From 9504d389b2f7258f238a6657621a642dd3de446c Mon Sep 17 00:00:00 2001
From: nsbagrova <31707825+nsbagrova@users.noreply.github.com>
Date: Mon, 5 Feb 2018 23:02:55 +0300
Subject: [PATCH] Add files via upload

---
 Python_HA3_Bagrova_Nataliya.ipynb | 932 ++++++++++++++++++++++++++++++
 1 file changed, 932 insertions(+)
 create mode 100644 Python_HA3_Bagrova_Nataliya.ipynb

diff --git a/Python_HA3_Bagrova_Nataliya.ipynb b/Python_HA3_Bagrova_Nataliya.ipynb
new file mode 100644
index 0000000..8437c64
--- /dev/null
+++ b/Python_HA3_Bagrova_Nataliya.ipynb
@@ -0,0 +1,932 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "X = np.random.rand(100000,3)\n",
+    "Y = X.dot(np.array([1,2,3])) + np.random.randn(100000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class OLS:\n",
+    "    \n",
+    "    def __init__(self, y, x):\n",
+    "        self.y = y\n",
+    "        self.x = x\n",
+    "        nrows = self.x.shape[0]\n",
+    "        l = np.full((nrows,1), 1) # add intercept (sorry, can't do without it, Sergei allowed)\n",
+    "        self.x = np.concatenate((l,x),axis=1) # merge with the 1s column\n",
+    "        # self.x = np.vstack((l, self.x))\n",
+    "        self.bh = np.dot(np.linalg.inv(np.dot(self.x.T,self.x)), np.dot(self.x.T,self.y)) # betas' calculation\n",
+    "        self.pred = self.bh[0]\n",
+    "        for i in range(len(self.bh) - 1):\n",
+    "            self.pred = self.pred + self.x[:, i+1] * self.bh[i+1]\n",
+    "        \n",
+    "        self.n = self.x.shape[0]\n",
+    "        self.k = self.x.shape[1]\n",
+    "        \n",
+    "        self.VCV = np.true_divide(1,self.n-self.k) * np.dot(np.dot(self.pred.T,self.pred),\\\n",
+    "                                                            np.linalg.inv(np.dot(self.x.T,self.x)))\n",
+    "        self.stderror = np.sqrt(np.diagonal(self.VCV))\n",
+    "        \n",
+    "        self.check = self.y - self.pred\n",
+    "        \n",
+    "    def beta(self):           \n",
+    "        return self.bh\n",
+    "            \n",
+    "    def predict(self):\n",
+    "        return self.pred\n",
+    "    \n",
+    "    def V(self):\n",
+    "        return self.VCV\n",
+    "    \n",
+    "    def std(self):\n",
+    "        return self.stderror\n",
+    "    \n",
+    "    def check_distr_res(self):\n",
+    "        return self.check\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "model = OLS(Y,X)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 2.99045934,  4.52315569,  3.97512765, ...,  0.64473915,\n",
+       "        4.57571085,  4.85057031])"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model.predict()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[  1.01973613e-03,  -6.13675553e-04,  -6.12250496e-04,\n",
+       "         -6.08961296e-04],\n",
+       "       [ -6.13675553e-04,   1.22754383e-03,   1.14200284e-06,\n",
+       "          2.08860051e-07],\n",
+       "       [ -6.12250496e-04,   1.14200284e-06,   1.22191884e-03,\n",
+       "         -3.79491424e-06],\n",
+       "       [ -6.08961296e-04,   2.08860051e-07,  -3.79491424e-06,\n",
+       "          1.22309893e-03]])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model.V()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 0.03193331,  0.03503632,  0.03495596,  0.03497283])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model.std()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x0000022A93276470>]], dtype=object)"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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sTHJ2kpczmCjetfJqS5KO1aI9gCSfB2aAM5LsBz4GzCQ5l8EwzqPALwFU1d4ktzKY3J0H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\n1P8HPOP5lyPcVX0AAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x22a9321bda0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# check errors are distributed normally\n",
+    "import pandas as pd\n",
+    "% matplotlib inline\n",
+    "pd.DataFrame(model.check_distr_res()).hist(bins = 100)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# 1-3\n",
+    "bh = np.random.uniform(0,1,11)\n",
+    "xh = np.random.uniform(-5,5,200)\n",
+    "uh = 10 * np.random.rand(200)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def factorial(n):\n",
+    "    \n",
+    "    if (n == 1):\n",
+    "        return 1\n",
