RamzanShahidkhan/PhillyCrime-RegressionModel.ipynb

## gistfile1.txt
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fire up pandas create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load some house value vs. crime rate data\n",
    "\n",
    "Dataset is from Philadelphia, PA and includes average house sales price in a number of neighborhoods.  The attributes of each neighborhood we have include the crime rate ('CrimeRate'), miles from Center City ('MilesPhila'), town name ('Name'), and county name ('County')."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales = pd.read_csv('Philadelphia_Crime_Rate_noNA.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>HousePrice</th>\n",
       "      <th>HsPrc ($10,000)</th>\n",
       "      <th>CrimeRate</th>\n",
       "      <th>MilesPhila</th>\n",
       "      <th>PopChg</th>\n",
       "      <th>Name</th>\n",
       "      <th>County</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>140463</td>\n",
       "      <td>14.0463</td>\n",
       "      <td>29.7</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>Abington</td>\n",
       "      <td>Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>113033</td>\n",
       "      <td>11.3033</td>\n",
       "      <td>24.1</td>\n",
       "      <td>18.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Ambler</td>\n",
       "      <td>Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>124186</td>\n",
       "      <td>12.4186</td>\n",
       "      <td>19.5</td>\n",
       "      <td>25.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>Aston</td>\n",
       "      <td>Delaware</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>110490</td>\n",
       "      <td>11.0490</td>\n",
       "      <td>49.4</td>\n",
       "      <td>25.0</td>\n",
       "      <td>2.7</td>\n",
       "      <td>Bensalem</td>\n",
       "      <td>Bucks</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>79124</td>\n",
       "      <td>7.9124</td>\n",
       "      <td>54.1</td>\n",
       "      <td>19.0</td>\n",
       "      <td>3.9</td>\n",
       "      <td>Bristol B.</td>\n",
       "      <td>Bucks</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   HousePrice  HsPrc ($10,000)  CrimeRate  MilesPhila  PopChg        Name  \\\n",
       "0      140463          14.0463       29.7        10.0    -1.0    Abington   \n",
       "1      113033          11.3033       24.1        18.0     4.0      Ambler   \n",
       "2      124186          12.4186       19.5        25.0     8.0       Aston   \n",
       "3      110490          11.0490       49.4        25.0     2.7    Bensalem   \n",
       "4       79124           7.9124       54.1        19.0     3.9  Bristol B.   \n",
       "\n",
       "     County  \n",
       "0  Montgome  \n",
       "1  Montgome  \n",
       "2  Delaware  \n",
       "3     Bucks  \n",
       "4     Bucks  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploring the data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The house price in a town is correlated with the crime rate of that town. Low crime towns tend to be associated with higher house prices and vice versa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x=sales['CrimeRate'],y=sales['HousePrice'])\n",
    "plt.title(\"Scatter Plot\")\n",
    "plt.ylabel('HousePrice')\n",
    "plt.xlabel('CrimeRate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create a Regression Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime_model = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# split data for training and testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "target = sales['HousePrice']\n",
    "features = sales['CrimeRate']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(features,target, test_size = 0.20, random_state=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit the regression model using crime as the feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime_model.fit(x_train.values.reshape(-1,1),y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05552690736364807\n"
