islr_ch05_exercises_Nika_Natsvlishvili.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mB1U1G3P8FZM"
   },
   "source": [
    "# ISLR Chapter 5 - Resampling Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Uc6Lt6kx8FZO"
   },
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-15T19:18:34.154137Z",
     "start_time": "2022-04-15T19:18:33.862590Z"
    },
    "id": "3d8EE5dA8FZO"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits import mplot3d\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression, LinearRegression\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis as QDA\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from sklearn.utils import resample\n",
    "from sklearn.model_selection import train_test_split, cross_val_score, LeaveOneOut, KFold\n",
    "from sklearn.preprocessing import OneHotEncoder, PolynomialFeatures\n",
    "\n",
    "from sklearn.datasets import load_boston"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dOw2NYSq8FZP"
   },
   "source": [
    "## Exercise 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "60VlxiF-8FZP"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000\n"
     ]
    },
    {
     "data": {
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       "    }\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>default</th>\n",
       "      <th>student</th>\n",
       "      <th>balance</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>729.526495</td>\n",
       "      <td>44361.625074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>817.180407</td>\n",
       "      <td>12106.134700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>1073.549164</td>\n",
       "      <td>31767.138947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>529.250605</td>\n",
       "      <td>35704.493935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>785.655883</td>\n",
       "      <td>38463.495879</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  default student      balance        income\n",
       "0      No      No   729.526495  44361.625074\n",
       "1      No     Yes   817.180407  12106.134700\n",
       "2      No      No  1073.549164  31767.138947\n",
       "3      No      No   529.250605  35704.493935\n",
       "4      No      No   785.655883  38463.495879"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('Default.csv',index_col = False)\n",
    "\n",
    "print(len(df))\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DtIEHnk_8FZQ"
   },
   "source": [
    "### a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "nGojIPs68FZQ"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.64710797e-03, 2.08091984e-05]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df[[\"balance\", \"income\"]]\n",
    "y = df[\"default\"]\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X, y)\n",
    "clf.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZJ8T01db8FZQ"
   },
   "source": [
    "\n",
    "### b\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zaUK5-Fx8FZR"
   },
   "source": [
    "\n",
    "#### i\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "OsT7c6dc8FZR"
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df[[\"balance\", \"income\"]], df[\"default\"],test_size = 0.3, random_state = 42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hGVutf838FZS"
   },
   "source": [
    "\n",
    "#### ii\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "PFRLtyn08FZS"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf = LogisticRegression()\n",
    "clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b7IoGXM78FZS"
   },
   "source": [
    "\n",
    "#### iii\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "glmpred = clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2905,    1],\n",
       "       [  94,    0]], dtype=int64)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_mat = confusion_matrix(y_test, glmpred)\n",
    "conf_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0136"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round((conf_mat[0][1] + conf_mat[1][0]) / y_train.shape[0], 4)\n",
    "###accu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "07v_FO2g8FZT"
   },
   "source": [
    "\n",
    "#### iv\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "nTb4rHuT8FZT"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03166666666666662"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#validation set error\n",
    "1 - clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JI9_fhbX8FZT"
   },
   "source": [
    "\n",
    "### c\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "J2JfAEtY8FZT"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02833333333333332"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df[[\"balance\", \"income\"]], df[\"default\"],test_size = 0.3, random_state = 420)\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X_train, y_train)\n",
    "1 - clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03600000000000003"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df[[\"balance\", \"income\"]], df[\"default\"],test_size = 0.3, random_state = 910)\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X_train, y_train)\n",
    "1 - clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.029000000000000026"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df[[\"balance\", \"income\"]], df[\"default\"],test_size = 0.3, random_state = 652)\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X_train, y_train)\n",
