stats.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "stats.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/HarshaVardhanBabu/TutorialMaterial/blob/master/stats.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wda7KwNyT6tf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "from scipy import stats\n",
        "from matplotlib import pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rsl3VGekTljQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = \"\"\"4.5 4.7 5.0 5.0 5.3 5.5 5.5 5.7 5.7 5.7\n",
        "6.0 6.0 6.0 6.0 6.3 6.3 6.3 6.5 6.5 6.5\n",
        "6.7 6.7 6.7 6.7 7.0 7.0 7.0 7.0 7.3 7.3\n",
        "7.3 7.3 7.5 7.5 7.5 7.5 7.7 7.7 7.7 7.7\n",
        "8.0 8.0 8.0 8.0 8.3 8.3 8.3 8.5 8.5 8.5\n",
        "8.5 8.7 8.7 9.0 9.0 9.0 9.3 9.3 10.0\"\"\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ErW1F1uyTteu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = data.split()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YzZeL8vTT2aF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.array(data)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cj_dzqSnT3Ym",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "sleeps = pd.Series(data,dtype=np.float)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yaDKQD0iUuRS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "outputId": "fb389cbb-12c7-4337-d48e-ad85980e9673"
      },
      "source": [
        "sleeps.describe()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count    59.000000\n",
              "mean      7.181356\n",
              "std       1.282438\n",
              "min       4.500000\n",
              "25%       6.300000\n",
              "50%       7.300000\n",
              "75%       8.150000\n",
              "max      10.000000\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OuXgzZXqUvEu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "725d4548-9593-4915-8337-ace1512a3c73"
      },
      "source": [
        "sleeps.hist(bins=10)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f33cbdf29e8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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uAe4B/qfXosYoFy8tHMvlhQb6EsOjITLzKRbPwb6734o6tQfYk5l3DqevZzHgK/kQcFdm\n7uu7kA59APheZj6dmT8EbgDe13NNncrMqzNza2aeDjwLfKfvmjq2LyLeCjD8+tQ4BjHQDxIR6yPi\n2Fc+A7/G4o+DJWTmk8DjEXHycNYZwP09ljQO51HodMvQY8B7IuKYiAgW91uJX2a/IiJ+cvj17Sye\nP/9yvxV17kbgwuHnC4Gvj2MQbyw6SES8k/+/MmId8OXM/EKPJXUuIk4FrgKOBB4GPpGZz/ZbVTeG\n/wk/BrwzM/f3XU+XIuKPgY8BB4C7gU9l5n/3W1V3IuJfgTcDPwR+PzNv77mkxiJiBzDF4tMV9wGX\nAf8A/D3wduBR4Dcyc+kvTtuPbaBLUg2ecpGkIgx0SSrCQJekIgx0SSrCQJekIgx0SSrCQJekIgx0\nSSri/wCLRh90EofkmQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hsYhmR3YV3zo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "68b257b2-13d0-48e4-ecce-f371908e7336"
      },
      "source": [
        "sleeps.plot.box()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f33cbd49cf8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VsBk4ZdiWe2A",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "25014658-cb8c-4650-bfe8-02946b6e1586"
      },
      "source": [
        "sleeps.plot(kind='kde')"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f33c94677b8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LRqVRWdtkAwuaDllZmKCz6eBxyqrrmW93bHepWTlpiMDqPXZVlPk8KwsTdJZuPkRslIur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\nZWGMMcYnKwtjjDE+WVkYY4zx6f8DcsSLQc32RVUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hYVJ8CGSZIF_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.array([3,5,7,7,8])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dpL0WE3VbEpg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d19fdcb5-63e7-4c77-fca3-40faa2347f3f"
      },
      "source": [
        "np.var(data),np.var(data,ddof=1)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3.2, 4.0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WsjXxdZbbMqH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "279369d9-5d45-47f0-dcc4-8b0b039d7447"
      },
      "source": [
        "np.std(data),np.std(data,ddof=1)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1.7888543819998317, 2.0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xtPqK4gPcQUx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "z = (data - np.mean(data))/np.std(data,ddof=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6nQEV3UNgpEa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "725bcda0-cd15-4d6c-920b-db5a46fab819"
      },
      "source": [
        "z"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.5, -0.5,  0.5,  0.5,  1. ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q_QqhoU4gp3V",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.arange(10)\n",
        "y = 5*x + np.random.randn(10)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "03pPVgSCiTIu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from matplotlib import pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1LZfiY-1jJlx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "34dc043b-ebf8-420b-b5fe-0328e0cabcea"
      },
      "source": [
        "plt.plot(x,y,'o')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f33c93faac8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TK-e_3aIjK-V",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.vstack([x,y])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rZx39ifGjhtx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ace1e9b8-06ee-42ff-de32-da58fc5d2082"
      },
      "source": [
        "data.shape"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 10)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9yHewLkyjiqL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "21141b2f-136d-4e49-aafb-4971ad84e832"
      },
      "source": [
        "np.cov(data)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  9.16666667,  45.46055872],\n",
              "       [ 45.46055872, 226.00638821]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A2cxe1yijlkx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "e14b13d1-57e6-4306-bb8c-4f34a541ae8f"