     ]
    }
   ],
   "source": [
    "score = crime_model.score(x_test.values.reshape(-1,1),y_test)\n",
    "print(score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "170541.69260352003\n"
     ]
    }
   ],
   "source": [
    "print(crime_model.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make Prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[159940.63992411 162679.24519962 150708.88988246 157732.08728257\n",
      " 149295.41619187 162723.41625246 161928.3373015  157599.57412407\n",
      " 162811.75835812 155656.04779952 164799.45573551 150841.40304095\n",
      " 160779.8899279  150355.52145981 157422.88991275 159543.10044863\n",
      " 148721.19250507 163253.46888643 139666.12667474 151636.48199191]\n"
     ]
    }
   ],
   "source": [
    "y_pred = crime_model.predict(x_test.values.reshape(-1,1)) \n",
    "print(y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# compare the actual output values for y_test with the predicted values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>Actual</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>93</td>\n",
       "      <td>152624</td>\n",
       "      <td>159940.639924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>30</td>\n",
       "      <td>389302</td>\n",
       "      <td>162679.245200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>56</td>\n",
       "      <td>28000</td>\n",
       "      <td>150708.889882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>114233</td>\n",
       "      <td>157732.087283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>104923</td>\n",
       "      <td>149295.416192</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Actual      Predicted\n",
       "93  152624  159940.639924\n",
       "30  389302  162679.245200\n",
       "56   28000  150708.889882\n",
       "24  114233  157732.087283\n",
       "16  104923  149295.416192"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})  \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's see what our fit looks like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matplotlib is a Python plotting library that is also useful for plotting.  You can install it with:\n",
    "\n",
    "'pip install matplotlib'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales['CrimeRate'],sales['HousePrice'],'.',\n",
    "        sales['CrimeRate'],crime_model.predict(sales['CrimeRate'].values.reshape(-1,1)),'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_test,y_test,'.',\n",
    "        x_test,y_pred,'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: dots are original data, line (predicted) is the fit from the simple regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Remove Center City and redo the analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Center City is the one observation with an extremely high crime rate, yet house prices are not very low.  This point does not follow the trend of the rest of the data very well.  A question is how much including Center City is influencing our fit on the other datapoints.  Let's remove this datapoint and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales_noCC = sales[sales['MilesPhila'] != 0.0] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter( x=sales_noCC[\"CrimeRate\"], y=sales_noCC[\"HousePrice\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Refit our simple regression model on this modified dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target_noCC = sales_noCC['HousePrice']\n",
    "features_noCC = sales_noCC['CrimeRate']\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(features_noCC,target_noCC, test_size = 0.20, random_state=2)\n",
    "\n",
    "crime_noCC_model = LinearRegression()\n",
