simple linear regression.ipynb (delivery time )

simple linear regression.ipynb

{
  "cells": [
    {
      "metadata": {
        "trusted": true
      },
      "id": "bcb234e5",
      "cell_type": "code",
      "source": "# Delivery_time -> Predict delivery time using sorting time using datset = Delivery_time",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "7766861f",
      "cell_type": "code",
      "source": "import numpy as np \nimport pandas as pd\nimport seaborn as sns",
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "a38061eb",
      "cell_type": "code",
      "source": "dl=pd.read_csv(\"delivery_time.csv\")\n",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "dcfcb537",
      "cell_type": "code",
      "source": "dl",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "text/plain": "    Delivery Time  Sorting Time\n0           21.00            10\n1           13.50             4\n2           19.75             6\n3           24.00             9\n4           29.00            10\n5           15.35             6\n6           19.00             7\n7            9.50             3\n8           17.90            10\n9           18.75             9\n10          19.83             8\n11          10.75             4\n12          16.68             7\n13          11.50             3\n14          12.03             3\n15          14.88             4\n16          13.75             6\n17          18.11             7\n18           8.00             2\n19          17.83             7\n20          21.50             5",
            "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>Delivery Time</th>\n      <th>Sorting Time</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>21.00</td>\n      <td>10</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>13.50</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>19.75</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>24.00</td>\n      <td>9</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>29.00</td>\n      <td>10</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>15.35</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>19.00</td>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>9.50</td>\n      <td>3</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>17.90</td>\n      <td>10</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>18.75</td>\n      <td>9</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>19.83</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>10.75</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>16.68</td>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>11.50</td>\n      <td>3</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>12.03</td>\n      <td>3</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>14.88</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>13.75</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>18.11</td>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>8.00</td>\n      <td>2</td>\n    </tr>\n    <tr>\n      <th>19</th>\n      <td>17.83</td>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>21.50</td>\n      <td>5</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "cba47d75",
      "cell_type": "code",
      "source": "dl.info()",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": "<class 'pandas.core.frame.DataFrame'>\nRangeIndex: 21 entries, 0 to 20\nData columns (total 2 columns):\n #   Column         Non-Null Count  Dtype  \n---  ------         --------------  -----  \n 0   Delivery Time  21 non-null     float64\n 1   Sorting Time   21 non-null     int64  \ndtypes: float64(1), int64(1)\nmemory usage: 464.0 bytes\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "93488905",
      "cell_type": "code",
      "source": "dl=dl.rename({'Delivery Time':'Delivery'},axis=1)\ndl=dl.rename({'Sorting Time':'Sorting'},axis=1)\n",
      "execution_count": 5,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "46a77c60",
      "cell_type": "code",
      "source": "dl['Delivery']=pd.to_numeric(dl['Delivery'],errors='coerce')",
      "execution_count": 12,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "510eb12c",
      "cell_type": "code",
      "source": "dl['Sorting']=pd.to_numeric(dl['Sorting'],errors='coerce')",
      "execution_count": 13,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "d032e6e6",
      "cell_type": "code",
      "source": "#Outlier Detection\ndl['Sorting'].hist()\ndl['Delivery'].hist()",
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 14,
          "data": {
            "text/plain": "<AxesSubplot:>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "9ecf9e4e",
      "cell_type": "code",
      "source": "#Find missing value\ndl[dl.isnull().any(axis=1)]",
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 15,
          "data": {
            "text/plain": "Empty DataFrame\nColumns: [Delivery, Sorting]\nIndex: []",
            "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>Delivery</th>\n      <th>Sorting</th>\n    </tr>\n  </thead>\n  <tbody>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "059586e6",
      "cell_type": "code",
      "source": "#find correlation\ndl.corr()",
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 16,
          "data": {
            "text/plain": "          Delivery   Sorting\nDelivery  1.000000  0.825997\nSorting   0.825997  1.000000",
            "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>Delivery</th>\n      <th>Sorting</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Delivery</th>\n      <td>1.000000</td>\n      <td>0.825997</td>\n    </tr>\n    <tr>\n      <th>Sorting</th>\n      <td>0.825997</td>\n      <td>1.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "bd1634ce",
      "cell_type": "code",
      "source": "#make model \nimport statsmodels.formula.api as smf\nmodel=smf.ols(\"Delivery~Sorting\",data=dl).fit()",
