgp/7Ni5P2uT0dQaQ8G56Wg6ozFf7FpSzwVBqAUNIdwDYyESSdG+fEWAj9+0lhvWtHPPl59Pl2R1OQwSpkYZpAtLxRJ2DPu1wQn+4vtv5KyDPXOT0aEUkYRFzDQ5fnaapQEPDkNJ7FoQhLqhIYQb4NLlAe6/aQ1b1nak24Blbji2+90MT0XQlh3vjlsWGsX/9psXzWndy9xknIrESSSTexT2F8DgWJh2v4s/v+3yWl26IAhCFpXJ5S4zq9p8/H/3bOLGdZ1ZvRvv3txNwtKE4yZNHlu8DaVo9rpY3uJLJ8MMjIXSbpIUqfDHg7esJ27aHd2HJyMoZSfiuB122MXpUHQ2uSUkIghC3dAQM+4mT+5mu1vWd/AQG3jm0ADDUxEu7grkte6dODfNVCRBzLRwOwwCXifrljRnbTL2joTwOg2WNHvS8W2tNRPh+KzXFgRBqBUNMePOx6ETo3zn8CDDUxF6Opryujq2re/g7HSMSMIkYWqCMZPTk1GWt9htyLZv7OKpB7ayZW0Hy1uzy6yKN1sQhHqjIYVbKcXrJyf42397m9FQLB3f/uyzr7P7yPCsx+87Pkqr14llgcYu5+pQ8MPXzmQ9PjNsorX9U7zZgiDUGw0n3M1eJ93tPp48MIDbaeB3O9PdY1wOxaN7js96zsBYiEjcxO008LkceJwOXA4D09JZj9++sYvPffAKugJeJsJxugJeKRolCELd0RAxbrCdIO1NLjxOe5OxmFoh3e1+hibCWantWoPHacx6vHizBUGodxpixu1yGCxv9aZFG2wxDsezO9/ki0c/eMt6nIaRrjJoWRoLTcDrlPi1IAgNR0MId65Kq8XEo7dv7OL/2H4RhlIkLJ22+LmdDolfC4LQcDRMqGQmxdYK+ZP3XMLVq9uktoggCA1PQ3TAueGGG/ShQ4dqPQxBEIRq07gdcEql1N6QgiAI9URDxLhLIdUbcngqklVgKpffWxAEoRFo6Bl3ITNp6Q0pCMJio2GFO7PLeuZM+s7BcfYdH02L+bHhKZa3eLOeK70hBUFoZBpWuD//oyMMT0YwtcbtMFga8BA3Tf5+9zusbvelxXwqksDliLKk+bx4S/0RQRAamYYU7t1Hhjk6PI0jWYI1YWlOjUdQaExNVlik3e9iNBjH73ZKb0hBEBYFDSncqbi1tkChUAosNNGEpsmdXXd7SbOHhGnRFfCKf1sQhEVBwwn37iPDHO4fI25aaA0OrewO70k/usuhOH52Oqvu9oZlLTz1wNYaj1wQBKE8NJQdMLUhqbDbkzkUmJYmbmkMQ9HpdzGVbCBsKIiZFmenY2xb31HroQuCIJSNhhLuVIhkeasXUDgcBi6HwuVQdAW8dLV46Qq4cTsMLA1uh0FXwM2+46O1HrogCELZqEmoRCnVC0wBJpDQWt9QyPNSpVyVUqxsg7NTUaIJC6UVn/vgFfzZ916js8mT5SDRWov1TxCERUUtY9y/pbU+V8wTMjuyB7wuAl4XoViCroCX7Ru76N5z/vcpxPonCMJio6FCJTNLuZ6bjjA4FubomUl27NzPtvUd0npMEIRFT02qAyqlTgBj2C0gH9Va78zxmAeABwB6enqu7+vrA86nuR8bnmIqkqDd72JJsyftz77zulXsOz4q1j9BEBYDOasD1kq4V2qtTymluoCfAv9Ba70n3+NzlXXdsXP/rLBIKmwi1j9BEBYJOYW7JqESrfWp5M9h4J+BLcWeY2As9P+3dzchdtVnHMe/j3FMog60GkZiDGhKQerCOIRuWoJQUBPEl11cZSHoooW6cKEIIu4UbHemWipIKbFQ3wJCqUhDcFFllLySxNho8SVxNC0aaRVJHhfnTJ0Oc2fubfSeee58P3C4h/8cLs/Df+bHuWfOPX9Wj/3vl218Bomk5WDowR0RF0XE+Mw+cANwcND3GWTNSUkaJV2ccV8GvBoR+4DXgZcy88+Dvskga05K0igZ+u2AmXkcuPZc32fQNSclaVSUe1bJbNdfPWFQS1p2St3HLUkyuCWpHINbkooxuCWpGINbkooxuCWpGINbkooxuCWpGINbkooxuCWpGINbkoop9aySmdVv3vvXv1nvQ6UkLVNlzrh3H5nmwV2HmD79Bd9bPcb06S94cNchdh+Z7ro0SRqqMsH9xJ7jjK0ILrzgfCKa17EVwRN7jnddmiQNVZngdqkySWqUCW6XKpOkRpngdqkySWqUCe7rr57g4VuuYWJ8FZ/+5ysmxlfx8C3XeFeJpGWn1O2ALlUmSYXOuCVJDYNbkooxuCWpGINbkooxuCWpGINbkooxuCWpGINbkooxuCWpGINbkoopEdxHTp7mjif/5qIJkkSR4D7/vHDFG0lqlQhuwBVvJKlVJrjBFW8kCYoFtyveSFKh4HbFG0lqlFhI4czZZGJ8FXdv3uBCCpKWvcjMrmtY1KZNm3JqaqrrMiRp2GK+wTKXSiRJDYNbkooxuCWpGINbkooxuCWpGINbkooxuCWpGINbkooxuCWpGINbkoop8ZX3iPgY+EfXdXzL1gCfdF3Ed8C+arGvpe2TzLxp7mCJ4B5FETGVmZu6ruPbZl+12FdNXiqRpGIMbkkqxuDuzpNdF/Adsa9a7Ksgr3FLUjGecUtSMQa3JBVjcA9JRLwbEQciYm9ETLVjl0TEyxFxrH39ftd1LiYinoqI6Yg4OGusZx8RcX9EvB0RRyPixm6qXliPnh6KiA/a+dobEVtn/WzJ9wQQEesj4q8RcTgiDkXEL9vx6vPVq6/yc9a3zHQbwga8C6yZM/YocF+7fx/wSNd19tHHZmASOLhYH8CPgH3ASuAq4O/Aiq576LOnh4B75zm2RE9trWuByXZ/HHirrb/6fPXqq/yc9bt5xt2tW4Gn2/2ngds6rKUvmbkH+Oec4V593Ao8k5lfZuY7wNvAj4dS6AB69NRLiZ4AMvNEZr7Z7p8GDgPrqD9fvfrqpURfgzC4hyeBv0TEGxFxVzt2WWaegOaXEZjorLpz06uPdcB7s457n4X/wJaaX0TE/vZSyszlhJI9RcSVwHXAa4zQfM3pC0ZozhZicA/PTzJzEtgC/DwiNndd0BDEPGNV7j/dAfwA2AicAB5rx8v1FBEXA88C92TmZwsdOs/Yku1tnr5GZs4WY3APSWZ+2L5OA8/TfFT7KCLWArSv091VeE569fE+sH7WcVcAHw65tv9LZn6UmWcy8yzwW775aF2qp4gYowm3P2Tmc+1w+fmar69RmbN+GNxDEBEXRcT4zD5wA3AQ2AVsbw/bDrzYTYXnrFcfu4BtEbEyIq4Cfgi83kF9A5sJttbtNPMFhXqKiAB+BxzOzF/N+lHp+erV1yjMWd+6/u/octiADTT/1d4HHAIeaMcvBV4BjrWvl3Rdax+97KT5GPoVzZnMnQv1ATxA81/8o8CWrusfoKffAweA/TR/+Gsr9dTW+VOaSwL7gb3ttnUE5qtXX+XnrN/Nr7xLUjFeKpGkYgxuSSrG4JakYgxuSSrG4JakYgxuCYiIS2c9Ve7knKfM3Tjn2Hsi4vGuapUMbgnIzFOZuTEzNwK/AX7d7u8Ats05fBvNvd9SJwxuaWF/Am6OiJXw34caXQ682mFNWuYMbmkBmXmK5uvRN7VD24A/pt9cU4cMbmlxO/nmcomXSdQ5g1ta3AvAzyJiElid7UP8pa4Y3NIiMvNzYDfwFJ5tawkwuKX+7ASuBZ7puhDJpwNKUjGecUtSMQa3JBVjcEtSMQa3JBVjcEtSMQa3JBVjcEtSMV8DJenArYhhdccAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.lmplot(x = 'TV', y = 'Sales', data = Ad_df)\n",