    "1 - clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ElobLmh08FZT"
   },
   "source": [
    "\n",
    "### d\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0027279999999999995"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "with_student = {}\n",
    "without_student = {}\n",
    "\n",
    "#სტუდენტის ცვალით და მის გარეშე\n",
    "categorical_features = [\"student\"]\n",
    "categorical_transformer = Pipeline([(\"onehot\", OneHotEncoder(drop = \"first\"))])\n",
    "numerical_features = [\"income\", \"balance\"]\n",
    "with_student_preprocessor = ColumnTransformer([(\"cat\", categorical_transformer, categorical_features),(\"num\", \"passthrough\", numerical_features)])\n",
    "with_student_clf = Pipeline([(\"preprocessor\", with_student_preprocessor), (\"classifier\", LogisticRegression(penalty = \"none\", solver = \"lbfgs\"))])\n",
    "without_student_preprocessor = ColumnTransformer([(\"num\", \"passthrough\", numerical_features)])\n",
    "without_student_clf = Pipeline([(\"preprocessor\", without_student_preprocessor), (\"classifier\", LogisticRegression(penalty = \"none\", solver = \"lbfgs\"))])\n",
    "\n",
    "# ციკლში გავუშვი,რომ საშუალო გადახრა მეპოვა\n",
    "for i in range(50):\n",
    "    X_train, X_test, y_train, y_test = train_test_split(df, df[\"default\"], test_size = 0.25)\n",
    "    with_student_clf.fit(X_train, y_train)\n",
    "    \n",
    "    with_student[i] = 1 - with_student_clf.score(X_test, y_test)\n",
    "    \n",
    "    without_student_clf.fit(X_train, y_train)\n",
    "    \n",
    "    without_student[i] = 1 - without_student_clf.score(X_test, y_test)\n",
    "    \n",
    "errors = pd.DataFrame({\"with_student\": with_student, \"without_student\": without_student})\n",
    "errors[\"difference\"] = errors[\"with_student\"] - errors[\"without_student\"]\n",
    "errors[\"difference\"].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "### სტუდენტის ცვლადმა ცდომილება გაზარდა"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tnwlgXHw8FZU"
   },
   "source": [
    "## Exercise 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "vtBcyEhW8FZU"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.078948\n",
      "         Iterations 10\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "endog = (df[\"default\"] == \"Yes\").astype(int)\n",
    "exog = sm.add_constant(df[[\"income\", \"balance\"]],1)\n",
    "mod = sm.Logit(endog, exog)\n",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0OMtOfAf8FZU"
   },
   "source": [
    "### a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "###estimated standard error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "RBucdz828FZU"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.985245461753051e-06"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.bse[\"income\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0002273813847684474"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.bse[\"balance\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RnBpQphn8FZU"
   },
   "source": [
    "\n",
    "### b\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "IDhYVBzN8FZU"
   },
   "outputs": [],
   "source": [
    "def boot_fn(data, clf):\n",
    "    clf.fit(data[[\"income\", \"balance\"]], data[\"default\"])\n",
    "    return clf.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "duch-oUI8FZU"
   },
   "source": [
    "\n",
    "### c\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "tR3DreK18FZU"
   },
   "outputs": [],
   "source": [
    "# np.random.seed(17)\n",
    "# num_estimates = 10000\n",
    "# boot_estimates = np.empty((num_estimates, 2))\n",
    "# for i in range(num_estimates):\n",
    "#     clf = LogisticRegression()\n",
    "#     sample = resample(df)\n",
    "#     coefs = boot_fn(sample, clf)\n",
    "#     boot_estimates[i, 0] = coefs[0, 0]\n",
    "#     boot_estimates[i, 1] = coefs[0, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# boot_df = pd.DataFrame(boot_estimates, columns = [\"income\", \"balance\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# boot_df[\"income\"].std()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# boot_df[\"balance\"].std()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nSHMUDLD8FZU"
   },
   "source": [
    "\n",
    "### d\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ITbFpDel8FZV"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "v945aBvh8FZV"
   },
   "source": [
    "## Exercise 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "e6IonpXq8FZV"
   },
   "outputs": [
    {
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       "\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>Year</th>\n",
       "      <th>Lag1</th>\n",
       "      <th>Lag2</th>\n",
       "      <th>Lag3</th>\n",
       "      <th>Lag4</th>\n",
       "      <th>Lag5</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Today</th>\n",
       "      <th>Direction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1990</td>\n",
       "      <td>0.816</td>\n",
       "      <td>1.572</td>\n",
       "      <td>-3.936</td>\n",
       "      <td>-0.229</td>\n",
       "      <td>-3.484</td>\n",
       "      <td>0.154976</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>Down</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1990</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.816</td>\n",
       "      <td>1.572</td>\n",
