Simple_Linear_Regression.ipynb

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   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Basic Analytics in Python\n",
    "## Simple Linear Regression\n",
    "https://www.sfu.ca/~mjbrydon/tutorials/BAinPy/09_regression.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cb604acb-952c-465d-8f49-d339ac16f683",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Cement</th>\n",
       "      <th>Slag</th>\n",
       "      <th>FlyAsh</th>\n",
       "      <th>Water</th>\n",
       "      <th>SP</th>\n",
       "      <th>CoarseAgg</th>\n",
       "      <th>FineAgg</th>\n",
       "      <th>Strength</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>540.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>162.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1040.0</td>\n",
       "      <td>676.0</td>\n",
       "      <td>79.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>540.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>162.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1055.0</td>\n",
       "      <td>676.0</td>\n",
       "      <td>61.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>332.5</td>\n",
       "      <td>142.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>228.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>932.0</td>\n",
       "      <td>594.0</td>\n",
       "      <td>40.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>332.5</td>\n",
       "      <td>142.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>228.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>932.0</td>\n",
       "      <td>594.0</td>\n",
       "      <td>41.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>198.6</td>\n",
       "      <td>132.4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>192.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>978.4</td>\n",
       "      <td>825.5</td>\n",
       "      <td>44.30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Cement   Slag  FlyAsh  Water   SP  CoarseAgg  FineAgg  Strength\n",
       "0   540.0    0.0     0.0  162.0  2.5     1040.0    676.0     79.99\n",
       "1   540.0    0.0     0.0  162.0  2.5     1055.0    676.0     61.89\n",
       "2   332.5  142.5     0.0  228.0  0.0      932.0    594.0     40.27\n",
       "3   332.5  142.5     0.0  228.0  0.0      932.0    594.0     41.05\n",
       "4   198.6  132.4     0.0  192.0  0.0      978.4    825.5     44.30"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "con = pd.read_csv('Data/ConcreteStrength.csv')\n",
    "\n",
    "con.drop(columns=['age'], inplace=True)\n",
    "con.rename(columns={\n",
    "    'cement': 'Cement',\n",
    "    'blast_furnace_slag': 'Slag',\n",
    "    'fly_ash': 'FlyAsh',\n",
    "    'water': 'Water',\n",
    "    'superplasticizer': 'SP',\n",
    "    'coarse_aggregate': 'CoarseAgg',\n",
    "    'fine_aggregate ': 'FineAgg',\n",
    "    'concrete_compressive_strength': 'Strength'}, inplace=True)\n",
    "\n",
    "con.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82085cf2-a869-47a8-9eab-e043fb7e408c",
   "metadata": {},
   "source": [
    "### Linear Regression with a single explanatory variable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad0c6ae1-4f08-4674-b65e-472c6f4657ae",
   "metadata": {},
   "source": [
    "#### Import the Statsmodels library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b009d1bb-fa3d-4b46-8034-2b39f1b346f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.0\n",