      },
      "source": [
        "np.corrcoef(data)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.        , 0.99877737],\n",
              "       [0.99877737, 1.        ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fCfTBInRj2T9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "normal_sample = np.random.randn(10000)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5R3cPBxGJcP7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def getSampleMeans(x,sample_size,n_samples):\n",
        "  sample =[]\n",
        "  for i in range(n_samples):\n",
        "    sample.append(np.random.choice(x,sample_size))\n",
        "  sample = np.array(sample)\n",
        "  sample_means = np.mean(sample,axis=1)\n",
        "  return sample_means\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kXwRLvPEKSeS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "sample_100 = getSampleMeans(normal_sample,100,10000)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "smC1qQvlKXrS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b19dab68-ce72-4913-b19a-bc0bc897320c"
      },
      "source": [
        "sample_100.mean(),normal_sample.mean()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-0.01712075109882178, -0.01617849082224386)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YOhfuUO8LIIH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 371
        },
        "outputId": "606f67b5-b173-4456-bbb3-0d37e1245baf"
      },
      "source": [
        "plt.hist(sample_100)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([  13.,  119.,  629., 1699., 2811., 2708., 1487.,  450.,   75.,\n",
              "           9.]),\n",
              " array([-0.39020953, -0.31411894, -0.23802835, -0.16193776, -0.08584718,\n",
              "        -0.00975659,  0.066334  ,  0.14242459,  0.21851517,  0.29460576,\n",
              "         0.37069635]),\n",
              " <a list of 10 Patch objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lxNVt+mrgvNkGJfkdYBXwuTH1td+c/VXVj6vqR232aMa7dzZMf9+oqrva9LeBB4CVy6W/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\nGQKS1LH/B4mT4SosulTfAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dZjdpzJ1xEF_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 813
        },
        "outputId": "ad3ba8f7-d6c5-41d5-aee3-204a0c0f221e"
      },
      "source": [
        "fig,ax = plt.subplots(1,1)\n",
        "ax.hist(normal_sample,bins=100,)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([  1.,   1.,   2.,   5.,   3.,   1.,   8.,  10.,   8.,   4.,  11.,\n",
              "          7.,  22.,  17.,  15.,  20.,  26.,  36.,  30.,  42.,  51.,  49.,\n",
              "         67.,  58.,  79.,  72., 115., 122., 112., 114., 133., 160., 152.,\n",
              "        153., 206., 199., 213., 233., 236., 244., 264., 267., 272., 322.,\n",
              "        282., 284., 263., 278., 300., 269., 250., 270., 268., 250., 280.,\n",
              "        246., 214., 197., 214., 168., 182., 179., 144., 133., 142., 133.,\n",
              "         96.,  88.,  84.,  82.,  65.,  78.,  52.,  61.,  39.,  42.,  29.,\n",
              "         30.,  25.,  19.,  17.,  21.,  14.,  13.,  13.,   8.,   2.,   2.,\n",
              "          1.,   2.,   4.,   2.,   0.,   0.,   0.,   0.,   0.,   1.,   0.,\n",
              "          2.]),\n",
              " array([-3.34985986, -3.27912904, -3.20839823, -3.13766741, -3.06693659,\n",
              "        -2.99620578, -2.92547496, -2.85474414, -2.78401333, -2.71328251,\n",
              "        -2.64255169, -2.57182088, -2.50109006, -2.43035924, -2.35962843,\n",
              "        -2.28889761, -2.21816679, -2.14743598, -2.07670516, -2.00597434,\n",
              "        -1.93524353, -1.86451271, -1.79378189, -1.72305108, -1.65232026,\n",
              "        -1.58158944, -1.51085863, -1.44012781, -1.36939699, -1.29866618,\n",
              "        -1.22793536, -1.15720454, -1.08647373, -1.01574291, -0.94501209,\n",
              "        -0.87428128, -0.80355046, -0.73281964, -0.66208883, -0.59135801,\n",
              "        -0.52062719, -0.44989638, -0.37916556, -0.30843474, -0.23770393,\n",
              "        -0.16697311, -0.09624229, -0.02551148,  0.04521934,  0.11595016,\n",
              "         0.18668097,  0.25741179,  0.32814261,  0.39887342,  0.46960424,\n",
              "         0.54033506,  0.61106587,  0.68179669,  0.75252751,  0.82325832,\n",
              "         0.89398914,  0.96471996,  1.03545077,  1.10618159,  1.17691241,\n",
              "         1.24764323,  1.31837404,  1.38910486,  1.45983568,  1.53056649,\n",
              "         1.60129731,  1.67202813,  1.74275894,  1.81348976,  1.88422058,\n",
              "         1.95495139,  2.02568221,  2.09641303,  2.16714384,  2.23787466,\n",
              "         2.30860548,  2.37933629,  2.45006711,  2.52079793,  2.59152874,\n",
              "         2.66225956,  2.73299038,  2.80372119,  2.87445201,  2.94518283,\n",
              "         3.01591364,  3.08664446,  3.15737528,  3.22810609,  3.29883691,\n",
              "         3.36956773,  3.44029854,  3.51102936,  3.58176018,  3.65249099,\n",
              "         3.72322181]),\n",
              " <a list of 100 Patch objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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yf5I9Sb6U5EXjrmkxST6U5NtdvbckOWncNS0myVuSPJjk6SQTOZthmm7TkeSGJIeSPDDu\nWpaSZGOSO5I81P3/XzHumhaT5DlJ7k7yza7W94+7pn6SnJDkG0k+v5zj1nzQAx+qqpdV1Vbg88Df\njLugJewGXlpVLwP+C7hqzPUs5QHgT4A7x13IQnpu0/E64HTg4iSnj7eqJX0SOH/cRQzgCPCuqjod\nOAu4bIL/XZ8Ezq2qlwNbgfOTnDXmmvq5Ati73IPWfNBX1c96Vp8HTOxJi6r6UlUd6Va/zvz1CROp\nqvZW1TgughvUM7fpqKr/BY7epmMiVdWdwI/GXUc/VXWwqu7rlp9gPpTWj7eqhdW8n3erJ3ZfE/v7\nn2QD8Hrgn5Z77JoPeoAkVyd5DPgzJrtH3+vtwL+Pu4gpttBtOiYykKZVks3AGcBd461kcd1QyB7g\nELC7qia2VuDvgL8Cnl7ugWsi6JN8OckDC3xtA6iq91TVRuAm4PJJrrXb5z3Mv0W+aXyVDlar1qYk\nzwc+C7zzmHfNE6WqnuqGbTcAZyZ56bhrWkiSNwCHqurelRy/Jj5KsKr+eMBdb2J+7v97R1jOkvrV\nmuQvgTcA59WY58Yu4991EvW9TYdWJsmJzIf8TVX1uXHXM4iq+kmSO5g/DzKJJ7zPBt6Y5ALgOcBv\nJPmXqvrzQQ5eEz36pSTZ0rO6Dfj2uGrpJ8n5zL91e2NV/WLc9Uw5b9MxAkkCXA/sraqPjruepSSZ\nOTpzLclzmf/8jIn8/a+qq6pqQ1VtZv5n9SuDhjwY9ADXdMMN9wOvYf6s9qT6OPACYHc3HfQfxl3Q\nYpK8Ocl+4FXAF5J8cdw19epOah+9TcdeYOck36YjyaeBrwG/n2R/kkvHXdMizgbeCpzb/Yzu6Xqh\nk2gdcEf3u38P82P0y5q2OC28MlaSGmePXpIaZ9BLUuMMeklqnEEvSY0z6CWpcQa9JDXOoJekxhn0\nktS4/wNz8rkCl77OCgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EW7DQpbVxILI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "4957df2a-c514-46d2-a66b-508829e8c360"