      "execution_count": 17,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "7ed1a597",
      "cell_type": "code",
      "source": "sns.regplot(x=\"Sorting\", y=\"Delivery\", data=dl);",
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "722d1930",
      "cell_type": "code",
      "source": "#to get Bo and B1 value\nmodel.params",
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 19,
          "data": {
            "text/plain": "Intercept    6.582734\nSorting      1.649020\ndtype: float64"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "67b720d4",
      "cell_type": "code",
      "source": "#to get t and p value\nprint(model.tvalues,'\\n',model.pvalues)",
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": "Intercept    3.823349\nSorting      6.387447\ndtype: float64 \n Intercept    0.001147\nSorting      0.000004\ndtype: float64\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "311f40ed",
      "cell_type": "code",
      "source": "# to get R^2 value\nprint(model.rsquared, model.rsquared_adj)",
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": "0.6822714748417231 0.6655489208860244\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "81c709a3",
      "cell_type": "code",
      "source": "from sklearn.preprocessing import StandardScaler\n",
      "execution_count": 23,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "40da7d23",
      "cell_type": "code",
      "source": "array=dl.values\nscaler=StandardScaler().fit(array)\nrescaled=scaler.transform(array)\nprint(rescaled)",
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": "[[ 0.84986692  1.53562462]\n [-0.66449036 -0.88298415]\n [ 0.59747404 -0.07678123]\n [ 1.45560983  1.13252315]\n [ 2.46518134  1.53562462]\n [-0.2909489  -0.07678123]\n [ 0.44603831  0.32632023]\n [-1.47214757 -1.28608562]\n [ 0.22393258  1.53562462]\n [ 0.39555973  1.13252315]\n [ 0.61362718  0.72942169]\n [-1.21975469 -0.88298415]\n [-0.02240287  0.32632023]\n [-1.06831896 -1.28608562]\n [-0.96130438 -1.28608562]\n [-0.38584862 -0.88298415]\n [-0.61401178 -0.07678123]\n [ 0.26633458  0.32632023]\n [-1.77501902 -1.68918708]\n [ 0.20979858  0.32632023]\n [ 0.95082407 -0.47988269]]\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "5a266f82",
      "cell_type": "code",
      "source": "dl1=pd.DataFrame(rescaled,columns=['Delivery','Sorting'])",
      "execution_count": 25,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "af18f5cc",
      "cell_type": "code",
      "source": "dl1\n",
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 26,
          "data": {
            "text/plain": "    Delivery   Sorting\n0   0.849867  1.535625\n1  -0.664490 -0.882984\n2   0.597474 -0.076781\n3   1.455610  1.132523\n4   2.465181  1.535625\n5  -0.290949 -0.076781\n6   0.446038  0.326320\n7  -1.472148 -1.286086\n8   0.223933  1.535625\n9   0.395560  1.132523\n10  0.613627  0.729422\n11 -1.219755 -0.882984\n12 -0.022403  0.326320\n13 -1.068319 -1.286086\n14 -0.961304 -1.286086\n15 -0.385849 -0.882984\n16 -0.614012 -0.076781\n17  0.266335  0.326320\n18 -1.775019 -1.689187\n19  0.209799  0.326320\n20  0.950824 -0.479883",
            "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>Delivery</th>\n      <th>Sorting</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.849867</td>\n      <td>1.535625</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>-0.664490</td>\n      <td>-0.882984</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.597474</td>\n      <td>-0.076781</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1.455610</td>\n      <td>1.132523</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>2.465181</td>\n      <td>1.535625</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>-0.290949</td>\n      <td>-0.076781</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.446038</td>\n      <td>0.326320</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>-1.472148</td>\n      <td>-1.286086</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.223933</td>\n      <td>1.535625</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>0.395560</td>\n      <td>1.132523</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>0.613627</td>\n      <td>0.729422</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>-1.219755</td>\n      <td>-0.882984</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>-0.022403</td>\n      <td>0.326320</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>-1.068319</td>\n      <td>-1.286086</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>-0.961304</td>\n      <td>-1.286086</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>-0.385849</td>\n      <td>-0.882984</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>-0.614012</td>\n      <td>-0.076781</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>0.266335</td>\n      <td>0.326320</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>-1.775019</td>\n      <td>-1.689187</td>\n    </tr>\n    <tr>\n      <th>19</th>\n      <td>0.209799</td>\n      <td>0.326320</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>0.950824</td>\n      <td>-0.479883</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "beafbe5e",
      "cell_type": "code",
      "source": "#make new model \nimport statsmodels.formula.api as smf\nmodel1=smf.ols(\"Delivery~(Sorting)\", data=dl1).fit()\n",
      "execution_count": 48,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "id": "e0f33b76",
      "cell_type": "code",
      "source": "model1.summary()",
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 49,
          "data": {