       "      <td>-3.936</td>\n",
       "      <td>-0.229</td>\n",
       "      <td>0.148574</td>\n",
       "      <td>-2.576</td>\n",
       "      <td>Down</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1990</td>\n",
       "      <td>-2.576</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.816</td>\n",
       "      <td>1.572</td>\n",
       "      <td>-3.936</td>\n",
       "      <td>0.159837</td>\n",
       "      <td>3.514</td>\n",
       "      <td>Up</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1990</td>\n",
       "      <td>3.514</td>\n",
       "      <td>-2.576</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.816</td>\n",
       "      <td>1.572</td>\n",
       "      <td>0.161630</td>\n",
       "      <td>0.712</td>\n",
       "      <td>Up</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1990</td>\n",
       "      <td>0.712</td>\n",
       "      <td>3.514</td>\n",
       "      <td>-2.576</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.816</td>\n",
       "      <td>0.153728</td>\n",
       "      <td>1.178</td>\n",
       "      <td>Up</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year   Lag1   Lag2   Lag3   Lag4   Lag5    Volume  Today Direction\n",
       "0  1990  0.816  1.572 -3.936 -0.229 -3.484  0.154976 -0.270      Down\n",
       "1  1990 -0.270  0.816  1.572 -3.936 -0.229  0.148574 -2.576      Down\n",
       "2  1990 -2.576 -0.270  0.816  1.572 -3.936  0.159837  3.514        Up\n",
       "3  1990  3.514 -2.576 -0.270  0.816  1.572  0.161630  0.712        Up\n",
       "4  1990  0.712  3.514 -2.576 -0.270  0.816  0.153728  1.178        Up"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weekly_filepath = \"Weekly.csv\"\n",
    "weekly = pd.read_csv(weekly_filepath)\n",
    "weekly.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AG8PfAX38FZV"
   },
   "source": [
    "### a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "S1FGsoc68FZV"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-0.03869814,  0.06020749]]), array([0.22122502]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = weekly[[\"Lag1\", \"Lag2\"]]\n",
    "y = weekly[\"Direction\"]\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X, y)\n",
    "clf.coef_, clf.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5u5qY5fs8FZV"
   },
   "source": [
    "\n",
    "### b\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "RElMt_Ba8FZV"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-0.03840931,  0.06080633]]), array([0.22324404]))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_loo = weekly.loc[weekly.index != 0, [\"Lag1\", \"Lag2\"]]\n",
    "y_loo = weekly.loc[weekly.index != 0, \"Direction\"]\n",
    "clf = LogisticRegression()\n",
    "clf = clf.fit(X_loo, y_loo)\n",
    "clf.coef_, clf.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pQ3cEC4n8FZV"
   },
   "source": [
    "\n",
    "### c\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "id": "ETeagKCS8FZV"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.42861856, 0.57138144]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.predict_proba(weekly.loc[0, [\"Lag1\", \"Lag2\"]].to_frame().T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Up'], dtype=object)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.predict(weekly.loc[0, [\"Lag1\", \"Lag2\"]].to_frame().T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Year             1990\n",
       "Lag1            0.816\n",
       "Lag2            1.572\n",
       "Lag3           -3.936\n",
       "Lag4           -0.229\n",
       "Lag5           -3.484\n",
       "Volume       0.154976\n",
       "Today           -0.27\n",
       "Direction        Down\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weekly.iloc[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "###თურმე არასწორი ყოფილა  (0,429 იყო down და 0,571 კი up მაგრამ თურმე down არის)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MHkTB2mj8FZV"
   },
   "source": [
    "\n",
    "### d\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "id": "jnCH_Qca8FZW"
   },
   "outputs": [],
   "source": [
    "n = weekly.shape[0]\n",
    "scores = np.empty(n)\n",
    "clf = LogisticRegression(penalty = \"none\", solver = \"lbfgs\")\n",
    "for i in range(n):\n",
    "    X_loo = weekly.loc[weekly.index != i, [\"Lag1\", \"Lag2\"]]\n",
    "    y_loo = weekly.loc[weekly.index != i, \"Direction\"]\n",
    "    clf.fit(X_loo, y_loo)\n",
    "    scores[i] = clf.score(weekly.loc[i, [\"Lag1\", \"Lag2\"]].to_frame().T, pd.Series(weekly.loc[i, \"Direction\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LS7Se-fc8FZW"
   },
   "source": [
    "\n",
    "#### i\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "SLOHjoFt8FZW"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AknnpKcP8FZW"
   },
   "source": [
    "\n",
    "#### ii\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "92I8QOR58FZW"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "g72a5Ixf8FZW"
   },
   "source": [
    "\n",
    "#### iii\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "NaR1tBg68FZW"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "y8el_uNM8FZW"
   },
   "source": [
    "\n",
    "#### iv\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "kDJCkjyG8FZW"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "n7ROsfm28FZW"
   },
   "source": [
    "\n",