+    "    elif (n == 0):\n",
+    "        return 1\n",
+    "    else:\n",
+    "        return n * factorial(n-1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# 4\n",
+    "yh = list()\n",
+    "\n",
+    "for i in range(200):\n",
+    "    temp = 0\n",
+    "    for k in range(11):   \n",
+    "        temp = temp + (bh[k] * (xh[i] ** k) / factorial(k))\n",
+    "    temp = temp - uh[i]\n",
+    "    yh.append(temp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.collections.PathCollection at 0x22a9452e908>"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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87HbjZHLizy9VtCKgZC9sWX4Y5zHv2D/TdELWJK/cam+WVsYVVUXEnDd5MaBb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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x22a94371eb8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "matplotlib.pyplot.scatter(xh, yh)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "xh = xh.reshape(200, 1)\n",
+    "model = OLS(np.asarray(yh), xh)\n",
+    "p = model.predict()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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ZiTMWpsmQLGFhXQ9zJydz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\nnU5j/8Q0UeYuJ1tns82vkxKNwMAA9PZCb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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x22a95980470>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "color_dict = {0:'r',1:'y',2:'g',3:'b'}\n",
+    "matplotlib.pyplot.figure(figsize=(16, 8), dpi=100)\n",
+    "matplotlib.pyplot.scatter(xh, yh)\n",
+    "for i in range(4):\n",
+    "    if (i == 0):\n",
+    "        temp_x = xh\n",
+    "    else:\n",
+    "        t = xh ** (i+1)\n",
+    "        temp_x = np.concatenate((temp_x, t), axis=1)\n",
+    "        # temp_x = np.vstack((t,(xh ** (i+1))))\\n\",\n",
+    "    # temp_x = temp_x.reshape(200,i+1)\\n\",\n",
+    "    y = np.asarray(yh)\n",
+    "    # y = y.reshape(200,)\\n\",\n",
+    "    # y = y.reshape(200,1)\\n\",\n",
+    "    model = OLS(y, temp_x)\n",
+    "    p = model.predict()\n",
+    "    p = p.reshape(200,1)\n",
+    "    tt = np.concatenate((xh, p), axis=1) # join х and predicted values (p)\n",
+    "    tt = np.sort(tt, axis = 0) # sort by x\n",
+    "    matplotlib.pyplot.plot(tt[:,0],tt[:,1], color = color_dict[i], linewidth = 3, label = 'K = ' + str(i))\n",
+    "    matplotlib.pyplot.legend()\n",
+    "    # matplotlib.pyplot.plot(xh,p, snap = False, color = color_dict[i], linewidth = 3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True, False,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True, False,  True,  True,  True, False,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True, False, False,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "       False,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True, False,  True,  True], dtype=bool)"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "nrows, ncols = 100, 100\n",
+    "matrix = np.random.normal(0, 1, size=(nrows, ncols)).astype('float64')\n",
+    "\n",
+    "# 1A (for columns)\n",
+    "from scipy import stats\n",
+    "n = len(matrix)\n",
+    "col_means = np.mean(matrix, axis=0)\n",
+    "col_stds = np.std(matrix, axis=0)\n",
+    "col_ses = np.sqrt(col_stds / n)\n",
+    "t_cr = stats.t.isf(0.05, n-1)\n",
+    "col_width = col_ses * t_cr\n",
+    "col_ci_up = col_means + col_width\n",
+    "col_ci_low = col_means - col_width\n",
+    "col_zero = (col_ci_up > 0) & (col_ci_low < 0)\n",
+    "col_zero"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "93"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 2A\n",
+    "sum(col_zero)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ True,  True,  True,  True,  True, False,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True, False,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True, False,  True, False,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True, False,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
+       "        True,  True,  True,  True,  True,  True,  True,  True,  True,  True], dtype=bool)"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 1B\n",
+    "nrows, ncols = 100, 100\n",
+    "matrix = np.random.normal(0, 1, size=(nrows, ncols)).astype('float64')\n",