    "\n",
    "sns.lmplot(x = 'Radio', y = 'Sales', data = Ad_df )\n",
    "\n",
    "sns.lmplot(x = 'Newspaper', y = 'Sales', data = Ad_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GGCcusUsz_Az"
   },
   "source": [
    "# LVC  2 - Model Evaluation: Cross validation and Bootstrapping\n",
    "\n",
    "- We realize that the newspaper can be omitted from the list of significant features owing to the p-value.\n",
    "- Let us now run the regression analysis adding a multiplicative feature in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "zTSASn2az9-B"
   },
   "outputs": [],
   "source": [
    "Ad_df['TVandRadio'] = Ad_df['TV']*Ad_df['Radio']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "h_EfN22CWf5W"
   },
   "outputs": [],
   "source": [
    "# let us remove the sales_predicted and the error column generated earlier\n",
    "Ad_df.drop(columns = [\"Error\", \"Sales_Predicted\"], inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rz8DKNiF2QxK",
    "outputId": "03de5d64-01ed-4699-bb1f-8830b5247928"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.968\n",
      "Model:                            OLS   Adj. R-squared:                  0.967\n",
      "Method:                 Least Squares   F-statistic:                     1466.\n",
      "Date:                Sat, 28 Aug 2021   Prob (F-statistic):          2.92e-144\n",
      "Time:                        15:28:22   Log-Likelihood:                -270.04\n",
      "No. Observations:                 200   AIC:                             550.1\n",
      "Df Residuals:                     195   BIC:                             566.6\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      6.7284      0.253     26.561      0.000       6.229       7.228\n",
      "TV             0.0191      0.002     12.633      0.000       0.016       0.022\n",
      "Radio          0.0280      0.009      3.062      0.003       0.010       0.046\n",
      "Newspaper      0.0014      0.003      0.438      0.662      -0.005       0.008\n",
      "TVandRadio     0.0011   5.26e-05     20.686      0.000       0.001       0.001\n",
      "==============================================================================\n",
      "Omnibus:                      126.161   Durbin-Watson:                   2.216\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1123.463\n",
      "Skew:                          -2.291   Prob(JB):                    1.10e-244\n",
      "Kurtosis:                      13.669   Cond. No.                     1.84e+04\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.84e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "# Let us do the modelling with the new feature.\n",
    "import statsmodels.formula.api as smf\n",
    "lm2 = smf.ols(formula= 'Sales ~ TV+Radio+Newspaper+TVandRadio', data = Ad_df).fit()\n",
    "lm2.params\n",
    "print(lm2.summary())  #Inferential statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NslaNwMQFjL1"
   },
   "source": [
    "**Observations**\n",
