StatisticsforDataSciencewithPython.ipynb

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  {
   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as pyplot\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston_url = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork/labs/boston_housing.csv'\n",
    "boston_df=pd.read_csv(boston_url)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "   Unnamed: 0     CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  \\\n",
       "0           0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0   \n",
       "1           1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0   \n",
       "2           2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0   \n",
       "3           3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0   \n",
       "4           4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0   \n",
       "\n",
       "     TAX  PTRATIO  LSTAT  MEDV  \n",
       "0  296.0     15.3   4.98  24.0  \n",
       "1  242.0     17.8   9.14  21.6  \n",
       "2  242.0     17.8   4.03  34.7  \n",
       "3  222.0     18.7   2.94  33.4  \n",
       "4  222.0     18.7   5.33  36.2  "
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     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "boston_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "       Unnamed: 0        CRIM          ZN       INDUS        CHAS         NOX  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean   252.500000    3.613524   11.363636   11.136779    0.069170    0.554695   \n",
       "std    146.213884    8.601545   23.322453    6.860353    0.253994    0.115878   \n",
       "min      0.000000    0.006320    0.000000    0.460000    0.000000    0.385000   \n",
       "25%    126.250000    0.082045    0.000000    5.190000    0.000000    0.449000   \n",
       "50%    252.500000    0.256510    0.000000    9.690000    0.000000    0.538000   \n",
       "75%    378.750000    3.677082   12.500000   18.100000    0.000000    0.624000   \n",
       "max    505.000000   88.976200  100.000000   27.740000    1.000000    0.871000   \n",
       "\n",
       "               RM         AGE         DIS         RAD         TAX     PTRATIO  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     6.284634   68.574901    3.795043    9.549407  408.237154   18.455534   \n",
       "std      0.702617   28.148861    2.105710    8.707259  168.537116    2.164946   \n",
       "min      3.561000    2.900000    1.129600    1.000000  187.000000   12.600000   \n",
       "25%      5.885500   45.025000    2.100175    4.000000  279.000000   17.400000   \n",
       "50%      6.208500   77.500000    3.207450    5.000000  330.000000   19.050000   \n",
       "75%      6.623500   94.075000    5.188425   24.000000  666.000000   20.200000   \n",
       "max      8.780000  100.000000   12.126500   24.000000  711.000000   22.000000   \n",
       "\n",
       "            LSTAT        MEDV  \n",
       "count  506.000000  506.000000  \n",
       "mean    12.653063   22.532806  \n",
       "std      7.141062    9.197104  \n",
       "min      1.730000    5.000000  \n",
       "25%      6.950000   17.025000  \n",
       "50%     11.360000   21.200000  \n",
       "75%     16.955000   25.000000  \n",
       "max     37.970000   50.000000  "
      ],
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     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "boston_df.describe()"
   ]
  },
  {
   "source": [
    "# Box Plot\n",
    "\n",
    "* Task 4 - Generate Descriptive Statistics and Visualizations\n",
    "1. For the \"Median value of owner-occupied homes\" provide a boxplot\n",
    "\n",
    "This boxplot displays the distribution of the Median Value of Owner-Occupied Homes. It shows the minimum value, first quartile, median, third quartile, and maximum values of the data. As you can see, the minimum value is under $10,000. \n",
    "The median value is just above \\$20,000. and the maximum value is around $50,000. About hald of the values are between \\$15,000 and $25,000."
   ],
   "cell_type": "markdown",
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   "cell_type": "code",
   "execution_count": 17,
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     "data": {
      "text/plain": [
       "Text(0, 0.5, 'MEDV ($1000s)')"
      ]
     },
     "metadata": {},
     "execution_count": 17
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "ax = sns.boxplot(y='MEDV', data=boston_df)\n",
    "ax.set_title(\"Median Value of Owner-Occupied Homes, $1000's\")\n",
    "ax.set_ylabel('MEDV ($1000s)')"
   ]
  },
  {
   "source": [
    "* 2. Provide a histogram for the Charles river variable\n",
    "\n",
    "This plot shows how many how many houses are along the Charles River and how many are not. On the x-axis, '0' category is homes NOT bounding the river, and '1' category is homes bounding the river."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 360x360 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "ax = sns.catplot(x='CHAS', kind='count', data=boston_df).fig.suptitle('Charles River variable')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(array([471.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,  35.]),\n",
       " array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "metadata": {},
     "execution_count": 8
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "pyplot.hist(boston_df['CHAS'], color='orange')"
   ]
  },
  {
   "source": [
    "* 3. Boxplot for the MEDV variable vs the AGE variable\n",
    "\n",
    "This box plot shows the Median value of owner-occupied homes for three groups - homes 40 years old and younger, homes between 40 and 57 years, and homes older than 57 years. On average, newer homes are worth more. However, the maximum home price is similar for all three categories."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Boxplot MEDV variable vs AGE variable\n",
