lin_regress.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "59f23953",
   "metadata": {},
   "source": [
    "# __Simple Correlation and Linear Regression__\n",
    "\n",
    "## Using one independent variable to predict the dependent variable\n",
    "\n",
    "* Predicting how a **restaurant bill** relates to **server tips**.\n",
    "* First using the linear model of the **scikit-learn** module.\n",
    "* Then with the **statsmodel** module and Ordinary Least Squares (**OLS**).\n",
    "      \n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97531508-e6de-45be-abed-03277b9641fd",
   "metadata": {},
   "source": [
    "#### Import of pandas, seaborn, and sklearn from linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3dc9ebb6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns \n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89876912",
   "metadata": {},
   "source": [
    "#### Load the \"tips\" dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ac32476f",
   "metadata": {},
   "outputs": [],
   "source": [
    "tips = sns.load_dataset('tips')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63fc7d51",
   "metadata": {},
   "source": [
    "#### Tips dataset information:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8a07e81a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 244 entries, 0 to 243\n",
      "Data columns (total 7 columns):\n",
      " #   Column      Non-Null Count  Dtype   \n",
      "---  ------      --------------  -----   \n",
      " 0   total_bill  244 non-null    float64 \n",
      " 1   tip         244 non-null    float64 \n",
      " 2   sex         244 non-null    category\n",
      " 3   smoker      244 non-null    category\n",
      " 4   day         244 non-null    category\n",
      " 5   time        244 non-null    category\n",
      " 6   size        244 non-null    int64   \n",
      "dtypes: category(4), float64(2), int64(1)\n",
      "memory usage: 7.4 KB\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "print(tips.info())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22e94927",
   "metadata": {},
   "source": [
    "#### Number of rows and columns in \"tips\" dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "49f08797",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(244, 7)\n"
     ]
    }
   ],
   "source": [
    "print(tips.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa83aad0",
   "metadata": {},
   "source": [
    "#### Head and Tail ends of \"tips\" dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8af75e85",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     total_bill   tip     sex smoker   day    time  size\n",
      "0         16.99  1.01  Female     No   Sun  Dinner     2\n",
      "1         10.34  1.66    Male     No   Sun  Dinner     3\n",
      "2         21.01  3.50    Male     No   Sun  Dinner     3\n",
      "3         23.68  3.31    Male     No   Sun  Dinner     2\n",
      "4         24.59  3.61  Female     No   Sun  Dinner     4\n",
      "..          ...   ...     ...    ...   ...     ...   ...\n",
      "239       29.03  5.92    Male     No   Sat  Dinner     3\n",
      "240       27.18  2.00  Female    Yes   Sat  Dinner     2\n",
      "241       22.67  2.00    Male    Yes   Sat  Dinner     2\n",
      "242       17.82  1.75    Male     No   Sat  Dinner     2\n",
      "243       18.78  3.00  Female     No  Thur  Dinner     2\n",
      "\n",
      "[244 rows x 7 columns]\n"
     ]
    }
   ],
   "source": [
    "print(tips)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15459253",
   "metadata": {},
   "source": [
    "#### First 5 rows (head) of \"tips\" dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0780d6db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   total_bill   tip     sex smoker  day    time  size\n",
      "0       16.99  1.01  Female     No  Sun  Dinner     2\n",
      "1       10.34  1.66    Male     No  Sun  Dinner     3\n",
      "2       21.01  3.50    Male     No  Sun  Dinner     3\n",
      "3       23.68  3.31    Male     No  Sun  Dinner     2\n",
      "4       24.59  3.61  Female     No  Sun  Dinner     4\n"
     ]
    }
   ],
   "source": [
    "print(tips.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99584dad",
   "metadata": {},
   "source": [
    "#### Last 5 rows (tail) of \"tips\" dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2052eede",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     total_bill   tip     sex smoker   day    time  size\n",
      "239       29.03  5.92    Male     No   Sat  Dinner     3\n",
      "240       27.18  2.00  Female    Yes   Sat  Dinner     2\n",
      "241       22.67  2.00    Male    Yes   Sat  Dinner     2\n",
      "242       17.82  1.75    Male     No   Sat  Dinner     2\n",
      "243       18.78  3.00  Female     No  Thur  Dinner     2\n"
     ]
    }
   ],
   "source": [
    "print(tips.tail())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0db9c1d",
   "metadata": {},
   "source": [