    "crime_noCC_model.fit(x_train.values.reshape(-1,1),y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot is of new model which is trained and tested on data after removing the house with high price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales_noCC['CrimeRate'],sales_noCC['HousePrice'],'.',\n",
    "        sales_noCC['CrimeRate'],crime_noCC_model.predict(sales_noCC['CrimeRate'].values.reshape(-1,1)),'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Look at the fit on data after removing the house:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales_noCC['CrimeRate'],sales_noCC['HousePrice'],'.',\n",
    "        sales_noCC['CrimeRate'],crime_model.predict(sales_noCC['CrimeRate'].values.reshape(-1,1)),'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare coefficients for full-data fit versus no-Center-City fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visually, the fit seems different, but let's quantify this by examining the estimated coefficients of our original fit and that of the modified dataset with Center City removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-441.71052831]\n"
     ]
    }
   ],
   "source": [
    "print(crime_model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2002.58015335]\n"
     ]
    }
   ],
   "source": [
    "print(crime_noCC_model.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: We see that for the \"no Center City\" version, per unit increase in crime, the predicted decrease in house prices is 2002.  In contrast, for the original dataset, the drop is only 441 per unit increase in crime.  This is significantly different!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### High leverage points: \n",
    "Center City is said to be a \"high leverage\" point because it is at an extreme x value where there are not other observations.  As a result, recalling the closed-form solution for simple regression, this point has the *potential* to dramatically change the least squares line since the center of x mass is heavily influenced by this one point and the least squares line will try to fit close to that outlying (in x) point.  If a high leverage point follows the trend of the other data, this might not have much effect.  On the other hand, if this point somehow differs, it can be strongly influential in the resulting fit.\n",
    "\n",
    "### Influential observations:  \n",
    "An influential observation is one where the removal of the point significantly changes the fit.  As discussed above, high leverage points are good candidates for being influential observations, but need not be.  Other observations that are *not* leverage points can also be influential observations (e.g., strongly outlying in y even if x is a typical value)."
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}

## PhillyCrime-RegressionModel.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fire up pandas create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load some house value vs. crime rate data\n",
    "\n",
    "Dataset is from Philadelphia, PA and includes average house sales price in a number of neighborhoods.  The attributes of each neighborhood we have include the crime rate ('CrimeRate'), miles from Center City ('MilesPhila'), town name ('Name'), and county name ('County')."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales = pd.read_csv('Philadelphia_Crime_Rate_noNA.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>HousePrice</th>\n",
       "      <th>HsPrc ($10,000)</th>\n",
       "      <th>CrimeRate</th>\n",
       "      <th>MilesPhila</th>\n",
       "      <th>PopChg</th>\n",
       "      <th>Name</th>\n",
       "      <th>County</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>140463</td>\n",
       "      <td>14.0463</td>\n",
       "      <td>29.7</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>Abington</td>\n",