    "\n",
    "boston_df.loc[(boston_df['AGE'] <= 35), 'age_group'] = '35 years and younger'\n",
    "boston_df.loc[(boston_df['AGE'] > 35)&(boston_df['AGE'] < 70), 'age_group'] = 'between 35 and 70 years'\n",
    "boston_df.loc[(boston_df['AGE'] >= 70), 'age_group'] = '70 years and older'\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Age Group')"
      ]
     },
     "metadata": {},
     "execution_count": 22
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "ax = sns.boxplot(x=\"age_group\", y=\"MEDV\", data=boston_df)\n",
    "ax.set_title(\"MEDV ($1000s) vs. Age Group\")\n",
    "ax.set_xlabel('MEDV ($1000s)')\n",
    "ax.set_ylabel('Age Group')"
   ]
  },
  {
   "source": [
    "* 4. Provide a scatter plot to show the relationship between Nitric oxide concentrations and the proportion of non-retail business acres per town.\n",
    "\n",
    "This plot displays the relationship between two continuous dat, Nitric Oxide concentration and Non-retail business acres per town. As you can see, there seems to be a positive linear correlation between the variables. This is shown by upward and to the right trend in the plot."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Proportion of non-retail business acres per town vs. NOx Concentration')"
      ]
     },
     "metadata": {},
     "execution_count": 24
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "ax = sns.scatterplot(x='NOX', y='INDUS', data=boston_df, color = 'purple')\n",
    "ax.set_xlabel('Nitric Oxide Concentrations, parts per 10 million')\n",
    "ax.set_ylabel('Non-retail business acres per town')\n",
    "ax.set_title('Proportion of non-retail business acres per town vs. NOx Concentration')"
   ]
  },
  {
   "source": [
    "* 5. Create a histogram for the pupil to teacher ratio variable\n",
    "\n",
    "This plot shows all of the Pupil to Teacher ratios along the x-axis and the frequency of each ratio. The data does not follow normal distribution"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Pupil to Teacher Ratio')"
      ]
     },
     "metadata": {},
     "execution_count": 25
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "#Histogram pupil to teacher ratio variable\n",
    "\n",
    "ax = sns.distplot(boston_df['PTRATIO'],bins=20, kde=False, color='red')\n",
    "ax.set_xlabel('Pupil to Teacher Ratio')\n",
    "ax.set_ylabel('Count')\n",
    "ax.set_title('Histogram of Pupil to Teacher Ratio')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[Text(0.5, 0, 'Normal Distribution'), Text(0, 0.5, 'Frequency')]"
      ]
     },
     "metadata": {},
     "execution_count": 13
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "#Is there a significant difference in median value of houses bounded by the Charles river or not\n",
    "import scipy.stats\n",
    "\n",
    "ax = sns.distplot(boston_df['MEDV'],\n",
    "                  bins=20,\n",
    "                  kde=True,\n",
    "                  color='darkgreen',\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "ax.set(xlabel='Normal Distribution', ylabel='Frequency')"
   ]
  },
  {
   "source": [
    "* Task 5 - Use the appropriate tests to answer the questions provided.\n",
    "1. Is there a significant difference in median value of houses bounded by the Charles river or not? (T-test for independent samples)\n",
    "\n",
    "State the hypothesis\n",
    "\n",
    "[Math Processing Error] (\"there is no difference in median value for houses bounded by the Charles River or not\")\n",
    "[Math Processing Error] (\"there is a difference in median value for houses bounded by the Charles River or not\")"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-3.996437466090509, pvalue=7.390623170519905e-05)"
      ]
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "source": [
    "scipy.stats.ttest_ind(boston_df[boston_df['CHAS'] == 0.0]['MEDV'], boston_df[boston_df['CHAS'] == 1.0]['MEDV'], equal_var = True)"
   ]
  },
  {
   "source": [
    "Conclusion: Since the p-value is less than alpha value 0.05, we reject the null hypothesis as there is enough proof that there is a statistical difference in meadian house value based on whether the property bounds the Charles River.\n",
    "\n",
    "2. Is there a difference in Median values of houses (MEDV) for each proportion of owner occupied units built prior to 1940 (AGE)? (ANOVA)\n",
    "\n",
    "First, we group the data into categories as the one-way ANOVA can't work with continuous variable. We will create a new column for this newly assigned group. Our categories will be proportion of owner occupied units built prior to 1940 (AGE) values that are:\n",
    "\n",
    "55 or less\n",
    "between 55 and 90\n",
    "90 or greater\n",
    "These three categories are approximately the same size as eachother."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston_df.loc[(boston_df['AGE'] <= 55), 'age_group'] = '55 or less'\n",
    "boston_df.loc[(boston_df['AGE'] > 55)&(boston_df['AGE'] < 90), 'age_group'] = 'between 55 and 90'\n",
    "boston_df.loc[(boston_df['AGE'] >= 90), 'age_group'] = '90 or higher'"
   ]
  },
  {
   "source": [
    "State the hypothesis\n",
    "\n",
    "[Math Processing Error] (the three population means are equal)\n",
    "[Math Processing Error] At least one of the means differ\n",
    "Separate the three samples (one for each AGE category) into a variable each."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "7      27.1\n8      16.5\n10     15.0\n20     13.6\n22     15.2\n       ... \n488    15.2\n489     7.0\n490     8.1\n491    13.6\n503    23.9\nName: MEDV, Length: 170, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "lower = boston_df[boston_df['age_group'] == '55 or less']['MEDV']\n",