    "#### Independent variable \"total_bill\" added as \"x\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "63f1c9c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = tips['total_bill'].values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c38640ee",
   "metadata": {},
   "source": [
    "#### Dependent variable \"tip\" added as \"y\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "24103553",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      1.01\n",
       "1      1.66\n",
       "2      3.50\n",
       "3      3.31\n",
       "4      3.61\n",
       "       ... \n",
       "239    5.92\n",
       "240    2.00\n",
       "241    2.00\n",
       "242    1.75\n",
       "243    3.00\n",
       "Name: tip, Length: 244, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y=tips['tip']\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ab299609-2378-418c-8d2c-9c5d841ef845",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>total_bill</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.675734</td>\n",
       "      <td>0.598315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tip</th>\n",
       "      <td>0.675734</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.489299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>size</th>\n",
       "      <td>0.598315</td>\n",
       "      <td>0.489299</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            total_bill       tip      size\n",
       "total_bill    1.000000  0.675734  0.598315\n",
       "tip           0.675734  1.000000  0.489299\n",
       "size          0.598315  0.489299  1.000000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find Pearson Correlation Coefficient (r)\n",
    "r = tips.corr(method = 'pearson')\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f284f6d1-7113-4bdc-b57a-f41999eae08c",
   "metadata": {},
   "source": [
    "#### Pearson Correlation Coefficient as (r) defined:\n",
    "* ± 0.50 < r > ± 1 indicates a strong correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "3731067e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            total_bill       tip      size\n",
      "total_bill    1.000000  0.675734  0.598315\n",
      "tip           0.675734  1.000000  0.489299\n",
      "size          0.598315  0.489299  1.000000\n"
     ]
    }
   ],
   "source": [
    "r=tips.corr(method='pearson')\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e037531d",
   "metadata": {},
   "source": [
    "#### \n",
    "0.675734 shows strong correlation between the bill and the tip so, we proceed with linear regression. \n",
    "#### Linear regression model of sklearn added as \"lr\": "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d559b9db-a9b0-4d03-bf6c-01d94b49c06f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "lr = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac297962-0f3e-4248-b850-bb6269443b94",
   "metadata": {},
   "source": [
    "lr=linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2aeb81e6-7b15-429d-b1af-d16506e05fdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Regression line equation is **y = mx + b**, where...\n",
    "- y is the **dependent** variable\n",
    "- m is the **slope** of the line\n",
    "- x is the **independent** variable\n",
    "- b is the **Y-intercept**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6f6f797",
   "metadata": {},
   "source": [
    "#### Linear regression equation added to fit data as \"predicted\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "82f14cc0-13f1-4131-832c-806c52987c43",
   "metadata": {},
   "outputs": [],
   "source": [
    "predicted = lr.fit(X,y)\n",
    "m = predicted.coef_\n",
    "b = predicted.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "629d1ad9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#predicted=lr.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bcf72b2a-54d9-4a51-a1d6-411f07d7e9cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope of regression line is [0.10502452]\n",
      "The y-intercept is 0.920269613554674\n",
      "The regression line equation is y = [0.10502452]x + 0.920269613554674\n"
     ]
    }
   ],
   "source": [
    "print(f'Slope of regression line is {m}')\n",
    "print(f'The y-intercept is {b}')\n",
    "print(f'The regression line equation is y = {m}x + {b}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9f49398",
   "metadata": {},
   "source": [
    "#### Regression line from the results of fit():"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "76d0472d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slope of regression line is[0.10502452]\n",
      "The Y-intercept is 0.920269613554674\n",
      "The regression line equation is : y = [0.10502452]x + 0.920269613554674\n"
     ]
    }
   ],
   "source": [
    "m = predicted.coef_\n",
    "b = predicted.intercept_\n",
    "print(f'The slope of regression line is{m}')\n",
    "print(f'The Y-intercept is {b}')\n",
    "print(f'The regression line equation is : y = {m}x + {b}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a4f83c5",
   "metadata": {},
   "source": [