       "      <td>Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>113033</td>\n",
       "      <td>11.3033</td>\n",
       "      <td>24.1</td>\n",
       "      <td>18.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Ambler</td>\n",
       "      <td>Montgome</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>124186</td>\n",
       "      <td>12.4186</td>\n",
       "      <td>19.5</td>\n",
       "      <td>25.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>Aston</td>\n",
       "      <td>Delaware</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>110490</td>\n",
       "      <td>11.0490</td>\n",
       "      <td>49.4</td>\n",
       "      <td>25.0</td>\n",
       "      <td>2.7</td>\n",
       "      <td>Bensalem</td>\n",
       "      <td>Bucks</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>79124</td>\n",
       "      <td>7.9124</td>\n",
       "      <td>54.1</td>\n",
       "      <td>19.0</td>\n",
       "      <td>3.9</td>\n",
       "      <td>Bristol B.</td>\n",
       "      <td>Bucks</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   HousePrice  HsPrc ($10,000)  CrimeRate  MilesPhila  PopChg        Name  \\\n",
       "0      140463          14.0463       29.7        10.0    -1.0    Abington   \n",
       "1      113033          11.3033       24.1        18.0     4.0      Ambler   \n",
       "2      124186          12.4186       19.5        25.0     8.0       Aston   \n",
       "3      110490          11.0490       49.4        25.0     2.7    Bensalem   \n",
       "4       79124           7.9124       54.1        19.0     3.9  Bristol B.   \n",
       "\n",
       "     County  \n",
       "0  Montgome  \n",
       "1  Montgome  \n",
       "2  Delaware  \n",
       "3     Bucks  \n",
       "4     Bucks  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploring the data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The house price in a town is correlated with the crime rate of that town. Low crime towns tend to be associated with higher house prices and vice versa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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epi7v8WJmk12jM/T/BXgReEv6vBH4VFMi6iLjSRKlEWZDm4dHTab0bH0zm0waTS77R8RngRGAiBjm5U7+KWm8SWIsI8zMzLpVo8nlRUl9ZJ34SNofeKFpUXWB8SYJ7/FiZlNBo8nlXODfgZmSLgN+CHysaVF1gfEmiWojyTyZ0swmk0bXFruBbGb++4BvAYMRcVPzwup81ZJBQM0Vjz2Z0symgoaSi6R5wK8j4nqgH/hbSfs2NbIOl5ckSmr1vyyYO8CnTzqEgf4+BAz09/Hpkw7xaDEzm1QUkb+p1aiDpLuA1wO/Q7bW2MXASRHx+80Nr3UGBwdj5cqVYzqnNFqs2vL6A/193LxoSs8zNbNJTtKqiBisLG+0z+WlyLLQicCXIuKLwCuKDLAbLZg7UDN51NrTxcxsMmt0s7BnJZ0DvBf4PUk9QG/zwuouPRJbcmqAPZrSo7XNbAprtOZyCtnQ4zMi4ufAALCkaVF1mbzEUqvczGyya6jmkhLK58s+P0zW92JkfSt5TWADHl5sZlNUo6PFnpX0THr9WtIWSU83O7hu4eHFZmajNVpzGdV5L2kBcHhTIupCjS5g2U0LVnZTrGbWeRoaipx7onRrRBxRcDxtM56hyGNRuSUyZLWbTpzj0k2xmll7VRuK3OiS+yeVfZwGDJLWGbPG1FqLrNN+YXdTrGbWmRodinx82fuXgJ+SzXmxBlWb89KJc2G8uKaZTVSjfS5/0uxAJoO8fgqg5krJnTgXZqzbN5uZVWp0tNgMSd+W9LikX0i6RtKMZgfXTfL2d1l49RoWXrWmZu2kE+fCePSbmU3UWHaiXAbsTTaB8rpUZkleP8XIlmBka+3k0YlzYby4pplNVKN9LtMjojyZXCLp7FonSJpJNtHyN4GtwIUR8UVJewJXALPI+m7+KCKekiTgi8A7gOeB90XEj9O1Tgc+mS79qYi4NJUfBlwC9AHfAz4YEVHtHg3+XcdlPP0RnVwbWDB3wMnEzMat0ZrLE5LeK6knvd4L/LLOOS8BH4mI1wFHAGdJOhBYBPwwImaTbTq2KB1/HDA7vc4EvgKQEsW5wJvI5tacK2mPdM5X0rGl845N5dXu0TRj7Y/o7+vdrjawdPUQ885fwX6Lrq+5J4yZWadrNLn8KfBHwM+Bx4CTU1lVEfFYqeYREc8C95I1qZ0IXJoOuxRYkN6fCHwjMrcC/ZL2AuYDN0TEk6n2cQNwbPput4i4Ja3Y/I2Ka+Xdo2kWzp9Db0/jnfO/sdMO2yWWyj6banvCmJl1ukZ3onw4Ik6IiOkR8eqIWBARP2v0JpJmAXOB24DXRMRj6bqPAa9Ohw0Aj5SdtjGV1SrfmFNOjXtUxnWmpJWSVm7atKnRv051Y+ibr2xGqzW3xMys29Tsc5H0ZWr8yoyIv6l3A0m7AtcAZ0fEM6o+9DbvixhHecMi4kLgQshm6I/l3EpLlq+v23lfrn+X0TsWtHpuiZd3MbNmqldzWQmsSq8Tyt6XXjVJ6iVLLJdFxLWp+BepSYv05+OpfCMws+z0GcCjdcpn5JTXukfTjDUJPPfrl0Y1eVXrs2nG3BI3wZlZs9VMLhFxaekFPFX+uTRiq5o0+usi4N6I+HzZV8uA09P704HvlJWfpswRwNOpSWs5cIykPVJH/jHA8vTds5KOSPc6reJaefdomrEmgZGtwUeuXLOt8/7IA6a3bG6Jm+DMrNka7dCHsa8lNg/4Y+AoSXem1zuA84G3S7ofeHv6DNlQ4geBDcDXgL8CiIgngb8H7kivv0tlAH8