       "1    0.0\n",
       "2    0.0\n",
       "3    0.0\n",
       "4    0.0\n",
       "Name: FlyAsh, dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "Y = con['Strength']\n",
    "X = con['FlyAsh']\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16b0225a-31d0-4f86-96af-38c14d92affe",
   "metadata": {},
   "source": [
    "#### Adding a column for the constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "18d59dd1-2bbd-4c47-9cfc-b06f02d5340d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>FlyAsh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
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      "text/plain": [
       "   const  FlyAsh\n",
       "0    1.0     0.0\n",
       "1    1.0     0.0\n",
       "2    1.0     0.0\n",
       "3    1.0     0.0\n",
       "4    1.0     0.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = sm.add_constant(X)\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae9995ba-8689-4bd5-b622-d0d2ff6715b7",
   "metadata": {},
   "source": [
    "#### Running the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d5ce5860-470b-4290-a8d1-55811f21db69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>Strength</td>     <th>  R-squared:         </th> <td>   0.011</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.010</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   11.63</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 08 Jul 2023</td> <th>  Prob (F-statistic):</th> <td>0.000675</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>14:11:05</td>     <th>  Log-Likelihood:    </th> <td> -4355.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1030</td>      <th>  AIC:               </th> <td>   8715.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1028</td>      <th>  BIC:               </th> <td>   8725.</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>   37.3139</td> <td>    0.679</td> <td>   54.978</td> <td> 0.000</td> <td>   35.982</td> <td>   38.646</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>FlyAsh</th> <td>   -0.0276</td> <td>    0.008</td> <td>   -3.410</td> <td> 0.001</td> <td>   -0.043</td> <td>   -0.012</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>29.013</td> <th>  Durbin-Watson:     </th> <td>   0.848</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  27.218</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.351</td> <th>  Prob(JB):          </th> <td>1.23e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.625</td> <th>  Cond. No.          </th> <td>    110.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               Strength   R-squared:                       0.011\n",
       "Model:                            OLS   Adj. R-squared:                  0.010\n",
       "Method:                 Least Squares   F-statistic:                     11.63\n",
       "Date:                Sat, 08 Jul 2023   Prob (F-statistic):           0.000675\n",
       "Time:                        14:11:05   Log-Likelihood:                -4355.4\n",
       "No. Observations:                1030   AIC:                             8715.\n",
       "Df Residuals:                    1028   BIC:                             8725.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         37.3139      0.679     54.978      0.000      35.982      38.646\n",
       "FlyAsh        -0.0276      0.008     -3.410      0.001      -0.043      -0.012\n",
       "==============================================================================\n",