      },
      "source": [
        "sns.distplot(normal_sample)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f33c92ce6d8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Yp6NMuVsWZtI34OatI7YMiZlcVvSNX1BVjjacY05GfFA9MMVXxTNSSI6N4FUb4jGTzIq+\n8QtN53o5291PYYiN5w8Ld4Vx4/xM3jzcSP+g2+k4JohZ0Td+4UhjBwCFmaEzVXOkm4syaevup+RE\ni9NRTBCzefrGLxxtOEd6QhQpsZFOR5lyw/cp9A24CQ8TfrS1kpNnurh/5XSHk5lgZD1947i+ATcn\nmjuZG0I3ZI0mMjyMwox4DtW141ZbY99MDiv6xnEnmjsZcGvILL1wIYtyk2jr7qempcvpKCZIWdE3\njjvSeI4Il1CQFud0FMctyE7EFSYcqG1zOooJUlb0jeOONpxjZlocES775xgd4aIwI56Dde32GEUz\nKexTZhxV3dIVUqtq+mKxZ4jHHqNoJoNPRV9EVotIhYhUisjjoxx/TEQOich+EXlDRGZ4HRsUkb2e\nr00jzzWhbbvnDtRQW2/nQoaHeDYfOO10FBOExpyyKSIuYB1wM1ADlIjIJlU95NXsA6BYVbtE5MvA\nd4F7PMe6VXXZBOc2QWL7kSZSYiNIjQ+9qZrnMzzE87vdNcxMi/vIw2RsGqcZL196+iuASlU9rqp9\nwAZgrXcDVd2qqsPTDXYAeRMb0wSjvgE371U2U5iZgAThU7LGY7HN4jGTxJeinwtUe23XePadzxeB\nP3ttR4tIqYjsEJE7LyGjCVK7T7XS2TdoQzujsFk8ZrJM6IVcEXkAKAa+57V7hqoWA/cDPxSR2aOc\n95DnB0NpU5OtMhgqth9pIjxMmJ1uUzVH+sgsHrtRy0wgX4p+LZDvtZ3n2fcRInIT8A1gjar2Du9X\n1VrPn8eBbcDykeeq6jOqWqyqxenp6Rf1FzCBa/uRJooLUoiKcDkdxS/ZEI+ZDL4U/RKgUERmikgk\ncC/wkVk4IrIceJqhgt/otT9FRKI8r9OAawDvC8AmRDW291B+up3r52Y4HcVv2RCPmQxjFn1VHQAe\nBbYA5cBGVS0TkadEZI2n2feAeOC3I6ZmLgBKRWQfsBX4zohZPyZEbasYGsa7fq79Znc+NsRjJoNP\nq2yq6mZg84h9T3q9vuk8570HLB5PQBOc3jjcQE5SNAuyE9hrNyGd1+LcJA7Xn6OmpYvpqXbtw4yf\n3ZFrplzvwCBvH23mkwsybKrmGGyIx0w0K/pmyu083kJX3yA3zs90Oorfi45wMTczgQO1bTbEYyaE\nFX0z5d483Eh0RBhXzU51OkpAWJKbRHvPAKfO2CweM35W9M2UUlXeONzAtXPSiLapmj6Zn51AhEvY\nX2PXPsz4WdE3U6qysYPqlm5uXGBDO76KCncxLyuRg3XtDNhD0804WdE3U+r18qHbOG6YZ/PzL8aS\n3CQ6ewfYcdwemm7Gx4q+mVKvHapnUW4iWUnRTkcJKPOyEogMD+Ol/XVORzEBzoq+mTIN7T3sqTrL\nbYuynY4ScCJcYRRlJ/Lng/X0DdgQj7l0VvTNlNlSVg/ArQuzHE4SmJZ41uJ5t7LZ6SgmgFnRN1Pm\nlYP1zMmIZ05GvNNRAtKczHgSo8N5cZ8N8ZhLZ0XfTImWzj52nmhhtfXyL1l4WBirF2Xx6qEGevoH\nnY5jApRPa+8YM16vH2pg0K0osH5nldNxAtanl+awsbSGbRVNrF5kP0DNxbOevpkSr5TVk5scQ47N\n2hmXq2alkhoXabN4zCWzom8mXVt3P+8cbWb1oixbYG2cwl1h3LY4izfKG+nqG3A6jglAVvTNpNtS\nVk/foJs7lthUzYlwx5IcuvsHP7zRzZiLYUXfTLoX99UxfVosy/KTnY4SFK4omEZmYhQv2Swecwl8\nKvoislpEKkSkUkQeH+X4YyJySET2i8gbIjLD69iDInLU8/XgRIY3/mv9zirW76zi6e3HeOdoM7PS\n43h+V7XTsYKCK0z41OJstlU00d7T73QcE2DGLPoi4gLWAbcBRcB9IlI0otkHQLGqLgF+B3zXc+40\n4JvASmAF8E0RSZm4+MbfHahtQ4GledbLn0ifXppD36Cb18oanI5iAowvPf0VQKWqHlfVPmADsNa7\ngapuVdXhxb53AHme17cCr6lqi6q2Aq8BqycmugkE+2vayEqMJjPRZu1MpOX5yeQmx/CizeIxF8mX\nop8LeP9eXuPZdz5fBP58MeeKyEMiUioipU1NTT5EMoGgpbOPqpYuluYlOR0l6IgIdyzN5p2jzbR2\n9jkdxwSQCb2QKyIPAMXA9y7mPFV9RlWLVbU4PT19IiMZB+3zPPRjiQ3tTIpPL8lhwK284lnTyBhf\n+HJHbi2Q77Wd59n3ESJyE/AN4HpV7fU6d9WIc7ddSlATWFSVPadamZkWR0pcpNNxgob33cyq+uGN\nWvetmO5gKhNIfCn6JUChiMxkqIjfC9zv3UBElgNPA6tV1Xvy8Bbgn70u3t4CPDHu1MbvVbV0caaz\nj1X2sJRJIyIsyUtmW0UjT28/RkJ0xEeO37/SfhCYjxtzeEdVB4BHGSrg5cBGVS0TkadEZI2n2feA\neOC3IrJXRDZ5zm0B/pGhHxwlwFOefSbI7T7VSqQrjEW5iU5HCWpL8pJQ4GBdu9NRTIDwacE1Vd0M\nbB6x70mv1zdd4NxngWcvNaAJPN19gxyobWNRbhJR4fbw88mUmRhNZmIU+2vOctWsVKfjmABgd+Sa\nCbelrJ7eATeXzbALuFNhcW4yp8500dZtN2qZsVnRNxPut7urSYmNoCA1zukoIWGJZ0rsAc9sKWMu\nxIq+mVBVZ7p4t/IMl81IIcxW1JwSafFR5CRHs7+2zekoJgBY0TcTakNJFWECxTOmOR0lpCzJTaam\ntZsWu1HLjMGKvpkw/YNuNpbW8Mn5mSTFRIx9gpkwi22Ix/jIir6ZMG+UN9Dc0cv9K/PHbmwmVEps\nJNOnxdoQjxmTFX0zYdbvqiY7KZrr59oNWU5YnJvE6bYeGs/1OB3F+DEr+mZCVLd08fbRJu65Ih9X\nmF3AdcLi3CQEOFBjvX1zflb0zYT4TUk1AvxFsQ3tOCUxJoKCtDj217Shqk7HMX7Kir4Zt4FBNxtL\nq7lhXgY5yTFOxwlpS/KSaOropb7dhnjM6HxahsGYYd6rPA5Li4+k8Vwv99pKj45bmJPEi/vqbIjH\nnJf19M24Pb+riszEKG6YZ89CcFp8VDiz0+PZX2tDPGZ0VvTNuJzt6mPbkSbuKc4n3GX/nPzB4twk\nWjr7OGDTN80o7FNqxqX0VCsAf3GFXcD1FwtzknCJ8OI+e36u+Tgb0zeXzK3K7lOtFGbE89aRZqfj\nGI+YSBeFmfG8vP80T9y2gDCbQmu8+NTTF5HVIlIhIpUi8vgox68TkT0iMiAinxtxbNDzYJUPH65i\ngkNlYwdt3f1cbuvs+J0leUnUtfWwp6rV6SjGz4xZ9EXEBawDbgOKgPtEpGhEsyrgC8D6Ub5Ft6ou\n83ytGeW4CVAlJ1uIjXSxIDvB6ShmhAVZiUSFh/HS/tNORzF+xpee/gqgUlWPq2ofsAFY691AVU+q\n6n7APQkZjR/q6B3g8OlzXDY9hfAwuzTkb6IiXHxyfgYv7T/NwKB9LM3/58unNReo9tqu8ezzVbSI\nlIrIDhG586LSGb+1t6qVQVUun5EydmPjiLXLcmju6OXdY2ecjmL8yFR00WaoajFwP/BDEZk9soGI\nPOT5wVDa1NQ0BZHMeKgqpadayU+JITMx2uk45jxumJ9BUkwEf9hT43QU40d8Kfq1gPd8vDzPPp+o\naq3nz+PANmD5KG2eUdViVS1OT7cbfPxddUsXjed6KS6wC7j+LCrcxe1LstlS1kBn74DTcYyf8KXo\nlwCFIjJTRCKBewGfZuGISIqIRHlepwHXAIcuNazxD6WnWol0hbEkN8npKGYMdy3Ppbt/kC1l9U5H\nMX5izKKvqgPAo8AWoBzYqKplIvKUiKwBEJErRKQGuBt4WkTKPKcvAEpFZB+wFfiOqlrRD2C9/YPs\nr2ljcV4SUREup+OYMRTPSCF/Wgx/+MDnX85NkPPp5ixV3QxsHrHvSa/XJQwN+4w87z1g8TgzGj9y\noLaNvkE3xXYBNyCICHcty+XHWytpaO+xazDGlmEwF6f0VCvp8VFMnxbrdBTjozuX5+JWeGGP9faN\nFX1zEY42nKOqpYvighRE7Nb+QDErPZ4VM6fxm5IqW3nTWNE3vvtNSTVhAsun29BOoLlvRT4nz3Tx\n/nGbsx/qrOgbn/QNuHnhg1oWZCcSH2Xr9AWa2xZlkxgdzoZd1WM3NkHNir7xyRvlDbR09lFsi6sF\npOgIF5+5LI9XDtbT0tnndBzjIOuyGZ9sKKkmOymawsx4p6MYH418tGVidAR9g25e2FPDf/rELIdS\nGadZT9+Mqe5sN28dbeLuy/MIswu4ASsrKZrl05N5bmcVbrdd0A1VVvTNmH5bWoMq3F1sT8cKdH95\nzUxONHeytaLR6SjGIVb0zQW53crG0mqunZNGvs3ND3i3LcoiJyman799wukoxiFW9M0FvXusmdqz\n3fYM3CAR4QrjwasLeP/4Gcrq7MHpociKvrmg35RUkxwbwS1FmU5HMRPk3hXTiY108Yt3rLcfimz2\njjmv1s4+Xi1r4P6V04m2xdWCwvCMnqV5yfzpgzoKMxL48qqPPeLCBDHr6Zvz+sMHtfQNurnHhnaC\nzrVz0lCUt47YQ4tCjRV9MypV5Tcl1SzNS2JBdqLTccwES4mL5LLpKZScbKG+rcfpOGYKWdE3o9pT\ndZaKhnN2ATeIrZqXgVuVn24/5nQUM4Ws6JtR/eq9kyREhXPnslyno5hJMs3T21+/q8p6+yHEp6Iv\nIqtFpEJEKkXk8VGOXycie0RkQEQ+N+LYgyJy1PP14EQFN5Onvq2Hl/bXsSQviT/trWP9zqoPv0xw\nWTUvA7db+dGbR52OYqbImEVfRFzAOuA2oAi4T0SKRjSrAr4ArB9x7jTgm8BKYAXwTRGxdXn93L/v\nOIUqXDU7zekoZpJNi4vkgStn8PyuKo40nHM6jpkCvvT0VwCVqnpcVfuADcBa7waqelJV9wPuEefe\nCrymqi2q2gq8BqyegNxmkvT0D7J+VxXzsxKYFhfpdBwzBb52YyHxUeH88+Zyp6OYKeBL0c8FvBfh\nrvHs84VP