JfD2d8wDw/VRe7R5NkzfxsJ4tEdtqDtesGuIPDhtoydwSL+9iZs3W6DyXMYuIH5HfLwJwdM7xAZxV5VoXAxfnlK8EDs4p/2XePZopb9n9Iw+Yzo33bWpo/bDhkS3ceN8mbl50VLND9fIuZtZ09Tr0n+XlGssukp4pfUWWD3ZrZnDdptrEw7wl7PO0quawcP6c3CX1O3VCp5l1n5rJpXKTMBufylrNNCl3TbHx1BzGM+qr0c3NzMzGq2nNYlNZtV/4pV/e1TbjGmvNofI6pVFfQEMJxsnEzJplLB361oBGhvkWtTCkR32ZWadyzWUC8mooje7iWKo5lK7xoSvuZMny9dtqOY00d3nUl5l1KieXcarWJFWt0z7vF37eNRZetYZPfHstv3rx5etUa+7yqC8z61RuFhunajWUajtL5v3Cz90DZmuMSizl165s7vKmXmbWqVxzGadqTU9bIujr7anaWV/e3DXWWamV9/SoLzPrVE4u41StSWqgrO+l8hd+o/Ndat2zkkd9mVkncnIZp1oTEfN+4S9dPcRHrlyTO7+lEW7uMrNu4uQyTtWapADmnb+Coc3D9KTJkv19vfzqxZdqJhYBu6fjRraMPq6/r5fFJxzkGoqZdQ0nlwmorKFUNnuVksnm4ZGa1xno79u2ppj3WTGzycDJpUB5o78a8fyL2d4upWTlZGJm3c5DkQs03smLTz0/woeuuJNPLl1bcERmZu3hmkuBqo0ga0QAl936MIP77lmz5lKv2azW925yM7NWcXIpUN4IsrEI2G6ZmHL1Fqqs9T0w7kUuzczGys1iBSotSNnf1zvua9RqWjvvunU1F6qsta6ZF7k0s1ZycinYgrkD3HnuMbz3iH2qbsNZyzSJ/RZdz7zzV4xaSXnp6iGeej5/1FkpIdVayNKLXJpZKzm5NMmN922qurxLX28P8/bfMzf5bInIXaq/Vg2jNHO/2oKVe/f31fzOzKxoTi5NUqtG8OmTDuGy97+ZC045dNueLnkLXpY3W9W6XmnyZq2FLL3IpZm1kjv0m6TWyLFSwiif07Lfoutzjy0llWrX6+/r3XaNRhay9GgxM2sFJ5eClYb71hqSnDdSq1ry2D0NDqi2ltniEw4adXytSZieoGlmreJmsQKVb3FcT+VIrSMPmJ573DO/Htk2e7+IrZHNzFrBNZcCjXX5l1KT19LVQ1yzaij3mK0Bi5et89IwZtZVnFwKNNZhvaWRWvWS0ubhkZbPrvdsfjObCCeXAo11+ZdSU1gjSamVs+vrrQRgZlaP+1wKlDfct5Yb79sE1J9rMk3kzq4/77p1Yw+yAZ7Nb2YT5eRSoFKn+x67NLb8y9Dm4W0bi1Wbzd/bI7ZWmY351PMjo2bxF8Wz+c1sopxcCrZg7gC77NhYa6NgWzNapM/w8oTKgf4+lpz8egZq1GzOvuLO7ZaKmSjP5jeziXJyaYJG/4VfWSEpff7N3XfmC6ccys2LjmLB3IG6s+iHNg8Xuh+MZ/Ob2UQ5uTRBvX/h99Z56kObh1l41ZpttZEFcwfqrrQcwDdvfZhDz/tB7sKXY+E5NWY2UYqotrzi1DI4OBgrV64s5FqVo60q9UhsaeC59/f1cue5xzR0zTx9vT1OCmbWVJJWRcRgZblrLk1Q+pd/NY0kFsjmt1Res1b/SyWP8DKzdnFyaZIFcweqJoK8FZAbvebNi47iC6cc2vBeMR7hZWbt4OTSRNU6xt/9ppn0TqufHqoNaV4wd4D3NLgZmUd4mVk7NC25SLpY0uOS7i4r21PSDZLuT3/ukcol6UuSNki6S9Ibys45PR1/v6TTy8oPk7Q2nfMlKasOVLtHqyxdPcS881ew36LrWbJ8PX9w2MB2HeOD++5Zt2mst0ece/xBVb//1IJDtu0HU43AI7zMrC2aWXO5BDi2omwR8MOImA38MH0GOA6YnV5nAl+BLFEA5wJvAg4Hzi1LFl9Jx5bOO7bOPZqufFXk0m6S16waYuH8OTx0/ju3DS1evGxd1YmRkDWbnfLGmXU74kvNZNVqMIGXazGz9mja2mIR8V+SZlUUnwi8Nb2/FLgJ+Hgq/0ZkQ9duldQvaa907A0R8SSApBuAYyXdBOwWEbek8m8AC4Dv17hH09VaNmXB3IFti0GWd9Tn2RLBNauGGNx3z23XrbWAZLU1zcbS+W9mU0uzF6dt9cKVr4mIxwAi4jFJr07lA8AjZcdtTGW1yjfmlNe6x3YknUlW+2GfffYZ799pm1rLpnxy6Vouu/Xh7SZOVjM8soVzrr2LX49s3XZOtQUk8zYSE9X3iDGzqa0Vi9N2Sod+XstOjKN8TCLiwogYjIjB6dMn/ou4Wue5lE1wHGuAw2WJ5eWy7YcXL5g7wB8cNjDqoQRwzaqhpqw9ZmbdrRWL07Y6ufwiNXeR/nw8lW8EZpYdNwN4tE75jJzyWvdoumqrItfqXxmPvBrSjfdtaigRmZm1YnHaVieXZUBpxNfpwHfKyk9Lo8aOAJ5OTVvLgWMk7ZE68o8BlqfvnpV0RBoldlrFtfLu0XSVy6aMdz5LPXk1JK9kbGaNasXitM0civwt4BZgjqSNks4AzgfeLul+4O3pM8D3gAeBDcDXgL8CSB35fw/ckV5/V+rcB/4S+Ho65wGyznxq3KMlSiO4Hjr/nWxtwtI61YYXeyVjM2tUKxanbeZosXdX+eronGMDOKvKdS4GLs4pXwkcnFP+y7x7tEOtnSkFvGX/Pfnxw083vF6YgPccsU9uh1tep75XMjazPKXfIc0cLeaFK5MiF64sqbbYZH9fL4tPOGjU8ORHNw8zrcaClgMN/MevHFp45AHTufG+TU37n8fMrNrClU4uSTOSC4xtLHm1ZLTHLr2ce/xBY0oMS1cPsfCqNYyUjSbonSaW/OHrnWDMrDDVkkur57lMOQvmDoz6ZV5aHqZastm5d9p2yeWp50fGPAZ98bJ1oxILwMjWYPGydU4uZtZ0Ti4tVGviElBzv5bymf6NqLYKQL3VAfJibma7rJlNTk4uLVRv4lK9jv1WDytuxSxeM5ucOmWG/pRQbeTY0ObhhhLHWIYVV1uuv1p5nlbM4jWzycnJpYWqTarskeomjrEOKz73+IPo7Rl9v3rL+FfyxEwzGy8nlxaqNsx4S0TupKZSaijtAzOWpqgFcwdYcvLrR+0ls+TksY0U88RMMxsv97m00ECNpfGLmtRUZAe8J2aa2Xg5ubRQvV/WlcOWG1GeTHbv6+VXL77EyJashtRIB3ytZNSKWbxmNjl5EmXSrEmUlYqsWVSbdFlpoL+Pmxcd1dD5fb09Y26CM7Opy5MoO8R4aifV5I3mylOtA77ezplmZuPlDv0u1uiorWod8B4NZmbN4uTSxRoZtVWrA96jwcysWZxculje8OXeaWKPXXq3DT+u1X/Sij0dzGxqcp9LF5voaC6PBjOzZvFosaRVo8XMzCYTjxabpJqxarFXQjaziXJy6WL1Vi1eunqI865bx1PPZ8vsl++AOd5rmpk1wsmli9VbtXjh1Wu2zdaHbC+XhVetAaonCs99MbMieLRYF6s1T2XJ8vWjEkvJyNaouWS+576YWRGcXLpYrXkqtZJBre8898XMiuDk0sVqzVOplQxqfee5L2ZWBPe5dLmde6dt6yOp7LCv7HOBbJJlrUThuS9mVgQnly6Vt6LxCy9t3fa+lAzGOlqsdK6TiZlNhJNLl2pkVJeThJm1i/tcupRHdZlZJ3Ny6VIe1WVmnczJpUt5VJeZdTL3uXQpj+oys07m5NLF3GFvZp3KzWJmZlY4JxczMyuck4uZmRXOycXMzArn5GJmZoVTxPZ7fkxFkjYBP6tz2KuAJ1oQThG6JVbHWbxuidVxFq8dse4bEdMrC51cxkDSyogYbHccjeiWWB1n8bolVsdZvE6K1c1iZmZWOCcXMzMrnJPL