       "Omnibus:                       29.013   Durbin-Watson:                   0.848\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               27.218\n",
       "Skew:                           0.351   Prob(JB):                     1.23e-06\n",
       "Kurtosis:                       2.625   Cond. No.                         110.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.OLS(Y, X, missing='drop')\n",
    "model_result = model.fit()\n",
    "model_result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae660558-7637-48ab-b411-c532cd3d884d",
   "metadata": {},
   "source": [
    "#### Histogram of residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0623807b-69c8-48fb-ae2a-d90ed8afcefc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Count'>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "import seaborn as sns\n",
    "sns.histplot(model_result.resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6bc71ac2-e295-45e8-9372-3e9c288b362a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-9.713050213108942e-15, 16.60399385928785)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "mu, std = stats.norm.fit(model_result.resid)\n",
    "mu, std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "626f4a45-3f27-4dcf-94c7-3c9aca3113c6",
   "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": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.histplot(x=model_result.resid, ax=ax, stat=\"density\", linewidth=0, kde=True)\n",
    "ax.set(title='Distribution of residuals', xlabel='residual')\n",
    "\n",
    "xmin, xmax = plt.xlim()\n",
    "x = np.linspace(xmin, xmax, 100)\n",
    "p = stats.norm.pdf(x, mu, std)\n",
    "\n",
    "sns.lineplot(x=x, y=p, color='orange', ax=ax)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7b5594f-462b-458e-bd28-214bbffab4b3",
   "metadata": {},
   "source": [
    "#### Boxplot of residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3e536446-f2a0-46d2-bec1-bf53a7e6cdfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.boxplot(x=model_result.resid, showmeans=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2d77b71-2d2b-4a10-9646-b5ab6f219e97",
   "metadata": {},
   "source": [
    "#### Q-Q plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a4c48c0a-0aab-40ba-872a-e35a5a7aafac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sm.qqplot(model_result.resid, line='s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd8f7ce6-6e60-4c6d-9442-0d027db6754c",
   "metadata": {},
   "source": [
    "#### Fit plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "eacf4a39-c023-4c65-a974-ea7464d9881c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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SzznnHFVVXbBggf7kJz/Zs85RRx2ld999t6qqbt++XY888kh97rnnVFX1mmuu0TPPPFNVVd/73vfuCe385S9/WQ8++OCay1WNJGGZrXPXMBoIrwN3yRLHvNPb6wQlS9qx2/CdxGeeOb6zw2PbNud3NwRy1qxbt44HHniAY445BnBm5Jo5cyYvvfQSW7du5aijjgLgjDPO4Be/+EUuZaqGCb9hNBgDA/WLc1QncUMI/8qVY808frq6nN9zQlU5+OCDufPOO8fkb926dU9I5rLRlDZ+wzCiafhO4qOPhptuCo7LfNNNzu8pUhku2b984IEHsnnz5j3Cv2PHDh588EH23Xdf9tlnH379618DMFyiARcm/IbRgjRFJ3Gl+Gck+gCnnnoql156Ke973/t47LHH+PznP8/ZZ5/NnDlz2LVrF9dddx1f+9rXmD17NnPmzOE3v/kNACtXruScc87hyCOPZK+99kq9XLWSWVjmNLGwzIaRLsPDjhl8x47RvM5Ox0JSpKmnprDMt93mnMzKlZmIfqNQlrDMhmGUmMoGUknN0dU5+ujcOnKbBTP1GEYLsmQJbN8+Nm/79hYfAdxCmPAbRgtS5s7dRjA/l42k18yE3zBakLJ27k6aNIktW7aY+CdAVdmyZQuTJk2KvU1mNn4RORD4sS/rncAFwA/c/H5gPfCnqvpiVuUwDGM8S5eOHcAFjlPM0qXFlQlgv/32Y+PGjWzevLnYgjQYkyZNYr/99ou9fpZTL64D5gCISDvwNPAzYDGwWlUvEpHF7vLXsiqHYRjjSWsEcNp0dnay//77F1uIFiAvr575wGOqukFETgbmufmrgNsx4TeM3EljBLDRmORl4z8V+JH7fYaqbgJwP98atIGILBSREREZsdc+wygPNgNY45O58IvIBOAk4CdJtlPVFao6V1XnTp8+PZvCGYaRCC+424YNzmBIL7ibiX9jkUeL/zjgHlV91l1+VkRmArifz+VQBsMwUsBmAGsO8hD+0xg18wDcCCxwvy8AbsihDIaRGDNpjKfM/v9GfDIVfhHpAo4BfurLvgg4RkQecX+7KMsyGEYtmEkjmLL6/xvJyFT4VXWbqvao6ku+vC2qOl9VD3A/X8iyDGVi0SLo6HBionR0OMtGOTGTRjBLlzrB3Px0dhbv/28kw0bu5sSiRXDFFbBrl7O8a5ezbOJfThrVpJGHeappgru1MBaWOSc6OkZF3097O+zcmX95jGj6+x3zTiV9feUNBFk5nSI4o3FXrEjPX78Rr0srExaW2Vr8OREk+lH5RrEsXRo8uVOZTRpJzVO1vB006puQMRYT/pxob0+WbxTLwIDTUu7rc94g+/rSbTlnQRJRrrXz2jp3mwMT/pxYuDBZvlE8AwOO+WL3buezzKIPyUS51s7rRnwTMsZjwp8Ty5fD4OBoC7+93VlevrzYchnNQxJRrtVk04hvQsZ4TPhzZPlypyNX1flsFtG3gU7lIIko12OyabQ3IWM8JvxGXdhAp3LgVb5nnOEs//CH0aJsJpvWxoQ/R5qxZWwDnYqnlsrXTDatjfnx50QePtZF0NYWfE1FHFOAkT15+9YPD5dvAhcjmJby458wIVl+HjRry9jc+4onT996M+01B00p/Nu3J8vPg2Yd+GK24uKZOjU4v1rlW4vpsVkbMK1GUwp/GWnWlnEz2oobqS9meBhefDH4t+OPj96ulpZ7szZgWg5VLX069NBDNQnOoxycimJoSLWra2xZurqcfCM5Q0OqfX2qIs5nWtex0e5TX1/4s97Xl3y7qG3q2c4oBmBEAzS1cFGPk5pB+FWzE6tWI0txriZsZbuHIuHPukjy7aK2UW28irHVMeEvgfAb6ZBlqzNKEMsoelEt/vb28LLVcw3LVvkZ4YQJf9YzcO0rIteJyO9F5GEROVJEporILSLyiPs5JcsyGM1HlnbmqL6YMnZsBk2M4rFrV7jdvp5OeRu52/hk3bn7XeBfVPXdwGzgYWAxsFpVDwBWu8uGEZssO8qjBLGMHZsDA/Df/lv42JWwiqmeTvlG6vw2Qgh6DUgjAW8BnsAdJObLXwfMdL/PBNZV25eZegw/WZtcwkwZZezYDLoWSe329R6vaHNXrbSCyYq8bfzAHOC3wFXA74B/ACYDWyvWezFk+4XACDDS29ub8GRN+JudIv60ZRO9oSHHjh/1vKddMZWx8quFst3LrChC+OcCO4EPuMvfBb4RV/j9yVr8RlkoSysxTks/CzGr1RuobDRLBVaNMOHP0sa/Edioqne5y9cB7weeFZGZAO7ncxmWwTBSpSwdm0EdzZVkMZiuWQYilrG/Jk8yE35V/QPwlIgc6GbNBx4CbgQWuHkLgBuyKoNhNCvVBGpwMJuKqVlCdDRLBVYrWXv1/DkwLCL349j8/wa4CDhGRB4BjnGXjQalKA+PVvcsqSZQN9+czXGbJURHs1RgNRNk/ylbMht/OSmqg6xVOuY8gvoVhoZUOzvDn/NGs7mnRZI+mLL012QJNnLXhD9tiuogy/q4ZRKEsEpucDDao6fZOinj0GoNgjiY8Jvwp05RHh5Z3t9q4pF3pRBWyUWJvhdeotVI0iAoU+WeJWHCb2GZjZopqoOsvT1ZfhLCwjJ88YtOf8Lpp+c7CUlYJ+6uXeHbqNZ3zDL0n9RShrieOjaZDNbiN2qnqFfrLO9vVLTLIswqtbT4QXXChOr3IazvoGhzSa1liNvibxUfftXwFn/hoh4nmfCXlyJemXt6gu9tT0/9+46KdhllWsmKKBt/VOduNSEL22/Ytc1TFGsV5rgVRrMMQouDCb8Jf9MweXLwvZ08uf59xx0Rm6cohlWuQ0O1V0hJK7g8RbEeYY7TELEWvwl/rrRKh1LWZH1/K+9TW1v48Yr2GglroVcTsqQmrUZo8cclyBW2s7M5/49hwm+duzlhHUqNQ2VYhi9+MXi97u54g5cWLYKODmfAU0eHs5wGw8Pw8svBv02YMHYwUmVn6eTJwdtNnlz8wKZ6BlfF7RSuDGMdFta6aQmqDcqWmqHF30qvl1mTpaknDL/ffHu7sxx3u6Cyxt0+irBnqq1tbOs1ifmqp6ccb6a1lCGujT/suqXRR1Q2MFNPscLfSh1KWZNl525chobGlsMTzErCvG/a2+svQ7X5dj3BTGLPb+TnMW7jKuq6NZu5J0z4zdSTE60eFCpNXnghWX7aDA/DmWfCli2jeVu2wFlnjTcthPnbR/nhxyXq2VGfOXHDhnT2WXbi+vFHnWOR02jmiQl/TrR8UKgUybMSDbIZL1kCO3aMX3f79vHCkcZgszC79fHHV99227bwY1XatRv9eYz7XESdY6uEZS7cjBMnNYOpR7UcttNmIEu7uZ8wm3ESU0m9ZY2yW0d59MRJ8+c31/OYZOBXGcYr5AFm4y9e+I10yKujvJbBXEFlqLVjOKoMSUQ/rJ+hUUQui4ib8+eHV4bNhAl/CYTfWvzpkNf9TerrHidMQtZlqExRbyiN0JGbVQiJLDvdy0SY8Gdq4xeR9SLyHyJyr4iMuHlTReQWEXnE/ZySZRnKgvnxp0eWQdpg1KauGn+bnh648sr0JySppd+ip2fsJCl9fentO2/CgubV2wmbZad7QxBUG6SVgPXAtIq8S4DF7vfFwMXV9tMMLX7z40+PLO9vLSEbsnyuwsoTNpo4yKW1DIHXaiUrN+ioIHeNcF3iQoncOU8GVrnfVwGfKqAMuRPmUpfE1c6IHvUa1rJNQpxJzPPEm+qwp2ds/u7d49ft6oLvfjd8H404XWJWHlwLF4b/1gounaIx32dF5O1AH9Dh5anqr6ps8wTwIqDA/6eqK0Rkq6ru61vnRVWNNPfMnTtXR0ZGYpXT2Wf4b0le39OkoyP4NbK9HXbuzL88jUrYdQQYGqpfzNrakj8jPT3w/PP1Hbca/f3BjYT2dqcS6O113BQbQcyT4I2Z8LvPdnbCypX1n2uYTogEV6yNiIisVdW5lfkdQSsHbHwx8FngIcD72ykQKfzAh1T1GRF5K3CLiPw+QYEXAgsBehvBGFmFlrcppkTU9UpD9Hp7k72FTZgQ3MpOm6gJWfr6nN+9lmqziX9WcXX6+oLvdRPITXWC7D+VCVgHTIyzbsQ+LgS+7O5rpps3E1hXbVuz8RseWXtjJLHx5+mZFdd907OJN4vXWJb/m0bu+4gLddr4Hwc6k1QoIjJZRPb2vgMfBx4AbgQWuKstAG5Ist9GZelSp3XopzKColGdMNtslM02CQMDsGBBdQ+hri5n5OySJcVOUViJZ6basAHOOCO9SKBFETcMQy00ct9HvUSaekTk/8Ux6WwD7hWR1cCb3u+q+qWIzWcAPxPnvawDuFpV/0VE7gauFZEvAE8Cp9R3Co1Dpe24qP6GRmb5cudzxQrHzNHe7oi+l18vw8OwalV1E9y2bfD9748VWq/ySVs4hofHxgWKi6pTxg99qHHFLMz0NnWqU9k++WR9/RsDA417beohsnNXRBaE/ujYTX6QfpHG0wydu2Gdc319Tsx3oxyE3ae4pH0/vfEf9XgaNfIzFnT+nZ3Of3z79tG8rq7Waa0nIaxzN9LUo6qrVHUVsK/33ZfXEgOv0sLcORuDek0IaQf5inIv7ewcbz5MUqa4k5YUSZA55i1vGSv6UPugrka4BpkQZPivTMA9AXm/i7NtGqkZOndbZYh4o9PdnawTNa1Ox7B4PtVix8eJtx9Upkbu2ExrUFcjX4O4UEvnroicJiL/BOwvIjf60m1ADVbH1sXcORuD114L/83f6jz77PTCbC9aBFdcMfos7NrlLC9aFO5a6A1WW7LEadF7YRoqCXMgyCoUQh6kNajrvPMa9xrUTVBt4CWcAVvzgDuBo3zp/UBH1LZppmZo8Zdh1iijOnGfnbgzcMUh6m0wrFU6OBjP7TTs+WrkGeGiWupxAyEODUW/zTULhLT4I716VHUDsAE4MsO6xzAagv7+0dZzZYfj66/Xvt+ot0Gvs9Jr2XseLHFDS4R5A4V5yzTC4KWwawJj70uUp1VUq74RrkHdBNUGlQl4BXi5Ij0F/Ax4Z5x91JOaocXfyC2sMpJViOtqLeiurvTf3mrp/4kbrllk9NpUm7wlrn07j/DitRwjyWCvVpl3l3ri8QN/DXwR2Bt4C04ohQtwwjjcHmcf9aRmEH4buZseaXXKBZlr6p3VqhbRiDNLV6UQJimnJ5ydndXXiXPNsu4QrfUYSRpXYddv8uT0zqMM1Cv8dwXk/bv7eV+cfdSTmkH4W8GDIC/SqESrCWGtqdZWf9QsXUNDziQv/uO0t4/PC0teZREl+nHJowFT6zGSbNcqfW71Cv+dwJ/i+P23ud894b83zj7qSc0g/Ko2A1dapGE2q2VaxbgpbaJap/7fwmL0e89cVMUQlzzOu9b7m6Rx1Sqm1zDhjxurZwA4A3gOeNb9frqI7AWcm7xnoTUZGHBGUO7e7XzaKMPaSMOdL+2BVlkS1kH72mtjO5XDYvQvXRp9bZJct6xnP4Pa72+S2DtZxflvGIJqg7KlZmnxG+mQhtksqxZ/UIuxnsnWVZOXob19/FtlmGkr6TzBefy3ytyP0GhQp6lnOvB1YAVwpZfibJtGMuE3KqnXbJaVjb/yGYvTcVuNWjqcg65LGmMP8nJSKKvnUKMRJvyxZuASkd8AdwBrGZ2IBVW9PvVXkACaIUibURzDw84oTc9k0tMzOnnKWWeNj/tSL/5nLI2Z14JmoYpL2sHLgoKmWYC08lJTkDYfXar6NVW9VlWv91LKZTSM1PFE028n37LFEXyAN9+EwcF0bdR+0gjVMTDgTDXot13HxQtBkFYwsrLHsG/ZoGtJCXoNqEzAN4Hj46ybRTJTj1ErSd0Y6zXzVLoDphWcrx4/fs9+XYs9O8wcUm+/RRa0it0+CdRp438F2A28gTNq9xXg5TjbppFM+I1aSerGWI/oB3WUpmHjDxK0zs7xfvxRLophlVSUjTtMSOfPr/+cssAGSY6nLuGvJwHtwO+Am9zlqcAtwCPu55Rq+2gW4W+FzqSykbTFX+vI3aj7WW/rOOwcKoV7cDDclz/uW4H/HJJ6PhUdYrwW3/xm/0/W2+IX4HTgf7vL7wAOj7ntXwBX+4T/EmCx+30xcHG1fTSD8NtraDEkdWMcGoovnnmZOKpVOH7Rqkf4KyvDuPGAyvD/Uo3X4vcLfU/P+LemZvtP1iv8VwCXAw+7y1OAu2Nstx+wGvhjn/CvA2a632cC66rtpxmE315D0yVJSy0oOFlbW7BoB4VHKPq+hfUTZJH8reOyt/grn4GgUNV+IQ9qfBV9b7OmXuG/x/38nS+vaowe4DrgUJyY/p7wb61Y58WQbRcCI8BIb29vwpMtn/C3yhDxPKjl7SmurT2u2OXZKkxb3KM6hytbx2W18UfNUxDWIIh7b5vpP1mv8N/l2uq9CmA6VaZeBE4ElrvfEwu/P1mL3/BTy7WM610T17yRJtUGVqXZ4veuUdyKMKh/YmjIiRPkbRP29pQltTwDce9tM/0n6xX+AeBGYCOw1DXXnFJlm2+5668H/gBsA4Za1dRjNv70qOXtKe4zEadV2N2dznlExcf390GkJfr+fca1h8fxJursdM4jzw7SWp6BOPe22f6TNQs/ziCvDwLvBs7BCcp2ULXtKvbhb/FfWtG5e0m17WsV/p2gu0F3QuHCr9r8HgR5UUtI3bgt/jh24DRC98Y5jifCacQVamsb+7zFEc5aj5tFXJ3K/00tLf5qYTrqmT6zrNTb4r8zznoR2/uFv8ft8H3E/ZxabftahN8Tfa0Q/8Lx/nHNZEjMmahWcpjbZBJ/+ihh8d+6Slv3/PnxzyGOqHrHSTOukHdd4ghnLV49cQQ4CUnmHK5W4VTruG8mE49HvcL/18BnwIntk3dKKvx+0feSJ/6FUvlPMvGviSSCVCn+cfzpqwl/X194B2dc8Y9zDp4QBQlWR0ftouyVs5pw1vOmkdajHVVBJX2DrnY+zfh3rFf4vZG72yn7yN0A0feLvxYl/ubWkxpJBKmW0AhRJhhPHOMcN6rDM845zJ8f7Zs/a1btwtzeXl0447o/RlVa9ZLm36ZaZWst/pKlpMJfNeVNtSeu0cV/zRrVGTOctGZN5odLKkhJqNbST9rh6nnBVHrtBJkqgsQ5qjxe5VKrSSYOYSYyL/m9eyrPOw3S9IaLupbN1qnrUW+Lf3WcvKxSw7f4y1gZpcWaNaoTJ46ex8SJtYt/VAXi/dbdrdrWplvedrDudu/pm7TtaRWfzzLdQbuez7I94piEuC3MuOIqEj5yOMrW7t++2mNTTZzDKo04VCtfWKd51jb+MJGOeosJu07d3c0p+qpam/ADk3Bi69yHM1p3qpv6cUfx5pEa3sbfrC3+StGvR/yjKpCA4+yu+L6dNj2fZWM69M9n2WjL0/vXd3Y6tpNly8YqwaRJqqC7ED2fZXueIe+52e1L3v630p1YcIPEMcrjqFqLX7X6OkH5cVvk9XTwpuW9FteWX62SaMWxNLUK/3nAE8CbwOO+dB9wbtS2aaam8OppNht/mOjXIv5RFciyZdHH8d3joMp+nMDHSEH7ilrP/3xVvnHMY41uYYrPtVh0C1N0EzP0aNaoLlumO2nTN2jfs6/NTNkjzlH9CV5HclJxFokvxmm4kuZlRqkm7M32F4xDrcJ/mDvI6s/d5QXuQK7vxXHDTCs1ix9/U3n1xFGEOE2pahVIgyT/m4G3/HcM6puE+2FuJ7g5vhv0lc4pzrXp7tbdoE8zY0xFs4M23UnbuLeRoPQqk3Qbnbob9GecFPvWqKbnSppHq7qasFuLP77w3+MJPPBR4BnXrfMbwHVR26aZmmHk7h6axY8/rRZ/VrOeFyT+Uctp7rvWY3gV1CbcfhS/Lai7e7R/xetTmTJF35zYrTsRfYlu3cQMncca3cH4CsarVKLEN0uqCXsrjp6vVfjv832/HLjQt3xv1LZppqYS/mYiDRt/k7T4myp1dkY284P60Ly0hSk6jzW6iRm6iRn6dwzuMX1ddpKv837ZMkeR6/ACSxqdU3XsWA6RsY+ejdz1foQHgA73+++Bj/p/i9o2zWTCX2LS8OqJqEBGPrdMt1GbjV9D8ixllyrvg9/05TdtefmvSZfe8vWQ52XZMkelly1T/eAHx5i8LmdQ57et2VMJ7UL0q53LdOukGXvyXqJ7jJB7Lf77cTzC7ufgcacQNk9Do1Kr8C8B/i9wA84sWuLmvwv4v1HbpplM+EtOGn78IRVIX5/TQVop/pXislNcTx3/zV62TC9n0MS/5OlVAsS/4l7uDvjcWbGfIFPbGxNHI+r19Y2Kvve7Pz1Gv4LP5u+veDQgz/v+wQ86xxwcdJ7jOt9k0qSeIG1HAJ8GJvvy/gh4f7Vt00om/C1CQAXidYl45oOX6NadtO35A3sdnXuo+LOC6t8FiH+U505cr56g7YoW0UZNr0nXqFhWVuB1JL/4+0U/bN3H6Hf6IwIaEbHK5cXS6Ooa7SuprAj8z7lXaZx0Uqz/Q1JaZ+SuRt8Xo7GI2/cb5pfu2XM98d9Gp+50ff69vF04ni87QXeLuC6W4/34vYP5f/OLxjjb9+BgpK18u+vCWbTolib19aUq+v574/+stu4WpqRz7IkTR99i/RVBWJ+WX/xTGhhpwu8mo7GI604YNhI16ajWOK59XmXkd7HcCTp5so574/iL9wX78W/pnKHHTlzjDhYb68evU6aM87hJy6unrGlPiz/PeSbzvqYTJ1Z/mE86KdWBkSb8bjIaj6gJS+Lc28qonFH7iON2GHcC96jBV94gqrARqUNDqie/ZY2+RDp+/EGeOKHeOVW8etJOY2z8Gbb4GyaFReWDxOJvwu8mo7GJO6FKFNUCsUURJ2RznONEPYtJBk0lCVZ3B45nzJt07vHH979peH76lX782t3t1E5+P/8Ikd2JjFkec5Mq8gO9ejKy8evBB6e230JTghFnJvxuKpK48eCNcJJMqBJGtRZ7WEs8TlRQ/xtDnABrQRQ5pi1pUDtVdSoC94L+4V0f1FNnOB3xz7XN0N/PHxw1ffk7K6v58Wfg1aOq8cR/Sko2/lpTI7f43QBvv3Xj+jwI/LWbPxW4xZ2B6xZgSrV9NYPwpyFYhkMaFWjYBOdRozuTRqmIWj9q3t56AqOFpcp9RsX4r/capoavv+S3nWP9+P+OQZ3HWD/+81mmm5gxWiEEXOShIdWH20c9wsZdgP7+0WP785N69fg7dv2i3ew2fkCAbvd7J3CX6xp6CWPn3L242r6aQfjTMFEY2RMm1nH7HCvt9EH/88r5b+OWoTK5AUWrJn8IaP9bTNhELnEq0rj9HGkQZ+KbykoubD/+St0zfe0xdfX0j90goR//7+cP6qkz1ugT9OmpM9Y4JizvgK3o1QN0uXF/PgCsA2a6+TOBddW2bwbhL2OZjPHU29qupJZWcVwb/4QJ8dZrawsW83oaI/X0kyShllnAwo5frUKtJ25P2JviLV9vQT9+oB24F3jVa9kDWyvWeTFk24XACDDS29ub8GTLJ7LW4o8mc7NBTOqxr6d5L+N6MnV3xy9fpfjX8z+ptf8iKVH3I8hcFSXeSeY5TqucRUf+LLrFvy9wG/CeuMLvT83Q4jcbfzh5mg3ilKXWeWazupe1VkTVKqasWvxp/s+ixLpyAnqR+uc5rjWKaFlj/YcJfxs5oKpbgduBY4FnRWQmgPv5XB5lKJrly2FwENrbneX2dmd5+fJiy1UGliyBHTvG52/f7vyWJwMDsGIF9PUl2y6Le7loEXR0pLe/XbvGLi9cGLxeWL6fpUvrL08cenuD89vbnefDjypcey3090Nbm/M5PDz6+9Kl0NVV2/FqLWet+8ucoNogjQRMB/Z1v+8F3AGcCFzK2M7dS6rtqxla/EY4Ua26olpMQ0PxO3SzKGPcEcc9PfHfUIJa8vV4SIV5BqVt8gqyncd9y6k0/fi9syqfuyxs/EVH+qQAr55DcCJ63o8T3vkCN78HWI3jzrmaGDN5mfA3N3l1FMYlqbknizLGqXQ8YRkcjN8pncYcuB55mS+DxlUk6YsJuz9x5/Ktp5xFk7vwp5lM+JubMtn4VZOJSlZljDqmf+KRWjqj02yJFjUoMUnlXLSdvUhM+E34S01ZvHpUk7l0trWFt/CSnFOlgIaVwTOj1NMJnfZbSlEt3crjhnlBFe1ZUyQm/Cb8RkziuFEGpc7OseEd4r7FJIkg6rWo6w3rkFYruEy27TKVpSyECX8uXj2G0SgMD8PWrbVtu2MHnHee8z2Jp9KKFeH7DPMCe/LJ2srokZa3yZIlsG3b2Lxt2/LxxhoeHuvBA6MeWSLO54oVjqeWMRYTfqMhqfzT+9326uG888a7PSZhyxbnM0qYK3+LOt5ON/DMzp1j3UXrEe6urvrcMf3XfsOG4HXqrZjilGHhQuf4qs6n54a6fj3s3u18mugHY8JvNBxhf/o0xN8T7nqJEuZaRPtjH3NasV4KepuIoq0tnVZw5bUPI2v/9SLfNOolq0ZLIoLsP2VLZuM3/GQ5PL4eu7n/GUti46+2r/nz6y9TT0/910Y1Xt9CHnb1soyUTdqxnXc/BNa5a8LfLGT5p6+1YzfoGav06pk82Ul+MY4aKOZ58KRRGaUliNWOkZdXT9h9SquCi0MtIh4V/TUbt2Dr3DWahCyGx3vhEeo19bT5/lEDA/D8885fe2jI6dh97bXR37dsgbPOgnnzgvcVJ3RCXNIyvYiE57eaXb0Wc1NY38euXemZK+Ngwm80HMcfnyy/GosWwRVX1Nep67F7d3B+lJfPo49mG8dpwoT0YuuoJsvPihdeSJZfSRp29jAR9/KDjhFVAefaRxH0GlC2ZKYew0/aNv64MXnipLAy1BOPqF4b/+TJtV2XIMry36rnGUjLzh5VhrBjDA5GD7xLu48CM/UYzUK1llZSam3pV5o9otwk6/HyufVWmDUrWdn8vPZaQZ4jGRIUaTOum2paHkFRZQg7xs03O15V3ttdJblF8wyqDcqWrMVv+ClTi7+nJ16nZj3xiJIEYUv6JpKUMnSqegR51MTxsknTOSDseFH3K4vooGFgXj0m/M1C2i5xSUImVKYkx611GsY0Jl9Py4RQpgmFKkU3yIwSFJY5rKJPM6ZPWOOk8l56y1l5Q5nwm/A3FWkHBvMHSUuasnLFU63uN58kHHOW5ck7EFpQ5R92LbyyRQW2S7u1XUv5ssCE34TfiEGtLeysBuGk0dpPs0VeloFTSYLUeWXL24e+snFSrXxZECb8mXXuisg7ROQ2EXlYRB4UkfPc/KkicouIPOJ+TsmqDIYRhue3L+J8Llrk5A8MwNlnB/urt0X8W7JyxUurs+/mm9PZT1mmGEzSke+VLWyb