54rIQyJSKiKlTU02hcxJm/bV0dLZx9VzrJcfKv58sJ5r56SxraKJb20qs6G8IOcXF3JV\n9RlVLVbV4vT0dKfjhCy3W/nZW8eZn5XArLQ4p+OYKXTlrFSmxUWy+cBpBm0FzqDmS9GvBbzn7eV5\n9vliPOeaKfbqoXqONnbw5VWz7Rm4ISbcFcbqhVk0nutl96lWp+OYSeRL0S8BCkVkpohEAvcCm3z8\n/luAW0QkxXMB9xbPPuNnVJUfb62kIDWWO5bkOB3HOGBhTiIzUmN5rbyBnv5Bp+OYSTJm0VfVAeBR\nhop1ObBRVctE5CkRWQMgIleISA1wN/C0iJR5zm0B/pGhHxwlwFOefcbPbD/SxMHadr68ajauMOvl\nhyIR4fbF2XT2DrDdlmcIWj4tuKaqm4HNI/Y96fW6hKGhm9HOfRZ4dhwZzSRTVdZtrSQnKZq7lo/6\nv9GEiLyUWJblJ/NuZTPVLV32DIUg5BcXco2znnrxECUnW7l8Rgq/211jMzdC3C1FmYjAt1+2KZzB\nyIp+iHO7lS1l9aTERnBFwTSn4xg/kBwbyQ3zMnilrN6GeYKQFf0Q9/KB09S19XDTgkzCXfbPwQy5\ndk4aM9Pi+NamMnoH7KJuMLFPeQjrH3Tz/VcryEqMZml+stNxjB8Jd4XxrTULOdHcac/TDTL25KwQ\n9vyuKk6e6eI/XjWDMJuXb0aobe2mKDuRH75+BGFo2Of+ldOdjmXGyXr6Iaq1s4/vv3qEq2alMi8z\nwek4xk/dviQbGBoGNMHBin6I+pfXj3Cup59vrimyu2/NeaXERrJqXgZlde0ctVU4g4IV/RB0uL6d\nf99xigeunMH8LHsUormwT8xJIzUukhf319lF3SBgRT/EqCrf2lRGYkwEj9081+k4JgCEu8K4Y0kO\nzR19/OIdu6gb6Kzoh5j/+tv97DjewvVz09l8oN5uxDI+mZeVwILsRH70RiV1Z7udjmPGwYp+CGnp\n7OPPB08zY1qs3YhlLtodi7Nxq/JPLx9yOooZByv6IeSfXj5ET/8gdy7PtSma5qKlxEXyyA1z2Hyg\nnreP2p26gcqKfoh460gTL+yp5brCdDITo52OYwLUQ9fNoiA1lr/740G6++yibiCyoh8C2rr7+dvf\n72dORjw3zM9wOo4JYNERLv4YIRBaAAANo0lEQVT5M4s5daaLH75xxOk45hJY0Q8B//TSIRrP9fL9\nu5cSYevrmHG6enYa9xTn8/O3T3Cwts3pOOYi+VQBRGS1iFSISKWIPD7K8SgR+Y3n+E4RKfDsLxCR\nbhHZ6/n66cTGN2N5o7yB3+6u4cvXz7b1dcyE+e+fWkBKbCR/87v99A24nY5jLsKYa++IiAtYB9wM\n1AAlIrJJVb0v4X8RaFXVOSJyL/A/gXs8x46p6rIJzm180Njew9/8bj/zsxL46o2FTscxQcB7iu+t\nCzN5bmcVP3rzKF+/ZZ6DqczF8KWnvwKoVNXjqtoHbADWjmizFviV5/XvgBvF7u13lNut/JeNe+nq\nG+TH9y8nMtyGdczEWpiTxGXTU1i3tdIeph5AfKkEuUC113aNZ9+obTzP1G0DUj3HZorIByKyXUQ+\nMc68xkf/tv0Y71ae4VtripiTYQuqmclxx5JsspNi+PrGvXT2Djgdx/hgsrt/p4HpqroceAxYLyIf\nW+xFRB4SkVIRKW1qsvm/4/VeZTPff7WCxblJDAwq63dWffhlzESKjnDxg79YSlVLF0+8cABVdTqS\nGYMvRb8WyPfazvPsG7WNiIQDScAZVe1V1TMAqrobOAZ8bMEXVX1GVYtVtTg9Pf3i/xbmQzWtXTz6\n/AekxUfxmeW5toKmmXQrZ6Xy9VvmsWlfHb9676TTccwYfCn6JUChiMwUkUjgXmDTiDabgAc9rz8H\nvKmqKiLpngvBiMgsoBA4PjHRzUjdfYN86de76R9088CVM4iKcDkdyYSIL18/m5sWZPJPL5dTerLF\n6TjmAsYs+p4x+keBLUA5sFFVy0TkKRFZ42n2CyBVRCoZGsYZntZ5HbBfRPYydIH3YVW1fxETbP3O\nKv59xyk++2/vcaiunbuW55IWH+V0LBNCwsKE7//FUvJSYnjo17s50dzpdCRzHuJvY3DFxcVaWlrq\ndIyA8tyOU2zaV8fOEy3csSSbq2enOR3JhKjmc7389K1jRIWHseW/XEdGgi35MVVEZLeqFo/Vzubx\nBYHtR5rYeaKFTxSmWcE3jkpLiOILVxfQ0TvAF54tobWzz+lIZgQr+gHuJ9sqefVQA8vyk7l1YZbT\ncYwhLyWWz6+cQWVTB/c88z4N7T1ORzJerOgHsHVbK/nuKxUszUvis5fl2XLJxm/MzUzgl395BbWt\n3Xzup+/ZGL8fsaIfgAbdyj+8WMb3tlRw1/Jc7i7OxxVmBd/4l6tnp/HcX19JR88Aa378Dm+UNzgd\nyWBFP+B09g7wpV+X8n/ePclfXTOT/3X3UuvhG7+0fmcVh+ra+eK1s0iICueLvyrle1sO0z9oC7Q5\nyYp+ADnScI47173Lm4cb+Yc1C3ny00XWwzd+b1pcJF+6fjaXT09h3dZj3LnuXQ7XtzsdK2SNucqm\ncYb3kgmqyu5Trby4v46kmAh+9Vcr+ESh3blsAkeEK4zPXp7HX183i2/84QBrfvQuD6+azVdWzSba\nbiKcUtbT93Pt3f38escpXviglryUWDZ/9RNW8E3Aauns40vXz2ZBdgL/+sZRrv7Om2w/YuttTSXr\n6fsptyqlJ1t5pew0A4PKpxZnc/XsVF4vb3Q6mjHjEh8Vzj1XTOfyGR1s2lfLg8/u4vbF2fz9HUVk\nJdnNXJPNir4fOlDTxtPbj1Hd2k1BahyfWZ5LWoItq2CCy5yMeL76yULOdvfz462VbKto5LFb5vHg\nVTMIt8d6ThpbhsGP1LR28b+2VPDHvXXERYXzqUVZLMtPtpUyTdA709HLi/vrONLQQXZSNGuX5fL4\nbfOdjhVQfF2GwXr6fuBEcyfPvHWM3++uRQS+vGo26fFRdoHLhIzU+CgevKqAg3XtvLy/jqe3H6Ot\nu5+/XT2P5NhIp+MFFSv6DukfdLP1cCMbS6t583Aj4a4w7i7O45Eb5pCTHGMPPDEhR0RYnJvE3Ix4\nXi9v4DclVWzaW8tti7JZPn3oN977V053OmbAs6I/hbr6Bnj/2BleLWvg9fIGznT2kRYfxcPXz+YL\nVxeQkWgXsYyJinBx+5IcLpuRwh8/qOV3e2ooPdXKHUuynY4WFGxMf5Ks31nFoFupae3iWFMHlY2d\nVLd0MahKQlQ4N8zP4NNLc1g1L53fltY4HdcYv+RWZffJVl4pq6e7f5A7l+Xw2M3zmJ4a63Q0v2Nj\n+g7o6R9kb/VZSk60sGlfHadauugbcCNAdnI018xJ5a+vm8XKmalEhtvsBGPGEibCFTOnsSg3ibeO\nNvHng/Vs2lfHrQuz+OK1M7l8RopNdLhIPvX0RWQ18L8BF/BzVf3OiONRwP8FLgfOAPeo6knPsSeA\nLwKDwFdVdcuF3iuQevqN53o4UNPGrpMtlJxo4UBtG/2DQ/89MxOjKEiNY1Z6PLPT4oiNsp+vxozX\njQsy+OV7J3luxynaewbIS4nh9iXZXFeYzrL8ZOJC+HPma09/zKLvecbtEeBmoIahZ+bep6qHvNp8\nBViiqg+LyL3AXap6j4gUAc8DK4Ac4HVgrqoOnu/9/LHod/UNcLK5ixPNnfy2tJq6tm5On+3hXO8A\nABGuoQtQVxRM44qCaRQXpLD5QL3DqY0JPsMXcjt7B3j5wGk2HzjNO0ebGXArrjBhTno8BWmxFKTF\nMTM1jhmpceSlxJCRGEVUeHDPhpvIon8V8C1VvdWz/QSAqv4PrzZbPG3eF5FwoB5Ix/Os3OG23u3O\n936TUfRVFdWh8UG3woDbTXffIN39g/T0D9Ld56atu5/mjl7PVx/NHb1Ut3Rx8kwnDe29H36vMIGM\nhGiyk6LJSY4hJzmG3OQYG64xxiF3LM1mz6lWSk+2Un66nZNnOqlu6aZvxGqesZEupk+LJTMxmszE\nKLISo5kWF0lsVDjxUeHERrqIiwrHFSYMlcWhuqEw9KenVooIIiDA0MjS0HaYCOFhQrhLCA8L++hr\n1/Axz/4wwRUmEzo0NZFj+rlAtdd2DbDyfG1UdUBE2oBUz/4dI87N9eE9L9qZjl4+8d2tHxZ29fzp\n9hT8ixHhEmIiXCTHRpKbHMOSvGRS4yJJi48iPSGKCLtb0Bi/8dK+0wAfdsJg6HPf1tVPc2cvbV39\ntPcM0N7TT2J0BI3neig/3U5zRy9uh+exDP9gEIaK/5K8JH7zpasm9z0n9bv7SEQeAh7ybHaISIUP\np6UBzZOX6pL5Yy5/zASW62L5Yy5/zAQBmuswsPHhS/7eM3xp5EvRrwXyvbbzPPtGa1PjGd5JYuiC\nri/noqrPAM/4EniYiJT68qvMVPPHXP6YCSzXxfLHXP6YCSzXhfgyTlECFIrITBGJBO4FNo1oswl4\n0PP6c8CbOjQAtgm4V0SiRGQmUAjsmpjoxhhjLtaYPX3PGP2jwBaGpmw+q6plIvIUUKqqm4BfAL8W\nkUqghaEfDHjabQQOAQPAIxeauWOMMWZy+TSmr6qbgc0j9j3p9boHuPs8534b+PY4Mp7PRQ0HTSF/\nzOWPmcByXSx/zOWPmcBynZffLcNgjDFm8tjcQ2OMCSFBUfRF5OsioiKS5gdZ/lFE9ovIXhF5VURy\nnM4EICLfE5HDnmx/EJFkpzMBiMjdIlImIm4RcXRWg4isFpEKEakUkcedzDJMRJ4VkUYROeh0Fm8i\nki8iW0XkkOf/39eczgQgItEisktE9nly/YPTmYaJiEtEPhCRl5zMEfBFX0TygVsAf1mA/nuqukRV\nlwEvAU+OdcIUeQ1YpKpLGFpW4wmH8ww7CHwGeMvJEJ7lRtYBtwFFwH2eZUSc9ktgtdMhRjEAfF1V\ni4ArgUf85L9XL/BJVV0KLANWi8iVDmca9jWg3OkQAV/0gX8B/oahu6Udp6rtXptx+E+uV1V1wLO5\ng6F7JhynquWq6svNeJNtBVCpqsdVtQ/YAKx1OBOq+hZDM+L8iqqeVtU9ntfnGCpmk3K3/cXQIR2e\nzQjPl+OfQRHJA24Hfu50loAu+iKyFqhV1X1OZ/EmIt8WkWrg8/hPT9/bXwF/djqEnxltuRHHi1gg\nEJECYDmw09kkQzzDKHuBRuA1VfWHXD9kqHPqHqvhZPOLZRguREReB7JGOfQN4L8zNLQzpS6USVX/\npKrfAL7hWZzuUeCb/pDL0+YbDP1q/txUZPI1lwlMIhIP/B74zyN+y3WM516gZZ7rVn8QkUWq6tg1\nERG5A2hU1d0issqpHMP8vuir6k2j7ReRxcBMYJ9npbo8YI+IrFDVSV3X+HyZRvEcQ/c3TEnRHyuX\niHwBuAO4Uadwru5F/Pdykk9Lhpj/T0QiGCr4z6nqC07nGUlVz4rIVoauiTh5IfwaYI2IfAqIBhJF\n5N9V9QEnwgTs8I6qHlDVDFUtUNUChn4dv2yyC/5YRKTQa3MtQ2soOc7zIJy/AdaoapfTefyQL8uN\nGA8Z6mn9AihX1R84nWeYiKQPz0wTkRiGngPi6GdQVZ9Q1TxPnbqXoWVqHCn4EMBF3499R0QOish+\nhoae/GIqG/BjIAF4zTOd9KdOBwIQkbtEpAa4CnjZ88yFKee5yD283Eg5sFFVy5zI4k1EngfeB+aJ\nSI2IfNHpTB7XAP8B+KTn39NeT0/WadnAVs/nr4ShMX1Hp0j6G7sj1xhjQoj19I0xJoRY0TfGmBBi\nRd8YY0KIFX1jjAkhVvSNMSaEWNE3xpgQYkXfGGNCiBV9Y4wJIf8PH1G8ypDW3iUAAAAASUVORK5C\nYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NMMSVs33yM8P",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PIO4vjm95kJt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5118faed-a9e0-4f5b-c914-4b8c1161a888"