    "- We see an increase in the R-square here. However, is this model useful for prediction? Does it predict well for the unseen data? Let us find out!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d46mQv0BUKZ8"
   },
   "source": [
    "## Performance assessment, testing and validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-EAcqssG3pr0"
   },
   "source": [
    "### Train, Test, and Validation set\n",
    "- We will split data into three sets, one to train the model, one to validate the model performance (not seen during training) and make improvements, and the last to test the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "uQTTvaQ_3C6D"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "RRerX1zyDUlM"
   },
   "outputs": [],
   "source": [
    "features_base = [i for i in Ad_df.columns if i not in (\"Sales\" , \"TVandRadio\")]\n",
    "features_added = [i for i in Ad_df.columns if i not in \"Sales\"]\n",
    "target  = 'Sales'\n",
    "train, test = train_test_split(Ad_df, test_size = 0.10, train_size = 0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "ztuTrjlsDUq0"
   },
   "outputs": [],
   "source": [
    "train, validation = train_test_split(train, test_size = 0.2, train_size = 0.80)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jgm44JjJDUtK",
    "outputId": "70e21eef-268e-4057-edaf-9ccad11bfb3c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((144, 5), (36, 5), (20, 5))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.shape, validation.shape,test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BCsbEBPoDUwm",
    "outputId": "c0379528-f2c5-4266-d184-084272c7c1a2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*********Training set Metrics**************\n",
      "R-Squared: 0.8728150345185592\n",
      "MSE:  3.0348049540098523\n",
      "********Validation set Metrics**************\n",
      "R-Squared: 0.9371872319571122\n",
      "MSE:  2.3343022717155604\n"
     ]
    }
   ],
   "source": [
    "# now let us start with the modelling\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "mlr = LinearRegression()\n",
    "mlr.fit(train[features_base], train[target])\n",
    "print(\"*********Training set Metrics**************\")\n",
    "print(\"R-Squared:\", mlr.score(train[features_base], train[target]))\n",
    "se_train = (train[target] - mlr.predict(train[features_base]))**2\n",
    "mse_train = se_train.mean()\n",
    "print('MSE: ', mse_train)\n",
    "print(\"********Validation set Metrics**************\")\n",
    "print(\"R-Squared:\", mlr.score(validation[features_base], validation[target]))\n",
    "se_val = (validation[target] - mlr.predict(validation[features_base]))**2\n",
    "mse_val = se_val.mean()\n",
    "print('MSE: ', mse_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BhMVT0OoI-ZR",
    "outputId": "04a4abfe-d2f9-46f0-87f7-721e493f15d1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*********Training set Metrics**************\n",
      "R-Squared: 0.9580235172472629\n",
      "MSE:  1.0016155394444397\n",
      "********Validation set Metrics**************\n",
      "R-Squared: 0.9795480571242043\n",
      "MSE:  0.7600527441072137\n"
     ]
    }
   ],
   "source": [
    "# Can we increase the model performance by adding the new feature? \n",
    "# We found that to be the case in the analysis above but let's check the same for the validation dataset\n",
    "\n",
    "mlr_added_feature = LinearRegression()\n",
    "mlr_added_feature.fit(train[features_added], train[target])\n",