3buzGXswMDA2blDYdJ5FTM+YpVfPTuAvVfUg4AjgHBGZhTPd4mpVPQBnBq7FGZbBMMZR6be/a5ez7In/hz4EU6eOrt/T4wzA+sEPoudszSIwWVr+92mVrR5vmjQJE8soT6uiK62yXDsgP1MPcANwDLAOmOnmzQTWVdvWTD1GmkSFSKjWcZxX56CfNEw9QWWrtZ+kDFMMRvnJh5WtDPH68752FGnjB/qBJ4G3AFsrfnsxZJuFwAgw0tvbm/BkTfiNcKoJZDXhzD/QVv2p0sZfBhGsl1pEtAyVVp6ECb84v2WHiHQD/wYsVdWfishWVd3X9/uLqhpp5587d66OjIwkOGb4bxmfrtEAdHQED9pqb3fssUHPiBeLxmN42LHpP/mkYypYujS7GDXTpoXHEOrpccIU9PbCq6+Gr9fX59iZPfr7g2PpV65nNDYislZV51bmZzpyV0Q6geuBYVX9qZv9rIjMdH+fCTyXZRnKRCnicBuhwc8WLoxvB67suMsyMNl3vwudnePzBwed33p7nQooKsBcpY0/TpyZadNG4/9Pm1bf85r2/ow6CXoNSCMBAvwA+E5F/qXAYvf7YuCSavtqBht/0MhN/xytRr5UTm7umULKagIJG6Uad8L1Sht/tTgztY4yDit7mvuLuiZF7KPMkLeNH/gwoMD9wL1uOh7owfHmecT9nFptX80g/GUa6m5EU0YxCCpTXF/2IIGNquCi9ltLB3ba+6tW/rgEhcIoQyWfJrkLf5qpGYS/jGUyGoMwkYsj+lFhIWqJMxM02KhaRVlPZNIw6h1BHDVQL+9RyFliwm/Cb5SUMLOTR9SI0yyEK0kLPU7LO4sWf70jiIsaSZs3YcJvYZlzoqcnWb7RGlQbTAbRszZlMSBo6dLgzuSgCV3ihDhOsr+41DsYK2pAWxEjaXMnqDYoW2qGFv/QkGNr9Zel3s4to/GpNt+uavWO2Cz6I+JGEo3b8q4lMql/2zgd29UGcPmJip4Ztk1lID/v3IPe0soCZuopVvhVy9lpaCQj7XsY51mNK3JxRS9Nso7WGWVKqiUss0dYeOm3vS24HHFCdycV/6hnqZ6K0o8JfwmE32hssnD1jNPi945dTeSCkicYaVZY/n319Ix/k03TMyZJxZLGumECHidkd+U9i6JahZaW+6sJvwm/USdZtG5rndgkSVjizs70xDlIsNranOSJX5pmjySduGmsGybgca91XKKepTQ7w8OE3zp3DSMmac/1C7B8uTMC15uDtb3dWV6+vLayBLFjB2zfPjav1jDSQZ25u3ePhrPYtQtWrUpvVG6STtw01oXwcB7ViLOOR9SzFHVv04qyasJvGBH4w2yExeNXrS8Ex/LlsHOns5+dO6uLPqTjeVKLiMTZJs25CZKEMg7yHursDF83jCABDwvzkXQdj6hKKurepuZxFPQaULbULKYe69xtLJKERPBMKlnd00pf//nzk5UtymyQpCMxrokpTV/4OP+boSHVyZPHlyPKLj5/fnDZw0xVYV49fhNRXDOX2fhbRPjLGgPGCCfpwClPNNMmrB9g/vzxHb5BoUGibPxJRSbuxPR5jn4NO4c4Zak2eC6KeieeN6+eFhD+skxSbcQnqrMwz2csrKLxBKNSOILELExkknYkxmnx592giTMhfRbE9cgqkjDhNxt/TmTRMWhkSx5T9cUJVxzU2QiOzGzYMPq5cKEz4nfVqrEjgVetcr4HhZFO2pEY53ldsCDbMNWVVCtTViNxw+5LWH6ZMOHPiaLn+zSSE9SxKALHH5/O/oeH4cwzx8bR37IFzjprrPhHTSzkZ9s2WLGieggFP0k7EuM8r2lN7B6XqDKJZDenbZgXTxLvnqIw4c+JUk20bMRiYMBpvfqFV3W0BV0vS5Y4rpaVbN8+VqgnT46/z7DWZlirOGkcnaDnOO6xsiLsHADOPju7t4+oCX1KT5D9p2ypGWz8qubV04gkGSiV9BmLG664Wp9CpX05aV9S0o7EqAnn8+y3qhxB7PfqqbUzNCn1dA7nAda5W7zwG41DkolO/CmJV0/cjtWogGKVnapJ4tXUe32ymFUryfGzPM+yC3pcchd+4Eqc+XQf8OVNBW7BmX3rFmBKnH2Z8Bt5Esd/PyhGTVLRiyueYdN2hgVly/rN0l8p+iufvFrZqtl6ydXrplkmwoQ/Sxv/VcCxFXmLgdWqegDOtIuLMzy+YdREUFgCP11dziTnV14JfX1OH0Bfn7OcxJ48MAArV46dk6GnJ3g/lR28IvChD+U34bvH8LBjw96wwVl22nP5k6WX3IoVyfIbkqDaIK0E9DO2xb8OmOl+nwmsi7Mfa/EbeRJlUy+ibyZJ6zZrE0g181depp4sW/zNpB+UxI9/hqpuciucTcBbw1YUkYUiMiIiI5s3b86tgIYR5h7Y15dfy9pPktZtnBmxsiiLR6VHUlZk6SXXyG6acSmtO6eqrlDVuao6d/r06UUXx2ghwlwWX301vaiTSUgyBiTrgYJx/PjzcOccGHBML35T24oV6VTKeblpLloEHR1O+Ts6xk63mTlBrwFpJczUYzQolS6OWXrIxClLXPNNETNiZXWsIsnaqyevDmSKcOcMEP5LgcXu98XAJXH2Y8JvFEGZ4ivFjVCZR2UVdpw8bfxeORp1XExecX5yF37gR8AmYAewEfgC0IPjzfOI+zk1zr5M+I0iSDKjU1GEuVZ6KUsXy7QiSNZ67EaOdpuXRoUJvzi/lZu5c+fqyMhI7PWjYps0wOkaJaG/f9Rt0Y/XyVs0nmtllOtpWcqaNmW/N9Xo6Aif6WvnzvSOIyJrVXVuZX5pO3cNo2jKHl+p2ngDaN7or40e7bboOD8m/IYRQpaeI2kQR+SaNfpro0e7rXWu5bQwU49hNChh5g6Prq5yVVRpEmTmaubzrRUz9RhGkxE2XwCU7+0kbcr+NlZ2OoougGEYteGJ3JIljtmnt9epDFpF/AYGWudc06YphX+vveD114PzDaOZMPEzaqEpTT1Boh+VbxiG0Uo0pfAbhmEY4ZjwG4ZhtBhNKfytEFbVMAyjVppS+HfvTpZvGIbRSjSl8E+dmizfMAyjlWhK4TcMwzDCaUrhf+GFZPmGYRitRFMKf6MHcDIMw8iSQoRfRI4VkXUi8qiILE57/2UPp2sYhlEkuQu/iLQDlwPHAbOA00RkVprHsABOhmEY4RQRq+dw4FFVfRxARK4BTgYeSvMgFsPEMAwjmCJMPW8HnvItb3TzDMMwjBwoQviDpkkZNz2KiCwUkRERGdm8eXMOxTIMw2gNihD+jcA7fMv7Ac9UrqSqK1R1rqrOnT59em6FMwzDaHaKEP67gQNEZH8RmQCcCtxYQDkMwzBaktw7d1V1p4icC/wr0A5cqaoP5l0OwzCMVqUhJlsXkc1AxLTSkUwDnk+xOGlh5UqGlSsZVq5kNGu5+lR1nK28IYS/HkRkJGiW+aKxciXDypUMK1cyWq1cTRmywTAMwwjHhN8wDKPFaAXhX1F0AUKwciXDypUMK1cyWqpcTW/jNwzDMMbSCi1+wzAMw4cJv2EYRovR1MKfddz/BOV4h4jcJiIPi8iDInKem3+hiDwtIve66fgCyrZeRP7DPf6ImzdVRG4RkUfczyk5l+lA3zW5V0ReFpHzi7heInKliDwnIg/48kKvj4j8T/d5Wycin8i5XJeKyO9F5H4R+ZmI7Ovm94vI677r9v2cyxV63wq+Xj/2lWm9iNzr5ud5vcK0IdtnTFWbMuGMCn4MeCcwAbgPmFVQWWYC73e/7w38J85cBBcCXy74Oq0HplXkXQIsdr8vBi4u+D7+Aegr4noBHwXeDzxQ7fq49/Q+YCKwv/v8tedYro8DHe73i33l6vevV8D1CrxvRV+vit+XARcUcL3CtCHTZ6yZW/x74v6r6nbAi/ufO6q6SVXvcb+/AjxMuUNRnwyscr+vAj5VXFGYDzymqrWO3K4LVf0VUDlbc9j1ORm4RlXfVNUngEdxnsNcyqWqv1TVne7iv+MEQMyVkOsVRqHXy0NEBPhT4EdZHDuKCG3I9BlrZuEvZdx/EekH3gfc5Wad676aX5m3ScVFgV+KyFoRWejmzVDVTeA8mMBbCyiXx6mM/UMWfb0g/PqU6Zk7C/iFb3l/EfmdiPybiHykgPIE3beyXK+PAM+q6iO+vNyvV4U2ZPqMNbPwx4r7nyci0g1cD5yvqi8DVwD/BZgDbMJ53cybD6nq+3GmwjxHRD5aQBkCESd660nAT9ysMlyvKErxzInIEmAnMOxmbQJ6VfV9wF8AV4vIW3IsUth9K8X1Ak5jbOMi9+sVoA2hqwbkJb5mzSz8seL+54WIdOLc2GFV/SmAqj6rqrtUdTfw92T0mhuFqj7jfj4H/Mwtw7MiMtMt90zgubzL5XIccI+qPuuWsfDr5RJ2fQp/5kRkAXAiMKCuUdg1C2xxv6/FsQv/UV5lirhvZbheHcCfAD/28vK+XkHaQMbPWDMLf2ni/rs2xH8EHlbVb/vyZ/pW+zTwQOW2GZdrsojs7X3H6Rx8AOc6LXBXWwDckGe5fIxpiRV9vXyEXZ8bgVNFZKKI7A8cAPw2r0KJyLHA14CTVHWbL3+6iLS739/pluvxHMsVdt8KvV4uHwN+r6obvYw8r1eYNpD1M5ZHz3VRCTgep5f8MWBJgeX4MM7r2P3AvW46Hvgh8B9u/o3AzJzL9U4cD4H7gAe9awT0AKuBR9zPqQVcsy5gC7CPLy/364VT8WwCduC0tr4QdX2AJe7ztg44LudyPYpj//Wese+7637Gvb/3AfcAn8y5XKH3rcjr5eZfBZxdsW6e1ytMGzJ9xixkg2EYRovRzKYewzAMIwATfsMwjBbDhN8wDKPFMOE3DMNoMUz4DcMwWgwTfqPlEZFdMjYaaL+IzBORm2Juf5+IVI3z4kap/HL9JTaM+ugougCGUQJeV9U5/gw3bkpVROQgnAbUR0Vksqq+ln7xDCNdrMVvGBGISJsbE326b/lREZnmrvI5nAFKv8SJK+Rt9yURecgNTHaNb5ezROR2EXlcRL6U24kYhg9r8RsG7OVNwgE8oaqf9n5Q1d0iMgQMAN/BGeJ/n6o+767yWeAY4EDgXEZDTCwG9lfVN8WdEMXl3cDROLHX14nIFaq6I5OzMowQrMVvGK6px02fDvj9SuDP3O9nASsBROQwYLM6cwWsBt7vCzl8PzAsIqfjRMr0+Gd1goA9jxN4a0YG52MYkZjwG0YVVPUpnGiJfwx8gNE496cB7xaR9TixU96CE+cF4ATgcuBQYK0bBRLgTd+ud2Fv3UYBmPAbRjz+ARgCrlXVXSLSBpwCHKKq/arajzM70mnub+9Q1duArwL7At3FFNswxmPCbxjxuBFHvFe6yx8FnlbVp33r/ApnTtS3A0Mi8h/A74DLVHVrjmU1jEgsOqdhxEBE5uIIeBHTFhpGqph90TCqICKLgUEczx7DaHisxW8YhtFimI3fMAyjxTDhNwzDaDFM+A3DMFoME37DMIwWw4TfMAyjxfj/AbbHewis9f2kAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sm.graphics.plot_fit(model_result, 1, vlines=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6816a56-bc61-4619-8d71-29960a157713",
   "metadata": {},
   "source": [
    "#### Fit plot in seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f6903124-f3ee-47ba-bdf1-25c94be00c79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       37.313896\n",
       "1       37.313896\n",
       "2       37.313896\n",
       "3       37.313896\n",
       "4       37.313896\n",
       "          ...    \n",
       "1025    34.821056\n",
       "1026    34.122619\n",
       "1027    34.315862\n",
       "1028    37.313896\n",
       "1029    35.152330\n",
       "Length: 1030, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_result.fittedvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c28b8af1-cf08-4577-b43a-68bb9ea28096",
   "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": [
    "Y_max = Y.max()\n",
    "Y_min = Y.min()\n",
    "\n",
    "ax = sns.scatterplot(x=model_result.fittedvalues, y=Y)\n",
    "ax.set(ylim=(Y_min, Y_max))\n",
    "ax.set(xlim=(Y_min, Y_max))\n",
    "ax.set_xlabel('Predicted value of Strength')\n",
    "ax.set_ylabel('Observed value of Strength')\n",
    "\n",
    "X_ref = Y_ref = np.linspace(Y_min, Y_max, 100)\n",
    "plt.plot(X_ref, Y_ref, color='red', linewidth=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb363118-25f0-4dcb-bb31-4cf9d23bf64b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}