      },
      "source": [
        "stats.norm().cdf(1.37)# P(Z<=z) # area to the left of the z in the distrubution"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.914656549178033"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2_DLlwXo5oJa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "36a46641-7541-4324-9108-3c3c2b0d6f6f"
      },
      "source": [
        "stats.norm().ppf(0.5) # P(Z<=z) = a finds z given a"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0mn-Aym064-3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5abd0cb5-d3f1-400d-c581-7d5d720b9a61"
      },
      "source": [
        "stats.norm().cdf(1.6) - stats.norm().cdf(-.155)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5067900496476889"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cVDDrWCr70zC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5058fafa-f42f-4789-e395-d5005ca4a1ea"
      },
      "source": [
        "stats.norm().ppf(1-0.025)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.959963984540054"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GCesCenf8XTh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "madison_fire = pd.Series(np.array(\"\"\"425 389 380 421 438 331 368 417 403 416 385 315\n",
        "427 417 386 386 378 300 321 286 269 225 268 317\n",
        "287 256 334 342 269 226 291 280 221 283 302 308\n",
        "296 266 238 286 317 276 254 278 247 336 296 259\n",
        "270 302 281 228 317 312 327 288 395 240 264 246\n",
        "294 254 222 285 254 264 277 266 228 347 322 232\n",
        "365 356 261 293 354 236 285 303 275 403 268 250\n",
        "279 400 370 399 438 287 363 350 278 278 234 266\n",
        "319 276 291 352 313 262 289 273 317 328 292 279\n",
        "289 312 334 294 297 304 240 303 255 305 252 286\n",
        "297 353 350 276 333 285 317 296 276 247 339 328\n",
        "267 305 291 269 386 264 299 261 284 302 342 304\n",
        "336 291 294 323 320 289 339 292 373 410 257 406\n",
        "374 268\"\"\".split(),dtype=np.float))\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wu1LDXNn-zUD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "outputId": "a14c52cf-c8bc-40ab-b1da-9f75b0af84ed"
      },
      "source": [
        "madison_fire.describe()"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count    158.000000\n",
              "mean     307.765823\n",
              "std       51.851720\n",
              "min      221.000000\n",
              "25%      269.250000\n",
              "50%      295.000000\n",
              "75%      336.000000\n",
              "max      438.000000\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hLnHtcgQ_Al0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d529b959-5d6b-4fe5-a105-e86b159d0332"
      },
      "source": [
        "stats.norm.interval(0.95,loc=307.765823,scale=52.851720/np.sqrt(158))"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(299.5248465505244, 316.00679944947564)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_r8arE-w_pYf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z2689y9mAD3b",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# the automated teller machine transaction times, suppose that, from\n",
        "# the measurements of a random sample of 38 transaction times, the sample\n",
        "# mean and standard deviation are found to be 261 and 22 seconds, respectively\n",
        "# Test the null hypothesis versus using a 2.5% level\n",
        "# of significance and state whether or not the claim m 270 is substantiated."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6p9WP0HHO5qz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "loc = 261\n",
        "scale = 22/np.sqrt(38)\n",
        "mu = 270"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JLQ1lGJcPAWT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "z = (loc - mu)/scale"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hjwBlkA2QbHV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e571b844-728c-431b-96a6-66077dd3b76e"
      },
      "source": [
        "z"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-2.5218057284873083"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_SstztOYQdp6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "c = 0.025\n",
        "zc = stats.norm.ppf(c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LHiqvfpnRfE0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1b81766c-c803-43be-96e7-4cc391767a73"
      },
      "source": [
        "zc"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-1.9599639845400545"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jsVedlEzRfnv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "f0c4854f-b400-4c05-842e-2d5510e82770"
      },
      "source": [
        "fig,ax = plt.subplots(1,1)\n",
        "ax.hist(normal_sample,bins=100)\n",
        "ax.axvline(z)\n",
        "ax.axvline(zc,marker=\"*\",color='r')"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.lines.Line2D at 0x7f33c9158b38>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ILB5czCobhmU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "4f264296-e369-42d2-8c37-d3fe12818d6a"
      },
      "source": [
        "stats.norm.cdf(z)"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0058377084397736485"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rckqALVLc4s9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# A brochure inviting subscriptions for a new diet program states that the participants are expected to lose over 22 pounds in five weeks. Suppose that, from\n",
        "# the data of the five-week weight losses of 56 participants, the sample mean and\n",
        "# standard deviation are found to be 23.5 and 10.2 pounds, respectively. Could\n",