+    "\n",
+    "# 1A (for )\n",
+    "from scipy import stats\n",
+    "n = len(matrix)\n",
+    "row_means = np.mean(matrix, axis=1)\n",
+    "row_stds = np.std(matrix, axis=1)\n",
+    "row_ses = np.sqrt(row_stds / n)\n",
+    "t_cr = stats.t.isf(0.05, n-1)\n",
+    "row_width = row_ses * t_cr\n",
+    "row_ci_up = row_means + row_width\n",
+    "row_ci_low = row_means - row_width\n",
+    "row_zero = (row_ci_up > 0) & (row_ci_low < 0)\n",
+    "row_zero"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "95"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 2B\n",
+    "sum(row_zero)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "# 4"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>n</th>\n",
+       "      <th>player</th>\n",
+       "      <th>season</th>\n",
+       "      <th>team</th>\n",
+       "      <th>position</th>\n",
+       "      <th>games_played</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>Cam Talbot</td>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>EDM</td>\n",
+       "      <td>G</td>\n",
+       "      <td>73</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2</td>\n",
+       "      <td>Braden Holtby</td>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>WSH</td>\n",
+       "      <td>G</td>\n",
+       "      <td>63</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3</td>\n",
+       "      <td>Sergei Bobrovsky</td>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>CBJ</td>\n",
+       "      <td>G</td>\n",
+       "      <td>63</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4</td>\n",
+       "      <td>Devan Dubnyk</td>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>MIN</td>\n",
+       "      <td>G</td>\n",
+       "      <td>65</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>5</td>\n",
+       "      <td>Tuukka Rask</td>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>BOS</td>\n",
+       "      <td>G</td>\n",
+       "      <td>65</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   n            player   season team position  games_played\n",
+       "0  1        Cam Talbot  2016-17  EDM        G            73\n",
+       "1  2     Braden Holtby  2016-17  WSH        G            63\n",
+       "2  3  Sergei Bobrovsky  2016-17  CBJ        G            63\n",
+       "3  4      Devan Dubnyk  2016-17  MIN        G            65\n",
+       "4  5       Tuukka Rask  2016-17  BOS        G            65"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 1\n",
+    "df = pd.read_csv('goalies-2014-2016.csv', skiprows = 0, sep = ';')\n",
+    "first_6_col = list(df.columns)[:6]\n",
+    "df.head()[first_6_col]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.00049999999999994493"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 2\n",
+    "df['save_percentage_self'] = df['saves'] / df['shots_against']\n",
+    "df['error'] = df['save_percentage'] - df['save_percentage_self']\n",
+    "df['error'].max()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "goals_against      53.351779\n",
+      "games_played       22.285395\n",
+      "save_percentage     0.071260\n",
+      "dtype: float64\n",
+      "goals_against      67.605735\n",
+      "games_played       28.476703\n",
+      "save_percentage     0.901179\n",
+      "dtype: float64\n"
+     ]
+    }
+   ],
+   "source": [
+    "# 3\n",
+    "col_std = ['goals_against', 'games_played', 'save_percentage']\n",
+    "print(df[col_std].std())\n",
+    "print(df[col_std].mean())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>player</th>\n",
+       "      <th>save_percentage</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>Sergei Bobrovsky</td>\n",
+       "      <td>0.931</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "             player  save_percentage\n",
+       "2  Sergei Bobrovsky            0.931"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 4\n",
+    "df_4 = df[df['season'] == '2016-17'] \n",
+    "df_4 = df_4[df_4['games_played'] > 40]\n",
+    "df_4[df_4['save_percentage'] == df_4['save_percentage'].max()][['player','save_percentage']]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>season</th>\n",
+       "      <th>player</th>\n",
+       "      <th>wins</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>Braden Holtby</td>\n",