2FzY7gDGoFtidZzF65ZYHWfxOiZW97mYmVnhXHMxM7PCObmYmVnhnFwaJOlYSeslbZC0qN3xlJP0U0lrJd0paWUq21PSDZLuT3/u0abYLpb0uKS7y8pyY1PmS+kZ3yXpDW2Oc7GkofRc75T0jrLvzklxrpc0v4VxzpR0o6R7Ja2T9MFU3lHPtEacnfhMd5Z0u6Q1KdbzUvl+km5Lz/QKSTum8p3S5w3p+1ltjvMSSQ+VPdNDU3nbfp4AiAi/6ryAHuAB4LXAjsAa4MB2x1UW30+BV1WUfRZYlN4vAj7Tpth+D3gDcHe92IB3AN8HBBwB3NbmOBcDH8059sD0/8BOwH7p/42eFsW5F/CG9P4VwE9SPB31TGvE2YnPVMCu6X0vcFt6VlcCp6byrwJ/md7/FfDV9P5U4Io2x5GZ2vsAAAVrSURBVHkJcHLO8W37eYoI11wadDiwISIejIgXgcuBE9scUz0nApem95cCC9oRRET8F/BkRXG12E4EvhGZW4F+SXu1Mc5qTgQuj4gXIuIhYAPZ/yNNFxGPRcSP0/tngXuBATrsmdaIs5p2PtOIiOfSx970CuAo4OpUXvlMS8/6auBoSWpjnNW07ecJ3CzWqAHgkbLPG6n9g9JqAfxA0ipJZ6ay10TEY5D9oAOvblt026sWWyc+5w+kJoWLy5oWOyLO1Bwzl+xfsB37TCvihA58ppJ6JN0JPA7cQFZz2hwRL+XEsy3W9P3TwCvbEWdElJ7pP6RneoGknSrjTFr6TJ1cGpP3r5JOGsM9LyLeABwHnCXp99od0Dh12nP+CrA/cCjwGPCPqbztcUraFbgGODsinql1aE5Zy2LNibMjn2lEbImIQ4EZZDWm19WIp22xVsYp6WDgHOAA4I3AnsDH2x0nOLk0aiMws+zzDODRNsWynYh4NP35OPBtsh+OX5SqwOnPx9sX4XaqxdZRzzkifpF+mLcCX+PlZpq2ximpl+wX9mURcW0q7rhnmhdnpz7TkojYDNxE1kfRL6m0FXx5PNtiTd/vTuNNqkXHeWxqgoyIeAH4FzrkmTq5NOYOYHYaPbIjWSfesjbHBICk35D0itJ74BjgbrL4Tk+HnQ58pz0R5qoW2zLgtDTK5Qjg6VJTTztUtE+/i+y5QhbnqWnU0H7AbOD2FsUk4CLg3oj4fNlXHfVMq8XZoc90uqT+9L4PeBtZH9GNwMnpsMpnWnrWJwMrIvWgtyHO+8r+USGyfqHyZ9q+n6dWjh7o5hfZyIufkLXFfqLd8ZTF9VqyUTZrgHWl2MjagH8I3J/+3LNN8X2LrPljhOxfUmdUi42sGv9P6RmvBQbbHOe/pjjuIvtB3avs+E+kONcDx7Uwzt8la9q4C7gzvd7Rac+0Rpyd+Ex/B1idYrob+D+p/LVkCW4DcBWwUyrfOX3ekL5/bZvjXJGe6d3AN3l5RFnbfp4iwsu/mJlZ8dwsZmZmhXNyMTOzwjm5mJlZ4ZxczMyscE4uZmZWOCcXswmQ9JuSLpf0gKR7JH1P0m/nHPc/Bd3vfZI2pdVv75P0oQbOeauktxRxf7NGObmYjVOatPZt4KaI2D8iDgT+FnhN2TE9ABFR5C/3KyJbAmQe8AlJM+sc/1bAycVaysnFbPyOBEYi4qulgoi4E+hRtpfJv5FNXkPSc+nPt0r6T0lXSvqJpPMlvSft07FW0v7puOmSrpF0R3rNq7x5RPySbCJfaYb28cr2F1kt6T8kvSYtGvkXwIdSbed/NXJts4naof4hZlbFwcCqKt8dDhwc2fLxlV5PtjDik8CDwNcj4nBlG2r9NXA28EXggoj4kaR9gOVULKaYyncmm7EN8CPgiIgISX8GfCwiPiLpq8BzEfG5dN6/1bu22UQ5uZg1x+1VEgvAHZHWeJL0APCDVL6WrDYE2bpRB+rlbUJ2K60hB5wi6UhgDvD+iPh1Kp8BXJHWmtoRqHb/3GtHtu+KWSGcXMzGbx0vL2xY6Vc1znuh7P3Wss9beflnchrw5ogYLj8xJYQrIuIDkt4MXC/p+xHxc+DLwOcjYpmkt5Lt+pgn99pmRXKfi9n4rQB2kvT+UoGkNwK/X8C1fwB8oOy6h1YeEBG3kC0E+cFUtDswlN6fXnbos2RbDTd8bbOJcnIxG6fIVn19F/D2NBR5HVltoYg9M/4GGFS2u+A9ZJ3yeT4D/ElqMlsMXCXpv4Enyo65DnhXqUN/DNc2GzevimxmZoVzzcXMzArn5GJmZoVzcjEzs8I5uZiZWeGcXMzMrHBOLmZmVjgnFzMzK9z/B4bP0sO1jzmqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x=sales['CrimeRate'],y=sales['HousePrice'])\n",
    "plt.title(\"Scatter Plot\")\n",
    "plt.ylabel('HousePrice')\n",
    "plt.xlabel('CrimeRate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create a Regression Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime_model = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# split data for training and testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "target = sales['HousePrice']\n",
    "features = sales['CrimeRate']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(features,target, test_size = 0.20, random_state=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit the regression model using crime as the feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime_model.fit(x_train.values.reshape(-1,1),y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05552690736364807\n"
     ]
    }
   ],
   "source": [
    "score = crime_model.score(x_test.values.reshape(-1,1),y_test)\n",
    "print(score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "170541.69260352003\n"
     ]
    }
   ],
   "source": [
    "print(crime_model.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make Prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[159940.63992411 162679.24519962 150708.88988246 157732.08728257\n",
      " 149295.41619187 162723.41625246 161928.3373015  157599.57412407\n",
      " 162811.75835812 155656.04779952 164799.45573551 150841.40304095\n",
      " 160779.8899279  150355.52145981 157422.88991275 159543.10044863\n",
      " 148721.19250507 163253.46888643 139666.12667474 151636.48199191]\n"