        "# the statement in the brochure be substantiated on the basis of these findings?\n",
        "# Test with a \u0001 alpha = .05. Also calculate the P–value and interpret the result."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0Ymlpj-6dL8n",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n = 56\n",
        "xbar = 23.5\n",
        "s = 10.2\n",
        "scale = s/np.sqrt(n)\n",
        "loc = xbar\n",
        "z = (loc - 22)/scale"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V6tACX0VegI2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "49eab234-4efb-4445-903a-64b167b2bfee"
      },
      "source": [
        "z"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.100487466698218"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_I3w8E-qeg0g",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "zc = stats.norm.ppf(1-0.05)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7EO6tyCyfIPi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b4556d64-ca23-4f13-941d-8b9b93c689ce"
      },
      "source": [
        "zc"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.6448536269514722"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ux4uOwAcfI5L",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "c4d3d359-7865-41a6-de38-cb97dd1f353f"
      },
      "source": [
        "1-stats.norm.cdf(z)"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.13555989373583288"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nZzRH-ivfYsB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "85e87fad-fb98-42d7-c4f4-b4a4df2b2ea5"
      },
      "source": [
        "stats.t.cdf(0.5,df=19)"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6885917543567792"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DMoEN-cIivrh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "## Students T test"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7kmKwIiOjFJ2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.array(\"\"\"175 190 205 193 184\n",
        "207 204 193 196 180\"\"\".split(),dtype=float)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9IxnkfI_jMEP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "xbar,s = data.mean(),data.std(ddof=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PQV0PdDBjMsr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n = data.shape[0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DMpOKD_pjbi0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e6b443d4-f0cb-41b1-a12c-56fd72006890"
      },
      "source": [
        "n"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E6cMQ6yOjjUD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "t = (xbar - 200)/(s/np.sqrt(n))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6g72i1z9j_3g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "8ecef0fe-d69d-45c0-bcc9-22771c255d04"
      },
      "source": [
        "t"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-2.135087139095554"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q-cA5MANkAXV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tc = stats.t.ppf(0.05,df=n-1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-uEunNBTkPS_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1c256b29-4240-4bbb-9acc-4155b9bf1e05"
      },
      "source": [
        "tc"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-1.8331129326536337"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xWKhnP9tkbPB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pval = stats.t.cdf(t,df=n-1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZIVVcebIkplw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "0c0eb4ff-b3c7-424f-ba3d-4869e2d4dfa7"
      },
      "source": [
        "pval"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.030755340818943256"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1_ptNno9kqDp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = \"\"\"3 9\n",
        "3 5\n",
        "4 12\n",
        "5 9\n",
        "6 14\n",
        "6 16\n",
        "7 22\n",
        "8 18\n",
        "8 24\n",
        "9 22\"\"\".split()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "osLgt7M9PTYr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = [(x,y) for x,y in zip(data[::2],data[1::2])]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6ET4Evo8PURp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.array(data,dtype=np.float)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8BaOa5mnQFJC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "affeee9e-5a0a-4110-886f-9699e17b6c21"
      },
      "source": [
        "data"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 3.,  9.],\n",
              "       [ 3.,  5.],\n",
              "       [ 4., 12.],\n",
              "       [ 5.,  9.],\n",
              "       [ 6., 14.],\n",
              "       [ 6., 16.],\n",
              "       [ 7., 22.],\n",
              "       [ 8., 18.],\n",
              "       [ 8., 24.],\n",
              "       [ 9., 22.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-0HUlymjQRPh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "bdcef77e-683f-4ae0-cbb5-f74965727ecd"
      },
      "source": [
        "plt.plot(data[:,0],data[:,1],\"o\")"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f33c8fc6e48>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD8CAYAAABw1c+bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NBsbcOoKQeHv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "0b19ec5a-bb3b-4340-a95f-b6f40d2bdaac"
      },
      "source": [
        "np.corrcoef(data[:,0],data[:,1])"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.        , 0.91015538],\n",
              "       [0.91015538, 1.        ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L516kIKEQo1N",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn import preprocessing"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jDFa6Y46TTVL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = data[:,0]\n",