            "text/plain": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n                            OLS Regression Results                            \n==============================================================================\nDep. Variable:               Delivery   R-squared:                       0.682\nModel:                            OLS   Adj. R-squared:                  0.666\nMethod:                 Least Squares   F-statistic:                     40.80\nDate:                Tue, 24 Aug 2021   Prob (F-statistic):           3.98e-06\nTime:                        23:29:13   Log-Likelihood:                -17.759\nNo. Observations:                  21   AIC:                             39.52\nDf Residuals:                      19   BIC:                             41.61\nDf Model:                           1                                         \nCovariance Type:            nonrobust                                         \n==============================================================================\n                 coef    std err          t      P>|t|      [0.025      0.975]\n------------------------------------------------------------------------------\nIntercept  -5.135e-16      0.129  -3.97e-15      1.000      -0.271       0.271\nSorting        0.8260      0.129      6.387      0.000       0.555       1.097\n==============================================================================\nOmnibus:                        3.649   Durbin-Watson:                   1.248\nProb(Omnibus):                  0.161   Jarque-Bera (JB):                2.086\nSkew:                           0.750   Prob(JB):                        0.352\nKurtosis:                       3.367   Cond. No.                         1.00\n==============================================================================\n\nNotes:\n[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n\"\"\"",
            "text/html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>        <td>Delivery</td>     <th>  R-squared:         </th> <td>   0.682</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.666</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   40.80</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Tue, 24 Aug 2021</td> <th>  Prob (F-statistic):</th> <td>3.98e-06</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>23:29:13</td>     <th>  Log-Likelihood:    </th> <td> -17.759</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>   39.52</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>   41.61</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     1</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>Intercept</th> <td>-5.135e-16</td> <td>    0.129</td> <td>-3.97e-15</td> <td> 1.000</td> <td>   -0.271</td> <td>    0.271</td>\n</tr>\n<tr>\n  <th>Sorting</th>   <td>    0.8260</td> <td>    0.129</td> <td>    6.387</td> <td> 0.000</td> <td>    0.555</td> <td>    1.097</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td> 3.649</td> <th>  Durbin-Watson:     </th> <td>   1.248</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.161</td> <th>  Jarque-Bera (JB):  </th> <td>   2.086</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.750</td> <th>  Prob(JB):          </th> <td>   0.352</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 3.367</td> <th>  Cond. No.          </th> <td>    1.00</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "#Normalization of the data\nfrom numpy import set_printoptions\nfrom sklearn.preprocessing import MinMaxScaler",
      "execution_count": 51,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "dl.values",
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 53,
          "data": {
            "text/plain": "array([[21.  , 10.  ],\n       [13.5 ,  4.  ],\n       [19.75,  6.  ],\n       [24.  ,  9.  ],\n       [29.  , 10.  ],\n       [15.35,  6.  ],\n       [19.  ,  7.  ],\n       [ 9.5 ,  3.  ],\n       [17.9 , 10.  ],\n       [18.75,  9.  ],\n       [19.83,  8.  ],\n       [10.75,  4.  ],\n       [16.68,  7.  ],\n       [11.5 ,  3.  ],\n       [12.03,  3.  ],\n       [14.88,  4.  ],\n       [13.75,  6.  ],\n       [18.11,  7.  ],\n       [ 8.  ,  2.  ],\n       [17.83,  7.  ],\n       [21.5 ,  5.  ]])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": true
      },
      "cell_type": "code",
      "source": "array = dl.values\n\nscaler = MinMaxScaler(feature_range=(0,1))\nrescaledX = scaler.fit_transform(array)\n\n#transformed data\nset_printoptions(precision=2)\nprint(rescaledX)",
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "text": "[[0.62 1.  ]\n [0.26 0.25]\n [0.56 0.5 ]\n [0.76 0.88]\n [1.   1.  ]\n [0.35 0.5 ]\n [0.52 0.62]\n [0.07 0.12]\n [0.47 1.  ]\n [0.51 0.88]\n [0.56 0.75]\n [0.13 0.25]\n [0.41 0.62]\n [0.17 0.12]\n [0.19 0.12]\n [0.33 0.25]\n [0.27 0.5 ]\n [0.48 0.62]\n [0.   0.  ]\n [0.47 0.62]\n [0.64 0.38]]\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "dl2=pd.DataFrame(rescaledX,columns=['Delivery','Sorting'])",
      "execution_count": 55,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "dl2",
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 56,
          "data": {
            "text/plain": "    Delivery  Sorting\n0   0.619048    1.000\n1   0.261905    0.250\n2   0.559524    0.500\n3   0.761905    0.875\n4   1.000000    1.000\n5   0.350000    0.500\n6   0.523810    0.625\n7   0.071429    0.125\n8   0.471429    1.000\n9   0.511905    0.875\n10  0.563333    0.750\n11  0.130952    0.250\n12  0.413333    0.625\n13  0.166667    0.125\n14  0.191905    0.125\n15  0.327619    0.250\n16  0.273810    0.500\n17  0.481429    0.625\n18  0.000000    0.000\n19  0.468095    0.625\n20  0.642857    0.375",