     ]
    }
   ],
   "source": [
    "y_pred = crime_model.predict(x_test.values.reshape(-1,1)) \n",
    "print(y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# compare the actual output values for y_test with the predicted values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>Actual</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>93</td>\n",
       "      <td>152624</td>\n",
       "      <td>159940.639924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>30</td>\n",
       "      <td>389302</td>\n",
       "      <td>162679.245200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>56</td>\n",
       "      <td>28000</td>\n",
       "      <td>150708.889882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>114233</td>\n",
       "      <td>157732.087283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>104923</td>\n",
       "      <td>149295.416192</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Actual      Predicted\n",
       "93  152624  159940.639924\n",
       "30  389302  162679.245200\n",
       "56   28000  150708.889882\n",
       "24  114233  157732.087283\n",
       "16  104923  149295.416192"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})  \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's see what our fit looks like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matplotlib is a Python plotting library that is also useful for plotting.  You can install it with:\n",
    "\n",
    "'pip install matplotlib'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales['CrimeRate'],sales['HousePrice'],'.',\n",
    "        sales['CrimeRate'],crime_model.predict(sales['CrimeRate'].values.reshape(-1,1)),'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_test,y_test,'.',\n",
    "        x_test,y_pred,'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: dots are original data, line (predicted) is the fit from the simple regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Remove Center City and redo the analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Center City is the one observation with an extremely high crime rate, yet house prices are not very low.  This point does not follow the trend of the rest of the data very well.  A question is how much including Center City is influencing our fit on the other datapoints.  Let's remove this datapoint and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales_noCC = sales[sales['MilesPhila'] != 0.0] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAD4CAYAAAAZ1BptAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAdXklEQVR4nO3df4xc5X3v8ffX63VZ0ibLDyeFNYkd1TKhyY1dVuDKVxWBFpskClabFFBu40ZIXFW0Iil1Y1dItGmu6tRSHaq2UVGgIVe5YDfQxcqPblEMuvdGjck6a+QQsoobCHidYqf2kuaypcvyvX/MM2Z29pz5eWbOc858XtJqZ545M+eZ2Z3ne57f5u6IiIgkWZF3BkREJF4KEiIikkpBQkREUilIiIhIKgUJERFJtTLvDGTt4osv9rVr1+adDRGRQjly5MiP3X11fXrpgsTatWuZmprKOxsiIoViZj9MSldzk4iIpFKQEBGRVAoSIiKSSkFCRERSKUiIiEiq0o1ukuKbmJ5l7+QMJ+fmuXR0hJ1bN7B901je2RIZSAoSEpWJ6Vl2P3KM+YVFAGbn5tn9yDEABQqRHKi5SaKyd3LmXIComl9YZO/kTE45EhlsChISlZNz822li0hvKUhIVC4dHWkrXUR6S0FCorJz6wZGhoeWpI0MD7Fz64acciQy2NRxLVGpdk5rdJNIHBQkJDrbN40pKIhEQs1NIiKSSkFCRERSKUiIiEgqBQkREUmlICEiIqkUJEREJJWChIiIpFKQEBGRVAoSIiKSSjOuC6pfG/NoAyCRwaYgUUD92phHGwCJiJqbCqhfG/NoAyARUZAooH5tzKMNgEREQaKA+rUxjzYAEhEFiQLq18Y82gBIRNRxXUD92phHGwCJiLl73nnI1Pj4uE9NTeWdDRGRQjGzI+4+Xp+u5iYREUmlICEiIqkUJEREJJWChIiIpFKQEBGRVAoSIiKSSkFCRERSKUiIiEiqloOEmQ2Z2bSZfTncX2dmh83s+2a238xWhfSfCfePh8fX1rzG7pA+Y2Zba9K3hbTjZrarJj3xHCIi0h/t1CTuAJ6puf9pYJ+7rwfOAreG9FuBs+7+C8C+cBxmdgVwM/CLwDbgb0LgGQL+GrgBuAK4JRzb6BwiItIHLQUJM1sDvA/4XLhvwLXAl8IhDwDbw+0bw33C49eF428EHnL3V9z9WeA4cFX4Oe7uP3D3/wQeAm5scg4REemDVmsSnwH+EHgt3L8ImHP3V8P9E0B11bcx4AWA8PhL4fhz6XXPSUtvdI4lzOw2M5sys6nTp0+3+JZERKSZpkHCzN4PnHL3I7XJCYd6k8eySl+e6H6vu4+7+/jq1auTDhERkQ60slT4FuADZvZe4DzgjVRqFqNmtjJc6a8BTobjTwCXASfMbCXwJuBMTXpV7XOS0n/c4BySYmJ6Vkt7i0hmmtYk3H23u69x97VUOp4PufuHgceBD4bDdgCPhtsHw