    "middle = boston_df[boston_df['age_group'] == 'between 55 and 90']['MEDV']\n",
    "higher = boston_df[boston_df['age_group'] == '90 or higher']['MEDV']\n",
    "print(higher)"
   ]
  },
  {
   "source": [
    "Now, run a one-way ANOVA."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "F_Statistic: 41.80540024741085, P-Value: 1.600698198719595e-17\n"
     ]
    }
   ],
   "source": [
    "f_statistic, p_value = scipy.stats.f_oneway(lower, middle, higher)\n",
    "print(\"F_Statistic: {0}, P-Value: {1}\".format(f_statistic,p_value))"
   ]
  },
  {
   "source": [
    "Conclusion: Since the p-value is less than 0.05, we will reject the null hypothesis as there is significant evidence that at least one of the means differ.\n",
    "\n",
    "3. Can we conclude that there is no relationship between Nitric oxide concentrations and proportion of non-retail business acres per town? (Pearson Correlation)\n",
    "\n",
    "State the hypothesis:\n",
    "\n",
    "[Math Processing Error] Nitric Oxide concentration is not correlated with proportion of non-retail business acres per town\n",
    "[Math Processing Error] Nitric Oxide concentration is correlated with proportion of non-retail business acres per town\n",
    "Since they are both continuous variables we can use a pearson correlation test"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(-0.4273207723732824, 7.06504158625191e-24)"
      ]
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "source": [
    "scipy.stats.pearsonr(boston_df['MEDV'],boston_df['NOX'])"
   ]
  },
  {
   "source": [
    "Conclusion: Since the p-value < 0.05, we reject the Null hypothesis and conclude that there exists a relationship between nitric oxide concentration and proportion of non-retail business acres per town.\n",
    "\n",
    "4. What is the impact of an additional weighted distance to the five Boston employment centres on the median value of owner occupied homes? (Regression analysis)\n",
    "\n",
    "State the hypothesis:\n",
    "\n",
    "[Math Processing Error] = 0 (DIS has no effect on MEDV)\n",
    "[Math Processing Error] is not equal to 0 (DIS has an effect on MEDV)"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.062\n",
       "Model:                            OLS   Adj. R-squared:                  0.061\n",
       "Method:                 Least Squares   F-statistic:                     33.58\n",
       "Date:                Thu, 14 Jan 2021   Prob (F-statistic):           1.21e-08\n",
       "Time:                        10:37:11   Log-Likelihood:                -1823.9\n",
       "No. Observations:                 506   AIC:                             3652.\n",
       "Df Residuals:                     504   BIC:                             3660.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         18.3901      0.817     22.499      0.000      16.784      19.996\n",
       "DIS            1.0916      0.188      5.795      0.000       0.722       1.462\n",
       "==============================================================================\n",
       "Omnibus:                      139.779   Durbin-Watson:                   0.570\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              305.104\n",
       "Skew:                           1.466   Prob(JB):                     5.59e-67\n",
       "Kurtosis:                       5.424   Cond. No.                         9.32\n",
       "==============================================================================\n",
       "\n",
       "Notes:\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>MEDV</td>       <th>  R-squared:         </th> <td>   0.062</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.061</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   33.58</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 14 Jan 2021</td> <th>  Prob (F-statistic):</th> <td>1.21e-08</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>10:37:11</td>     <th>  Log-Likelihood:    </th> <td> -1823.9</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3652.</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3660.</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>const</th> <td>   18.3901</td> <td>    0.817</td> <td>   22.499</td> <td> 0.000</td> <td>   16.784</td> <td>   19.996</td>\n</tr>\n<tr>\n  <th>DIS</th>   <td>    1.0916</td> <td>    0.188</td> <td>    5.795</td> <td> 0.000</td> <td>    0.722</td> <td>    1.462</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>139.779</td> <th>  Durbin-Watson:     </th> <td>   0.570</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 305.104</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 1.466</td>  <th>  Prob(JB):          </th> <td>5.59e-67</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 5.424</td>  <th>  Cond. No.          </th> <td>    9.32</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     },
     "metadata": {},
     "execution_count": 33
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "## X is the input variables (or independent variables)\n",
    "X = boston_df['DIS']\n",
    "## y is the target/dependent variable\n",
    "y = boston_df['MEDV']\n",
    "## add an intercept (beta_0) to our model\n",
    "X = sm.add_constant(X) \n",
    "\n",
    "model = sm.OLS(y, X).fit()\n",
    "predictions = model.predict(X)\n",
    "\n",
    "# Print out the statistics\n",
    "model.summary()"
   ]
  },
  {
   "source": [
    "Conclusion: The p-value is less than the alpha (α) level = 0.05, so we reject the null hypothesis as there is evidence that there is a difference in MEDV based on DIS. The coefficient is 1.0916, which means that for each increase of 1 to the BIS value, the MEDV value increases by 1.0916 (representing a $1091.60 increase on MEDV)."
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}