            "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>Delivery</th>\n      <th>Sorting</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.619048</td>\n      <td>1.000</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.261905</td>\n      <td>0.250</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.559524</td>\n      <td>0.500</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.761905</td>\n      <td>0.875</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1.000000</td>\n      <td>1.000</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>0.350000</td>\n      <td>0.500</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.523810</td>\n      <td>0.625</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>0.071429</td>\n      <td>0.125</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.471429</td>\n      <td>1.000</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>0.511905</td>\n      <td>0.875</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>0.563333</td>\n      <td>0.750</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>0.130952</td>\n      <td>0.250</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>0.413333</td>\n      <td>0.625</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>0.166667</td>\n      <td>0.125</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>0.191905</td>\n      <td>0.125</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>0.327619</td>\n      <td>0.250</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>0.273810</td>\n      <td>0.500</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>0.481429</td>\n      <td>0.625</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>0.000000</td>\n      <td>0.000</td>\n    </tr>\n    <tr>\n      <th>19</th>\n      <td>0.468095</td>\n      <td>0.625</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>0.642857</td>\n      <td>0.375</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "\nmodel2=smf.ols(\"Delivery~(Sorting)\", data=dl2).fit()\n",
      "execution_count": 58,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "model2.summary()",
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 60,
          "data": {
            "text/plain": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n                            OLS Regression Results                            \n==============================================================================\nDep. Variable:               Delivery   R-squared:                       0.682\nModel:                            OLS   Adj. R-squared:                  0.666\nMethod:                 Least Squares   F-statistic:                     40.80\nDate:                Tue, 24 Aug 2021   Prob (F-statistic):           3.98e-06\nTime:                        23:40:02   Log-Likelihood:                 12.578\nNo. Observations:                  21   AIC:                            -21.16\nDf Residuals:                      19   BIC:                            -19.07\nDf Model:                           1                                         \nCovariance Type:            nonrobust                                         \n==============================================================================\n                 coef    std err          t      P>|t|      [0.025      0.975]\n------------------------------------------------------------------------------\nIntercept      0.0896      0.060      1.496      0.151      -0.036       0.215\nSorting        0.6282      0.098      6.387      0.000       0.422       0.834\n==============================================================================\nOmnibus:                        3.649   Durbin-Watson:                   1.248\nProb(Omnibus):                  0.161   Jarque-Bera (JB):                2.086\nSkew:                           0.750   Prob(JB):                        0.352\nKurtosis:                       3.367   Cond. No.                         4.18\n==============================================================================\n\nNotes:\n[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n\"\"\"",
            "text/html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>        <td>Delivery</td>     <th>  R-squared:         </th> <td>   0.682</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.666</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   40.80</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Tue, 24 Aug 2021</td> <th>  Prob (F-statistic):</th> <td>3.98e-06</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>23:40:02</td>     <th>  Log-Likelihood:    </th> <td>  12.578</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>  -21.16</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>  -19.07</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     1</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>Intercept</th> <td>    0.0896</td> <td>    0.060</td> <td>    1.496</td> <td> 0.151</td> <td>   -0.036</td> <td>    0.215</td>\n</tr>\n<tr>\n  <th>Sorting</th>   <td>    0.6282</td> <td>    0.098</td> <td>    6.387</td> <td> 0.000</td> <td>    0.422</td> <td>    0.834</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td> 3.649</td> <th>  Durbin-Watson:     </th> <td>   1.248</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.161</td> <th>  Jarque-Bera (JB):  </th> <td>   2.086</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.750</td> <th>  Prob(JB):          </th> <td>   0.352</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 3.367</td> <th>  Cond. No.          </th> <td>    4.18</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
          },
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        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# Predict new Data base upon our model\n\nnew_data= pd.Series([10,12,13,7,6,15,21,11])\ndata_pred = pd.DataFrame(new_data,columns=['Sorting'])\nmodel2.predict(data_pred)",
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 61,
          "data": {
            "text/plain": "0     6.371541\n1     7.627937\n2     8.256135\n3     4.486947\n4     3.858749\n5     9.512531\n6    13.281720\n7     6.999739\ndtype: float64"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "#model 2 is best for prediction delivery time ",
      "execution_count": null,
      "outputs": []
    }
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