    "print(\"*********Training set Metrics**************\")\n",
    "print(\"R-Squared:\", mlr_added_feature.score(train[features_added], train[target]))\n",
    "se_train = (train[target] - mlr_added_feature.predict(train[features_added]))**2\n",
    "mse_train = se_train.mean()\n",
    "print('MSE: ', mse_train)\n",
    "print(\"********Validation set Metrics**************\")\n",
    "print(\"R-Squared:\", mlr_added_feature.score(validation[features_added], validation[target]))\n",
    "se_val = (validation[target] - mlr_added_feature.predict(validation[features_added]))**2\n",
    "mse_val = se_val.mean()\n",
    "print('MSE: ', mse_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b6lpvtsONOad"
   },
   "source": [
    "**Observations**\n",
    "- We found the R-squared increased as we would expect after adding a feature. Also the error decreased. Let us now fit a regularized model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularization "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zvJSmJcAQ5-L",
    "outputId": "63767378-2ff9-4ee1-9b62-d8cb15a811a5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['TV', 'Radio', 'Newspaper', 'TVandRadio']"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features_added"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "aZoBlRnCKge6",
    "outputId": "35c9fbe9-98eb-45c0-c2a7-6b4a528cd5c7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*********Training set Metrics**************\n",
      "R-Squared: 0.958023517237818\n",
      "MSE:  1.0016155396698094\n",
      "********Validation set Metrics**************\n",
      "R-Squared: 0.9795476415861633\n",
      "MSE:  0.7600681866903618\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "#fitting Ridge with the default features\n",
    "ridge = Ridge()\n",
    "ridge.fit(train[features_added], train[target])\n",
    "\n",
    "print(\"*********Training set Metrics**************\")\n",
    "print(\"R-Squared:\", ridge.score(train[features_added], train[target]))\n",
    "se_train = (train[target] - ridge.predict(train[features_added]))**2\n",
    "mse_train = se_train.mean()\n",
    "print('MSE: ', mse_train)\n",
    "print(\"********Validation set Metrics**************\")\n",
    "print(\"R-Squared:\", ridge.score(validation[features_added], validation[target]))\n",
    "se_val = (validation[target] - ridge.predict(validation[features_added]))**2\n",
    "mse_val = se_val.mean()\n",
    "print('MSE: ', mse_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "oL3Px7TORUVN",
    "outputId": "7f4f9f05-2222-4172-b2d7-0c4d470bc211"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*********Training set Metrics**************\n",
      "R-Squared: 0.9575230612795557\n",
      "MSE:  1.0135570943626075\n",
      "********Validation set Metrics**************\n",
      "R-Squared: 0.9769399450467467\n",
      "MSE:  0.856977655028845\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "#fitting Lasso with the default features\n",
    "lasso = Lasso()\n",
    "lasso.fit(train[features_added], train[target])\n",
    "\n",
    "print(\"*********Training set Metrics**************\")\n",
    "print(\"R-Squared:\", lasso.score(train[features_added], train[target]))\n",
    "se_train = (train[target] - lasso.predict(train[features_added]))**2\n",
    "mse_train = se_train.mean()\n",
    "print('MSE: ', mse_train)\n",
    "print(\"********Validation set Metrics**************\")\n",
