Machine Learning/Data-Transformation-for-Normality.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dc958136",
   "metadata": {},
   "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",
    "# Try This If Your Linear Regression Model is Underperforming\n",
    "\n",
    "Post Link: [Substack](https://www.blog.dailydoseofds.com/p/try-this-if-your-linear-regression)\n",
    "\n",
    "LinkedIn Post: [LinkedIn](https://www.linkedin.com/feed/update/urn:li:share:7074341072188899328/)\n",
    "\n",
    "Twitter Post: [Twitter](https://twitter.com/_avichawla/status/1668575549499887616)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "22ae250f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "167e1705",
   "metadata": {},
   "outputs": [],
   "source": [
    "color_code = '#fe7c73'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2fd99100",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.random.gamma(2, 1, 1000) * 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "68602483",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.hist(data, bins=30, edgecolor='black', color = color_code)\n",
    "plt.title('Original Data Distribution', fontsize = 20, fontweight = \"bold\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d926c371",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Apply logarithmic transformation\n",
    "data_log = np.log(data)\n",
    "\n",
    "# Plot log-transformed data distribution\n",
    "plt.hist(data_log, bins=30, edgecolor='black', color = color_code)\n",
    "plt.title('Log-Transformed Data', fontsize = 20, fontweight = \"bold\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5b5b8edb",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Apply square root transformation\n",
    "data_sqrt = np.sqrt(data)\n",
    "\n",
    "# Plot square root-transformed data distribution\n",
    "plt.hist(data_sqrt, bins=30, edgecolor='black', color = color_code)\n",
    "plt.title('Square Root-Transformed Data', fontsize = 20, fontweight = \"bold\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "592ee9f2",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Apply Box-Cox transformation\n",
    "data_boxcox, _ = stats.boxcox(data)\n",
    "\n",
    "# Plot Box-Cox transformed data distribution\n",
    "plt.hist(data_boxcox, bins=30, edgecolor='black', color = color_code)\n",
    "plt.title('Box-Cox Transformed Data', fontsize = 20, fontweight = \"bold\");"
   ]
  }
 ],
 "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"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}