Machine Learning/Linear-Regression-Assumption.ipynb

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   "source": [
    "# Daily-Dose-of-Data-Science\n",
    "\n",
    "[Daily Dose of Data Science](https://avichawla.substack.com) is a publication on Substack that brings together intriguing frameworks, libraries, technologies, and tips that make the life cycle of a Data Science project effortless. \n",
    "\n",
    "Author: Avi Chawla\n",
    "\n",
    "[Medium](https://medium.com/@avi_chawla) | [LinkedIn](https://www.linkedin.com/in/avi-chawla/)\n",
    "\n",
    "# Most ML Folks Often Neglect This While Using Linear Regression\n",
    "\n",
    "\n",
    "Post Link: [Substack](https://avichawla.substack.com/p/most-ml-folks-often-neglect-this)\n",
    "\n",
    "LinkedIn Post: [LinkedIn](https://www.linkedin.com/feed/update/urn:li:activity:7037752570777415680/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "14ecc9b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "83e7fa00",
   "metadata": {},
   "outputs": [
    {
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       "\n",
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     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from drawdata import draw_scatter\n",
    "draw_scatter()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e1157c75",
   "metadata": {},
   "outputs": [
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       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('import pandas as pd'); }\n",
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       "      <th>0</th>\n",
       "      <td>28.849813</td>\n",
       "      <td>288.868621</td>\n",
       "      <td>a</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>57.103322</td>\n",
       "      <td>298.284255</td>\n",
       "      <td>a</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>327.270801</td>\n",
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       "      <th>169</th>\n",
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       "      <th>170</th>\n",
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       "      <td>211.757373</td>\n",
       "      <td>a</td>\n",
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       "      <th>171</th>\n",
       "      <td>-50.193608</td>\n",
       "      <td>232.314448</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>172 rows × 3 columns</p>\n",
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       "             x           y  z\n",
       "0    28.849813  288.868621  a\n",
       "1    57.103322  298.284255  a\n",
       "2    52.559254  327.270801  a\n",
       "3    80.426928  293.920127  a\n",
       "4    92.271886  335.209285  a\n",
       "..         ...         ... ..\n",
       "167  83.425353  180.832841  a\n",
       "168  84.296946  204.470036  a\n",
       "169  75.257573  249.517059  a\n",
       "170  10.790370  211.757373  a\n",
       "171 -50.193608  232.314448  a\n",
       "\n",
       "[172 rows x 3 columns]"
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_normal = pd.read_clipboard(sep=\",\")\n",
    "df_normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4e25dad3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"800\"\n",
       "            height=\"550\"\n",
       "            src=\"https://drawdata.xyz/scatter.html\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
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       "<IPython.lib.display.IFrame at 0x7fdfa23808e0>"
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from drawdata import draw_scatter\n",
    "draw_scatter()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ff6e103e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('import pandas as pd'); }\n",
       "    "
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       "<IPython.core.display.Javascript object>"
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       "      <td>a</td>\n",
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       "      <td>a</td>\n",
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       "              x           y  z\n",
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       "1     56.319240  236.620133  a\n",
       "2     77.279418  294.029280  a\n",
       "3     64.043181  305.319356  a\n",
       "4     79.194313  250.205104  a\n",
       "..          ...         ... ..\n",
       "370  418.918023  233.624989  a\n",
       "371  414.749348  252.554843  a\n",
       "372  441.084095  251.831245  a\n",
       "373  434.091452  290.169143  a\n",
       "374  410.823799  309.882328  a\n",
       "\n",
       "[375 rows x 3 columns]"
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     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_hetro = pd.read_clipboard(sep=\",\")\n",
    "df_hetro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "68a43a78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "        if (window._pyforest_update_imports_cell) { window._pyforest_update_imports_cell('import pandas as pd\\nimport matplotlib.pyplot as plt'); }\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use([\"seaborn-darkgrid\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7e5bfd01",
   "metadata": {},
   "outputs": [],
   "source": [
    "c_list = ['#46C7C7', '#00B9FF', '#FF7051']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2d54b2d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Heteroscedasticity')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(figsize=(10,5))\n",
    "sns.regplot(x='x', y='y',color= c_list[0], data=df_hetro, ci=None,  line_kws={'color': c_list[0]})\n",
    "\n",
    "axes.set_title(\"Heteroscedasticity\", fontsize = 20,fontweight=\"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "874d3ccc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Heteroscedasticity')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(figsize=(10,5))\n",
    "sns.regplot(x='x', y='y',color= c_list[0], data=df_hetro, ci=None,  line_kws={'color': c_list[0]})\n",
    "\n",
    "axes.set_title(\"Heteroscedasticity\", fontsize = 20,fontweight=\"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6cd05a3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}