    "#### Regression line scatterplot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "15d77d68",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'tip' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_12204/1458794973.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'MEAL COST'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"TIP\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtip\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m2.5\u001b[0m\u001b[1;33m,\u001b[0m  \u001b[0mc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m\"red\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.8\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mm\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mX\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'tip' is not defined"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('dark_background')\n",
    "plt.grid(True)\n",
    "plt.title('Relation of Meal Cost to Tip [in USD]')\n",
    "plt.xlabel('MEAL COST')\n",
    "plt.ylabel(\"TIP\")\n",
    "plt.scatter(X,y,s = tip * 2.5,  c = \"red\", alpha = 0.8)\n",
    "plt.plot(X, m * X + b)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2d107f9",
   "metadata": {},
   "source": [
    "#### Predicted tip for a $50.00 meal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "915a4d38",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The predicted tip for a $ 50.00 meal is $6.17\n"
     ]
    }
   ],
   "source": [
    "meal = 50.00\n",
    "tip = 0.105025 * meal + 0.920270\n",
    "print(f'The predicted tip for a ${meal: .2f} meal is ${tip:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed891cfc",
   "metadata": {},
   "source": [
    "#### Statsmodel module:\n",
    "* using **Ordinary Least Squares** (**OLS**)."
   ]
  },
  {
   "attachments": {
    "image_2021-06-20_130450.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "a961c56c",
   "metadata": {},
   "source": [
    "![image_2021-06-20_130450.png](attachment:image_2021-06-20_130450.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0252867f",
   "metadata": {},
   "source": [
    "#### Import statsmodels API formual as \"smf\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5bcc2df3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f61598b",
   "metadata": {},
   "source": [
    "#### Load \"tips\" dataset as \"tips\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5b1c908",
   "metadata": {},
   "outputs": [],
   "source": [
    "tips = sns.load_dataset('tips')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "133aa6bc",
   "metadata": {},
   "source": [
    "*\n",
    "*\n",
    "*\n",
    "The **OLS** method computes the least squares values.\n",
    "The response variable is left of the tilde and the\n",
    "predictor is to the right of the tilde.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eff665e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = smf.ols(formula = 'tip ~ total_bill',data = tips)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36248e96",
   "metadata": {},
   "source": [
    "#### Fit the data as \"results\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92afe5c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c910c8d8",
   "metadata": {},
   "source": [
    "#### Summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40db8acc",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1386fc3b",
   "metadata": {},
   "source": [
    "#### Scatterplot of correlation between tip and total bill:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b14a31e",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('dark_background')\n",
    "sns.lmplot(x='total_bill',y='tip',data=tips)\n",
    "sns.color_palette(\"Spectral\", as_cmap=True)\n",
    "sns.set(font_scale=1.25)\n",
    "plt.xlabel('TOTAL BILL')\n",
    "plt.ylabel('TIP')\n",
    "plt.title('CORRELATION: TOTAL BILL TO TIP [in USD]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd0ed713",
   "metadata": {},
   "source": [
    "*\n",
    "*\n",
    "*\n",
    "The params attribute yields the details for the equation of the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5b200f69",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(results.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28396883",
   "metadata": {},
   "source": [
    "#### Predicted tip for a $50.00 meal using params attribute values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "14510e23",
   "metadata": {},
   "outputs": [],
   "source": [
    "meal = 50.00\n",
    "tip = 0.105025 * meal + 0.920270\n",
    "print(f'The predicted tip for a ${meal:.2f} meal is ${tip:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1f1a2d1",
   "metadata": {},
   "source": [
    "#### Predicted tip for a $100.00 meal using params attribute values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5709aa6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "meal = 100.00\n",
    "tip = 0.105025 * meal + 0.920270\n",
    "print(f'The predicted tip for a ${meal:.2f} meal is ${tip:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b707383-ee2c-42f7-9f2f-3a061fd62632",
   "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": "3.8.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}