    "### e\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "4SxDoEXN8FZW"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5500459136822773"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44995408631772266"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errors = 1 - scores\n",
    "errors.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5500459136822773"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#LOOCV\n",
    "X = weekly[[\"Lag1\", \"Lag2\"]]\n",
    "y = weekly[\"Direction\"]\n",
    "clf = LogisticRegression()\n",
    "loo = LeaveOneOut()\n",
    "cv_scores = cross_val_score(clf, X, y, cv = loo)\n",
    "cv_scores.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4499540863177227"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - cv_scores.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dAnADQjv8FZW"
   },
   "source": [
    "## Exercise 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZNJ3aSRs8FZX"
   },
   "source": [
    "### a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "id": "JPSp_BVo8FZW"
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "x = np.random.normal(size = 100)\n",
    "y = x - 2*x**2 + np.random.normal(size = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lVeYXS0q8FZX"
   },
   "source": [
    "\n",
    "### b\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "id": "0PXBMsj58FZX"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (16, 9))\n",
    "ax.scatter(x, y)\n",
    "\n",
    "x_range = np.linspace(start = -2.5, stop = 2.5)\n",
    "parabola = x_range - 2*x_range**2\n",
    "ax.plot(x_range, parabola, color = \"orange\", linestyle = \"--\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "e5CB4mBm8FZX"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XCpfTrrR8FZX"
   },
   "source": [
    "\n",
    "### c\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "id": "zGB8_MsV8FZX"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nikan\\AppData\\Local\\Temp/ipykernel_5252/2074887066.py:2: DeprecationWarning: The default dtype for empty Series will be 'object' instead of 'float64' in a future version. Specify a dtype explicitly to silence this warning.\n",
      "  loocv_scores = pd.Series()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1    5.302957\n",
       "2    0.912764\n",
       "3    0.956957\n",
       "4    0.972772\n",
       "dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(312)\n",
    "loocv_scores = pd.Series()\n",
    "for i in range(1, 5):\n",
    "    poly_reg = Pipeline([(\"poly\", PolynomialFeatures(degree = i)), (\"reg\", LinearRegression())])\n",
    "    loo = LeaveOneOut()\n",
    "    cv_scores = cross_val_score(poly_reg, x.reshape(-1, 1), y, scoring = \"neg_mean_squared_error\", cv = loo)\n",
    "    loocv_scores.loc[i] = abs(cv_scores.mean())\n",
    "loocv_scores\n",
    "# წრფივი\n",
    "# კვადრატული\n",
    "# კუბური"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WRDtpTQu8FZX"
   },
   "source": [
    "\n",
    "### d\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "id": "bykhB1p88FZX"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nikan\\AppData\\Local\\Temp/ipykernel_5252/4124702694.py:2: DeprecationWarning: The default dtype for empty Series will be 'object' instead of 'float64' in a future version. Specify a dtype explicitly to silence this warning.\n",
      "  loocv_scores = pd.Series()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1    5.302957\n",
       "2    0.912764\n",
       "3    0.956957\n",
       "4    0.972772\n",
       "dtype: float64"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "loocv_scores = pd.Series()\n",
    "for i in range(1, 5):\n",
    "    poly_reg = Pipeline([(\"poly\", PolynomialFeatures(degree = i)), (\"reg\", LinearRegression())])\n",
    "    loo = LeaveOneOut()\n",
    "    cv_scores = cross_val_score(poly_reg, x.reshape(-1, 1), y, scoring = \"neg_mean_squared_error\", cv = loo)\n",
    "    loocv_scores.loc[i] = abs(cv_scores.mean())\n",
    "loocv_scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kERygmnh8FZX"
   },
   "source": [
    "\n",
    "### e\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "flFBoJou8FZX"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pXyB_chy8FZX"
   },
   "source": [
    "\n",
    "### f\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Cin4WMGv8FZX"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Vou_WupP8FZX"
   },
   "source": [
    "## Exercise 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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>crim</th>\n",
       "      <th>zn</th>\n",
       "      <th>indus</th>\n",
       "      <th>chas</th>\n",
       "      <th>nox</th>\n",
       "      <th>rm</th>\n",
       "      <th>age</th>\n",
       "      <th>dis</th>\n",
       "      <th>rad</th>\n",
       "      <th>tax</th>\n",
       "      <th>ptratio</th>\n",
       "      <th>lstat</th>\n",
       "      <th>medv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>9.67</td>\n",
       "      <td>22.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>9.08</td>\n",
       "      <td>20.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>5.64</td>\n",
       "      <td>23.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6.48</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>506</th>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7.88</td>\n",
       "      <td>11.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>506 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        crim    zn  indus  chas    nox     rm   age     dis  rad  tax  \\\n",