+       "      <td>42</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>Devan Dubnyk</td>\n",
+       "      <td>40</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>Tuukka Rask</td>\n",
+       "      <td>37</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>10</th>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>Corey Crawford</td>\n",
+       "      <td>32</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>11</th>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>Pekka Rinne</td>\n",
+       "      <td>31</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>12</th>\n",
+       "      <td>2016-17</td>\n",
+       "      <td>Henrik Lundqvist</td>\n",
+       "      <td>31</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>95</th>\n",
+       "      <td>2015-16</td>\n",
+       "      <td>Braden Holtby</td>\n",
+       "      <td>48</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>101</th>\n",
+       "      <td>2015-16</td>\n",
+       "      <td>Corey Crawford</td>\n",
+       "      <td>35</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>102</th>\n",
+       "      <td>2015-16</td>\n",
+       "      <td>Henrik Lundqvist</td>\n",
+       "      <td>35</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>103</th>\n",
+       "      <td>2015-16</td>\n",
+       "      <td>Pekka Rinne</td>\n",
+       "      <td>34</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>104</th>\n",
+       "      <td>2015-16</td>\n",
+       "      <td>Devan Dubnyk</td>\n",
+       "      <td>32</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>105</th>\n",
+       "      <td>2015-16</td>\n",
+       "      <td>Tuukka Rask</td>\n",
+       "      <td>31</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>188</th>\n",
+       "      <td>2014-15</td>\n",
+       "      <td>Pekka Rinne</td>\n",
+       "      <td>41</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>189</th>\n",
+       "      <td>2014-15</td>\n",
+       "      <td>Braden Holtby</td>\n",
+       "      <td>41</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>193</th>\n",
+       "      <td>2014-15</td>\n",
+       "      <td>Devan Dubnyk</td>\n",
+       "      <td>36</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>197</th>\n",
+       "      <td>2014-15</td>\n",
+       "      <td>Tuukka Rask</td>\n",
+       "      <td>34</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>198</th>\n",
+       "      <td>2014-15</td>\n",
+       "      <td>Corey Crawford</td>\n",
+       "      <td>32</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>200</th>\n",
+       "      <td>2014-15</td>\n",
+       "      <td>Henrik Lundqvist</td>\n",
+       "      <td>30</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "      season            player  wins\n",
+       "1    2016-17     Braden Holtby    42\n",
+       "3    2016-17      Devan Dubnyk    40\n",
+       "4    2016-17       Tuukka Rask    37\n",
+       "10   2016-17    Corey Crawford    32\n",
+       "11   2016-17       Pekka Rinne    31\n",
+       "12   2016-17  Henrik Lundqvist    31\n",
+       "95   2015-16     Braden Holtby    48\n",
+       "101  2015-16    Corey Crawford    35\n",
+       "102  2015-16  Henrik Lundqvist    35\n",
+       "103  2015-16       Pekka Rinne    34\n",
+       "104  2015-16      Devan Dubnyk    32\n",
+       "105  2015-16       Tuukka Rask    31\n",
+       "188  2014-15       Pekka Rinne    41\n",
+       "189  2014-15     Braden Holtby    41\n",
+       "193  2014-15      Devan Dubnyk    36\n",
+       "197  2014-15       Tuukka Rask    34\n",
+       "198  2014-15    Corey Crawford    32\n",
+       "200  2014-15  Henrik Lundqvist    30"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 6\n",
+    "df_6 = df[df['wins'] > 29][['season', 'player', 'wins']]\n",
+    "df_6 = df_6.groupby(\"player\").filter(lambda x: len(x) == 3)\n",
+    "df_6"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(['Braden Holtby', 'Devan Dubnyk', 'Tuukka Rask', 'Corey Crawford',\n",
+       "       'Pekka Rinne', 'Henrik Lundqvist'], dtype=object)"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df_6.player.unique()"
+   ]
+  }
+ ],
+ "metadata": {
+  "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": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}