linearreg_sessions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpye as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.arange(100,1001,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum()/181"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(181,)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ModeResult(mode=array([100]), count=array([1]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mode(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.random.rand(1,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5117974609379323"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.random.rand(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.76855298, 0.80588693, 0.7043592 , 0.59413583, 0.53861394])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 1., 0., 1., 2.]),\n",
       " array([0.53861394, 0.59206854, 0.64552314, 0.69897773, 0.75243233,\n",
       "        0.80588693]),\n",
       " <a list of 5 Patch objects>)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.hist(x,bins=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.004356898797434574"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  4., 12., 11., 14., 24., 13., 14.,  4.,  3.]),\n",
       " array([-2.81837828, -2.27862331, -1.73886833, -1.19911335, -0.65935837,\n",
       "        -0.1196034 ,  0.42015158,  0.95990656,  1.49966154,  2.03941652,\n",
       "         2.57917149]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.hist(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.random.normal(10,5,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.006151807960272"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 5.,  2.,  6., 16., 19., 15.,  9., 15.,  9.,  4.]),\n",
       " array([-1.99074897,  0.26061205,  2.51197307,  4.76333409,  7.01469511,\n",
       "         9.26605613, 11.51741715, 13.76877817, 16.02013919, 18.27150021,\n",
       "        20.52286122]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.hist(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.59753371368949"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.array([1,2,3,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "1,2,0,-1,-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10/5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma square=variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 1., 1., 1., 1.]),\n",
       " array([1. , 1.8, 2.6, 3.4, 4.2, 5. ]),\n",
       " <a list of 5 Patch objects>)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.hist(x,bins=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.array([1,2,3,4,5,100])\n",
    "y=np.array([50,51,47,68,49,70])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 6 artists>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.bar(y,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}