       "1    0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296   \n",
       "2    0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242   \n",
       "3    0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242   \n",
       "4    0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222   \n",
       "5    0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222   \n",
       "..       ...   ...    ...   ...    ...    ...   ...     ...  ...  ...   \n",
       "502  0.06263   0.0  11.93     0  0.573  6.593  69.1  2.4786    1  273   \n",
       "503  0.04527   0.0  11.93     0  0.573  6.120  76.7  2.2875    1  273   \n",
       "504  0.06076   0.0  11.93     0  0.573  6.976  91.0  2.1675    1  273   \n",
       "505  0.10959   0.0  11.93     0  0.573  6.794  89.3  2.3889    1  273   \n",
       "506  0.04741   0.0  11.93     0  0.573  6.030  80.8  2.5050    1  273   \n",
       "\n",
       "     ptratio  lstat  medv  \n",
       "1       15.3   4.98  24.0  \n",
       "2       17.8   9.14  21.6  \n",
       "3       17.8   4.03  34.7  \n",
       "4       18.7   2.94  33.4  \n",
       "5       18.7   5.33  36.2  \n",
       "..       ...    ...   ...  \n",
       "502     21.0   9.67  22.4  \n",
       "503     21.0   9.08  20.6  \n",
       "504     21.0   5.64  23.9  \n",
       "505     21.0   6.48  22.0  \n",
       "506     21.0   7.88  11.9  \n",
       "\n",
       "[506 rows x 13 columns]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston = pd.read_csv(\"Boston.csv\", index_col = \"Unnamed: 0\")\n",
    "boston"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EBPGWp8W8FZX"
   },
   "source": [
    "### a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "id": "OY-PHgyy8FZX"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.532806324110698"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston[\"medv\"].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vDEDnRd88FZY"
   },
   "source": [
    "\n",
    "### b\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "id": "avBkNs9l8FZY"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4088611474975351"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#estimat standard error\n",
    "sample_sd = boston[\"medv\"].std()\n",
    "sample_sd / boston.shape[0]**0.5\n",
    "#or\n",
    "boston[\"medv\"].sem()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vF-GuEuE8FZY"
   },
   "source": [
    "\n",
    "### c\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "id": "2xMKjnpG8FZY"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap estimate of mean:  22.535756719367594\n",
      "Bootstrap estimate of std. error:  0.405167335688298\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "n_bootstraps = 10000\n",
    "means = np.empty(n_bootstraps)\n",
    "for i in range(n_bootstraps):\n",
    "    sample = resample(boston[\"medv\"])\n",
    "    means[i] = sample.mean()\n",
    "print(\"Bootstrap estimate of mean: \", means.mean())\n",
    "print(\"Bootstrap estimate of std. error: \", means.std(ddof = 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "itxqWeK-8FZY"
   },
   "source": [
    "\n",
    "### d\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "YFfj_i-88FZY"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nnZ5e7rm8FZY"
   },
   "source": [
    "\n",
    "### e\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "id": "BtMpeAcc8FZY"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21.2"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston[\"medv\"].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X-_cFwSU8FZY"
   },
   "source": [
    "\n",
    "### f\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "id": "TvPmN5Ey8FZY"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap estimate of median:  21.18772\n",
      "Bootstrap estimate of std. error:  0.37699922339634057\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "n_bootstraps = 10000\n",
    "medians = np.empty(n_bootstraps)\n",
    "for i in range(n_bootstraps):\n",
    "    sample = resample(boston[\"medv\"])\n",
    "    medians[i] = sample.median()\n",
    "print(\"Bootstrap estimate of median: \", medians.mean())\n",
    "print(\"Bootstrap estimate of std. error: \", medians.std(ddof = 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QWB2O4P_8FZY"
   },
   "source": [
    "\n",
    "### g\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "id": "1U3c_5I78FZY"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.75"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston[\"medv\"].quantile(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7SrNW7ey8FZY"
   },
   "source": [
    "\n",
    "### h\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "id": "ZsRvMdHc8FZY"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap estimate of tenth percentile:  12.763160000000001\n",
      "Bootstrap estimate of std. error:  0.5005490678614172\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "n_bootstraps = 10000\n",
    "tenth_percs = np.empty(n_bootstraps)\n",
    "for i in range(n_bootstraps):\n",
    "    sample = resample(boston[\"medv\"])\n",
    "    tenth_percs[i] = sample.quantile(0.1)\n",
    "print(\"Bootstrap estimate of tenth percentile: \", tenth_percs.mean())\n",
    "print(\"Bootstrap estimate of std. error: \", tenth_percs.std(ddof = 1))"
   ]
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