    "print(\"R-Squared:\", lasso.score(validation[features_added], validation[target]))\n",
    "se_val = (validation[target] - lasso.predict(validation[features_added]))**2\n",
    "mse_val = se_val.mean()\n",
    "print('MSE: ', mse_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "auLl5-cWRhKb",
    "outputId": "547a604e-d1ce-4364-c753-a0860242ec4e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*****************Test set Metrics******************\n",
      "Rsquared:  0.9817005837522722\n",
      "MSE:  0.49043304766182383\n",
      "Intercept is 6.8067374349457 and Coefficients are [0.01801443 0.01332594 0.00500065 0.00118479]\n"
     ]
    }
   ],
   "source": [
    "#Let us predict on the unseen data using Ridge\n",
    "\n",
    "rsq_test = ridge.score(test[features_added], test[target])\n",
    "se_test = (test[target] - ridge.predict(test[features_added]))**2\n",
    "mse_test = se_test.mean()\n",
    "\n",
    "print(\"*****************Test set Metrics******************\")\n",
    "\n",
    "print(\"Rsquared: \", rsq_test)\n",
    "print(\"MSE: \", mse_test)\n",
    "print(\"Intercept is {} and Coefficients are {}\".format(ridge.intercept_, ridge.coef_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SvdZcoUc9r4C"
   },
   "source": [
    "- We will now evaluate the performance using the LooCV and KFold methods.\n",
    "\n",
    "### K-Fold and LooCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "tY9Rz4rf9ql5"
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 105
    },
    "id": "WMcwry-h64ZA",
    "outputId": "aac321a0-ab04-4655-95de-f9ab260b03c4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Score:\n",
      "0.9649887636257694 \n",
      "\n",
      "Confidence Interval:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.9430473456799696, 0.9869301815715691)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridgeCV = Ridge()\n",
    "cvs = cross_val_score(ridgeCV, Ad_df[features_added], Ad_df[target], cv = 10)\n",
    "print(\"Mean Score:\")\n",
    "print(cvs.mean(), \"\\n\")\n",
    "print(\"Confidence Interval:\")\n",
    "cvs.mean() - cvs.std(), cvs.mean() + cvs.std() \n",
    "\n",
    "# note that the same can be set as LooCV if cv parameter above is set to n, i.e, 200."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "id70R6LjYLEW"
   },
   "source": [
    "## Extra: Statsmodel to fit regularized model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "id": "XVfz6N4yCT09"
   },
   "outputs": [],
   "source": [
    "# You can also use the statsmodel for the regularization using the below code\n",
    "# import statsmodels.formula.api as smf\n",
    "# We will use the below code to fit a regularized regression.\n",
    "\n",
    "\n",
    "# Here, lasso is fit\n",
    "# lm3 = smf.ols(formula= 'Sales ~ TV+Radio+Newspaper+TVandRadio', data = Ad_df).fit_regularized(method = 'elastic_net', L1_wt = 1)\n",
    "# print(\"*************Parameters**************\")\n",
    "# print(lm3.params)\n",
    "\n",
    "# Here, ridge regularization has been fit\n",
    "# lm4 = smf.ols(formula= 'Sales ~ TV+Radio+Newspaper+TVandRadio', data = Ad_df).fit_regularized(method = 'elastic_net', L1_wt = 0)\n",
    "# print(\"*************Parameters**************\")\n",
    "# print(lm4.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "i6veKXLlmMWr"
   },
   "source": [
    "## Bootstrapping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "8FcvUb-YmLUP",
    "outputId": "d0785df0-11a5-4d5b-f419-778a4e0cfc30"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.612\n",