        "X_scale = preprocessing.scale(X)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HvAsKCW-TwjD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "outputId": "f2e7ec25-2367-4be1-d881-764151bc4260"
      },
      "source": [
        "pd.Series(X).describe()"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count    10.00000\n",
              "mean      5.90000\n",
              "std       2.13177\n",
              "min       3.00000\n",
              "25%       4.25000\n",
              "50%       6.00000\n",
              "75%       7.75000\n",
              "max       9.00000\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vSdPWdgZTzXC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "outputId": "528d086c-e33c-4903-8b48-f47b300c8633"
      },
      "source": [
        "pd.Series(X_scale).describe()"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count    1.000000e+01\n",
              "mean    -1.110223e-16\n",
              "std      1.054093e+00\n",
              "min     -1.433958e+00\n",
              "25%     -8.158725e-01\n",
              "50%      4.944682e-02\n",
              "75%      9.147661e-01\n",
              "max      1.532851e+00\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LYvxQuNfT-Uw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a198d60e-2a59-47ea-854f-457f6a8ca0a8"
      },
      "source": [
        "X_scale.std(ddof=1)"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0540925533894598"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zxahIFS_UHOk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.linear_model import LinearRegression"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_XIvlw3kabWm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "82f73a61-ae4e-49ea-c310-1470a88352a9"
      },
      "source": [
        "X.shape"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PpM2UevUaHjZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "653371ed-e1bf-4eaa-a903-a9be1dbf9dae"
      },
      "source": [
        "model = LinearRegression()\n",
        "model.fit(X.reshape(-1,1),data[:,1])"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m3z4Qx6caRrp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "ypred = model.predict(X.reshape(-1,1))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QjKrmhgrDnTJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e6554b27-43a0-498f-a632-10efe4493801"
      },
      "source": [
        "model.coef_,model.intercept_"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([2.7408313]), -1.0709046454767783)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jXegxg3dao5D",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "aff53fba-0817-43d9-dee5-f9581b8aee78"
      },
      "source": [
        "plt.plot(ypred,data[:,1],\"o\")"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f33c57f6048>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 79
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD8CAYAAABw1c+bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jM2WYU87a5Ja",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "07f9b1ce-8e26-42ea-9166-3c15ec8f0d39"
      },
      "source": [
        "model.score(X.reshape(-1,1),data[:,1])"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8283828208791013"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 80
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3JHYEgwpa_2P",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "eb148a82-7686-493a-912d-974f719bccdd"
      },
      "source": [
        "from sklearn.datasets import load_boston\n",
        "boston = load_boston()\n",
        "print(boston.data.shape)"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(506, 13)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1zjdcchPMLmb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = boston.data\n",
        "Y = boston.target"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y3IPRhGwMRk7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "07157b52-0bea-4e09-daf2-3763e6f673bc"
      },
      "source": [
        "X.shape,Y.shape"
      ],
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((506, 13), (506,))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3UqnRyeAMUa8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "65012402-4da4-404e-e4ff-ff2c80da5d7c"
      },
      "source": [
        "boston.feature_names"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
              "       'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6p5RqSxIMYCJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import statsmodels.api as sm"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0pcNJRbHNVYR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "fc8edcb2-8b6f-4998-abff-14ac0698ba46"
      },
      "source": [
        "X.shape,Y.shape"
      ],
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((506, 13), (506,))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1kPvlrg1MjfJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "res = sm.OLS(Y,X).fit()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9ugkvYqYM2op",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 709
        },
        "outputId": "77a0bfb6-d165-448c-8524-6111d372a6e1"
      },
      "source": [