      "Model:                            OLS   Adj. R-squared:                  0.610\n",
      "Method:                 Least Squares   F-statistic:                     312.1\n",
      "Date:                Sat, 28 Aug 2021   Prob (F-statistic):           1.47e-42\n",
      "Time:                        15:28:22   Log-Likelihood:                -519.05\n",
      "No. Observations:                 200   AIC:                             1042.\n",
      "Df Residuals:                     198   BIC:                             1049.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      7.0326      0.458     15.360      0.000       6.130       7.935\n",
      "TV             0.0475      0.003     17.668      0.000       0.042       0.053\n",
      "==============================================================================\n",
      "Omnibus:                        0.531   Durbin-Watson:                   1.935\n",
      "Prob(Omnibus):                  0.767   Jarque-Bera (JB):                0.669\n",
      "Skew:                          -0.089   Prob(JB):                        0.716\n",
      "Kurtosis:                       2.779   Cond. No.                         338.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# let us get a more detailed model through statsmodel.\n",
    "import statsmodels.formula.api as smf\n",
    "lm2 = smf.ols(formula= 'Sales ~ TV', data = Ad_df).fit()\n",
    "lm2.params\n",
    "print(lm2.summary())  #Inferential statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 278
    },
    "id": "_qjK1Fn9UOJT",
    "outputId": "a848a024-c4d4-4987-a72c-b838625a9a00"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, let us calculate the slopes a 1000 times using bootstrapping\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "\n",
    "Slope = []\n",
    "for i in range(1000):\n",
    "  bootstrap_df = Ad_df.sample(n = 200, replace = True )\n",
    "  lm3 = smf.ols(formula= 'Sales ~ TV', data = bootstrap_df).fit()\n",
    "  Slope.append(lm3.params.TV)\n",
    "  \n",
    "  plt.xlabel('TV Ads')\n",
    "  plt.ylabel('Sales')\n",
    "  plt.plot(bootstrap_df['TV'], lm3.predict(bootstrap_df['TV']), color='green', linewidth=3)\n",
    "  \n",
    "plt.scatter(Ad_df['TV'], Ad_df['Sales'],  color=(0,0,0.5))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "my0E81YkGwCN",
    "outputId": "e8aee2af-3ec0-489b-9e2c-d3a020689cb1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.04126775, 0.05293063])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's now find out the 2.5 and 97.5 percentile for the slopes obtained\n",
    "import numpy as np\n",
    "\n",
    "Slope = np.array(Slope)\n",
    "Sort_Slope = np.sort(Slope)\n",
    "\n",
    "\n",
    "Slope_limits = np.percentile(Sort_Slope, (2.5, 97.5))\n",
    "Slope_limits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "id": "tfuLE-9Hoh2G",
    "outputId": "a4719d2a-57ef-4abe-fc6a-660a53a50e07"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x22adda6d7f0>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the slopes and the upper and the lower limits\n",
    "\n",
    "plt.hist(Slope, 50)\n",
    "plt.axvline(Slope_limits[0], color = 'r')\n",
    "plt.axvline(Slope_limits[1], color = 'r')"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "LVC_1_&_2_Practical_Application_Effects_of_Advertising_on_Sales.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}