        "res.summary()"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.959</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.958</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   891.3</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Sun, 08 Sep 2019</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>13:26:17</td>     <th>  Log-Likelihood:    </th>          <td> -1523.8</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th>          <td>   3074.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>   493</td>      <th>  BIC:               </th>          <td>   3128.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>    13</td>      <th>                     </th>              <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "   <td></td>      <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x1</th>  <td>   -0.0929</td> <td>    0.034</td> <td>   -2.699</td> <td> 0.007</td> <td>   -0.161</td> <td>   -0.025</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x2</th>  <td>    0.0487</td> <td>    0.014</td> <td>    3.382</td> <td> 0.001</td> <td>    0.020</td> <td>    0.077</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x3</th>  <td>   -0.0041</td> <td>    0.064</td> <td>   -0.063</td> <td> 0.950</td> <td>   -0.131</td> <td>    0.123</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x4</th>  <td>    2.8540</td> <td>    0.904</td> <td>    3.157</td> <td> 0.002</td> <td>    1.078</td> <td>    4.630</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x5</th>  <td>   -2.8684</td> <td>    3.359</td> <td>   -0.854</td> <td> 0.394</td> <td>   -9.468</td> <td>    3.731</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x6</th>  <td>    5.9281</td> <td>    0.309</td> <td>   19.178</td> <td> 0.000</td> <td>    5.321</td> <td>    6.535</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x7</th>  <td>   -0.0073</td> <td>    0.014</td> <td>   -0.526</td> <td> 0.599</td> <td>   -0.034</td> <td>    0.020</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x8</th>  <td>   -0.9685</td> <td>    0.196</td> <td>   -4.951</td> <td> 0.000</td> <td>   -1.353</td> <td>   -0.584</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x9</th>  <td>    0.1712</td> <td>    0.067</td> <td>    2.564</td> <td> 0.011</td> <td>    0.040</td> <td>    0.302</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x10</th> <td>   -0.0094</td> <td>    0.004</td> <td>   -2.395</td> <td> 0.017</td> <td>   -0.017</td> <td>   -0.002</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x11</th> <td>   -0.3922</td> <td>    0.110</td> <td>   -3.570</td> <td> 0.000</td> <td>   -0.608</td> <td>   -0.176</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x12</th> <td>    0.0149</td> <td>    0.003</td> <td>    5.528</td> <td> 0.000</td> <td>    0.010</td> <td>    0.020</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x13</th> <td>   -0.4163</td> <td>    0.051</td> <td>   -8.197</td> <td> 0.000</td> <td>   -0.516</td> <td>   -0.317</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td>204.082</td> <th>  Durbin-Watson:     </th> <td>   0.999</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1374.225</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td> 1.609</td>  <th>  Prob(JB):          </th> <td>3.90e-299</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td>10.404</td>  <th>  Cond. No.          </th> <td>8.50e+03</td> \n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 8.5e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                                 OLS Regression Results                                \n",
              "=======================================================================================\n",
              "Dep. Variable:                      y   R-squared (uncentered):                   0.959\n",
              "Model:                            OLS   Adj. R-squared (uncentered):              0.958\n",
              "Method:                 Least Squares   F-statistic:                              891.3\n",
              "Date:                Sun, 08 Sep 2019   Prob (F-statistic):                        0.00\n",
              "Time:                        13:26:17   Log-Likelihood:                         -1523.8\n",
              "No. Observations:                 506   AIC:                                      3074.\n",
              "Df Residuals:                     493   BIC:                                      3128.\n",
              "Df Model:                          13                                                  \n",
              "Covariance Type:            nonrobust                                                  \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "x1            -0.0929      0.034     -2.699      0.007      -0.161      -0.025\n",
              "x2             0.0487      0.014      3.382      0.001       0.020       0.077\n",
              "x3            -0.0041      0.064     -0.063      0.950      -0.131       0.123\n",
              "x4             2.8540      0.904      3.157      0.002       1.078       4.630\n",
              "x5            -2.8684      3.359     -0.854      0.394      -9.468       3.731\n",
              "x6             5.9281      0.309     19.178      0.000       5.321       6.535\n",
              "x7            -0.0073      0.014     -0.526      0.599      -0.034       0.020\n",
              "x8            -0.9685      0.196     -4.951      0.000      -1.353      -0.584\n",
              "x9             0.1712      0.067      2.564      0.011       0.040       0.302\n",
              "x10           -0.0094      0.004     -2.395      0.017      -0.017      -0.002\n",
              "x11           -0.3922      0.110     -3.570      0.000      -0.608      -0.176\n",
              "x12            0.0149      0.003      5.528      0.000       0.010       0.020\n",
              "x13           -0.4163      0.051     -8.197      0.000      -0.516      -0.317\n",
              "==============================================================================\n",
              "Omnibus:                      204.082   Durbin-Watson:                   0.999\n",
              "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1374.225\n",
              "Skew:                           1.609   Prob(JB):                    3.90e-299\n",
              "Kurtosis:                      10.404   Cond. No.                     8.50e+03\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 8.5e+03. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bJVdYzDnM9I4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "sm.OLS?"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "42pSezR-N3TH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}