33C44e8sh75QeDmMPppHbAeeBL4FrA+jGRaFc5xMDwn7RySYGJ6lt2PHGN2bh4HZufm2f3IMSamZ/POmogUVDfzJD4B/L6ZHafSf3BfSL8PuCik/z6wC8DdnwYOAN8F/hG43d0XQy3hd4FJKqOnDoRjG51DEuydnGF+YXFJ2vzCInsnZ3LKkYgUnTYdKpF1u76S2GljwLN73tfv7IhIgWjToQFw6ehIW+kiIs0oSJTIzq0bGBkeWpI2MjzEzq0bcsqRiBRdK6ObpCCqo5g0uklEsqIgUTLbN40pKIhIZtTcJCIiqRQkREQklYKEiIikUpAQEZFUChIiIpJKQUJERFJpCGyHtNqqiAwCBYkOVFdbrS6mV11tFVCgEJFSUXNTB7TaqogMCgWJDpycm28rXUSkqBQkOqDVVkVkUChIdECrrYrIoFDHdQe02qqIDAoFiQ5ptVURGQRqbhIRkVQKEiIikkpBQkREUilIiIhIKgUJERFJpSAhIiKpFCRERCSVgoSIiKRSkBARkVQKEiIikkpBQkREUilIiIhIKgUJERFJpSAhIiKpFCRERCSVgoSIiKRSkBARkVQKEiIikqppkDCz88zsSTN7ysyeNrM/CenrzOywmX3fzPab2aqQ/jPh/vHw+Nqa19od0mfMbGtN+raQdtzMdtWkJ55Dym1iepYtew6xbtdX2LLnEBPTs3lnSWRgtVKTeAW41t3fDWwEtpnZZuDTwD53Xw+cBW4Nx98KnHX3XwD2heMwsyuAm4FfBLYBf2NmQ2Y2BPw1cANwBXBLOJYG55AMxFgYT0zPsvuRY8zOzePA7Nw8ux85FkXeRAZR0yDhFT8Nd4fDjwPXAl8K6Q8A28PtG8N9wuPXmZmF9Ifc/RV3fxY4DlwVfo67+w/c/T+Bh4Abw3PSziFdirUw3js5w/zC4pK0+YVF9k7O5JQjkcHWUp9EuOI/CpwCHgP+BZhz91fDISeAsXB7DHgBIDz+EnBRbXrdc9LSL2pwjvr83WZmU2Y2dfr06Vbe0sCLtTA+OTffVrqI9FZLQcLdF919I7CGypX/O5IOC78t5bGs0pPyd6+7j7v7+OrVq5MOkTqxFsaXjo60lS4ivdXW6CZ3nwOeADYDo2a2Mjy0BjgZbp8ALgMIj78JOFObXvectPQfNziHdCnWwnjn1g2MDA8tSRsZHmLn1g055UhksLUyumm1mY2G2yPArwLPAI8DHwyH7QAeDbcPhvuExw+5u4f0m8Pop3XAeuBJ4FvA+jCSaRWVzu2D4Tlp55AuxVoYb980xp/9+rsYGx3BgLHREf7s19/F9k2JLY0i0mMrmx/CJcADYRTSCuCAu3/ZzL4LPGRmnwKmgfvC8fcB/9PMjlOpQdwM4O5Pm9kB4LvAq8Dt7r4IYGa/C0wCQ8D97v50eK1PpJxDulQtdPdOznBybp5LR0fYuXVDFIXx9k1jUeRDRMAqF+zlMT4+7lNTU3lnIzcT07NRFvwiEjczO+Lu4/XprdQkpCCqw1qro5aqw1oBBQoR6YiW5SiRWIe1ikhxKUiUSKzDWkWkuNTcFKGkfgVo3sl86egIswkBIe9hrSJSXAoSkUnqV9j590+BwcKin0tL6mvYuXXDkudCHMNaRaS41NwUmaR+hYXX/FyAqErqa9AcAxHJmmoSkWmn/yDp2HbnGGjIrIg0oppEZNrpP+i2ryHWlWBFJB4KEpFJWi5jeIUxPLR0vcMs+ho0ZFZEmlFzU528m1/SlstISus2XxoyKyLNKEjUiGXGclq/QtZ50JBZEWlGzU01Bq35JdaVYEUkHqpJ1Bi05peYV4IVkTgoSNQYxOYXLcstIo2ouamGml9ERJZSTaKGml/S5T3qS0TyoSCBCsBmYhn1JSL9N/DNTZp13NygjfoSkdcNfJBQAdjcoI36EpHXDXyQUAHYXNrorjKP+hKRioEPEt0WgBPTs2zZc4h1u77Clj2HStlMpVFfIoNr4INENwXgoPRnaJ8KkcE18KObuhn22qg/o2wFqCbdiQymgQ8S0HkBmDQ7u1G6iEjRDHxzUzeGzNpKFxEpGgWJLiy6t5UuIlI0ChJdGEsZAZWWLiJSNAoSXdDQUBEpO3Vcd6GMCwJqHSuROOX13VSQ6FKZhoZqIT+ROOX53VRzkwCVf8I7DzyldaxEIpTnGnMKEnLuKiVtVJbWsRLJV55rzKm5qUf63X7YzfmSrlJqaSE/kXzlubWyahI90O81nbo9X6OrEY3WEslfniMpFSR6oN/th92eL+1qZMhMC/mJRCDPRTabNjeZ2WXAF4CfB14D7nX3e8zsQmA/sBZ4DvhNdz9rZgbcA7wXeBn4bXf/dnitHcBd4aU/5e4PhPQrgc8DI8BXgTvc3dPO0fW77rFW2w+zapJqdr5m59m5dcOSkRNQuUpRgBCJR14jKVupSbwK3Onu7wA2A7eb2RXALuDr7r4e+Hq4D3ADsD783AZ8FiAU+HcDVwNXAXeb2QXhOZ8Nx1afty2kp50jaq3sUdFqE1Er+1U0Ol8r5ynKUuCDsHeHSGzM21xnyMweBf4q/Fzj7j8ys0uAJ9x9g5n9bbj9YDh+Brim+uPu/z2k/y3wRPh53N0vD+m3VI+rPrf+HI3yNz4+7lNTU229pyxNTM/yxwefZm5+YUl6/ZX5lj2HEjuixkZH+Maua8+9Vv0VvgEejqvWCJKOq55v7+RM0/MUQaP3GFswEykiMzvi7uP16W31SZjZWmATcBh4i7v/CCD8fnM4bAx4oeZpJ0Jao/QTCek0OEd9vm4zsykzmzp9+nQ7bylT1YKsPkBccP7wssKslSappL6GakivrRE0qgmUZXtW7UUuko+Wh8Ca2c8CDwMfc/efWPpy2EkPeAfpLXP3e4F7oVKTaOe5WUobSnr+qpXLrnZbGdLWrCCv3eAorb0y7TwrzM4FmCIoS7CTfGnZmfa1VJMws2EqAeKL7v5ISH4xNAERfp8K6SeAy2qevgY42SR9TUJ6o3NEqZ2CrJUhba2MgW5WSCadByrLmRdpq9Vu9yIXGZTthrPWNEiE0Ur3Ac+4+1/UPHQQ2BFu7wAerUn/iFVsBl4KTUWTwPVmdkHosL4emAyP/buZbQ7n+kjdayWdI0rtFGStdBanFfCtnLP+PEkbIWXVXNOPDmWtuCvdUpNlZ1ppbtoC/BZwzMyOhrQ/AvYAB8zsVuB54EPhsa9SGf56nMoQ2I8CuPsZM/tT4FvhuE+6+5lw+3d4fQjs18IPDc4RpbShpGkFWbMhbbWrzM7OzZ/rtG7ltetf5+P7jyY+1m1zTb8WHivjirvSX2qy7EzTIOHu/5fkfgOA6xKOd+D2lNe6H7g/IX0KeGdC+r8lnSNWvSjIagNJN+2pvZrW3+jqLOsCvEwr7kr/5bm0RZFp7aaM9bIg6+a1263ltEpXZ1IUvfoOlJ2CxIDoVXONrs7ypxE7rVGTZWfankwXu7wn03WqqF90TXLLlz5/yUomk+mkN4o8NK8oS3qUlUbsSK+pualGXlfz/ez87YVO+0ry+ryLWmtLoj4h6TUFiSDPPWQH8Yvey8+7URAo2z7e6hOSXlNzU5BntX0QZxP36vNu1nRXtuYZTTKUXlOQCPK8mo/5i96r2dS9+rybBYGy1drUJyS9puamIM9qe6xD83rZNNOrz7tZEChj84wmGUovqSYR5H01v33TGN/YdS3P7nkf39h1bU++9O3WCnrZNNOrz7tZ013ef2eRolFNIuj31XyzETZZj8DppFbQy6aZXn3ezWbVxlprE4mVJtPloNkEqFZ3pGtHKzvhZfGcGJRpiKtIv6RNplNNIgfN5kW0siMdtNcv0EmtoJW1bmIskNVGL5IdBYkcNCuw29mRLk194T16/jBnX15YdlyjDttmTTNpTVhTPzzD4987HVXgEJHOKEjkoNkIm7THazUKJEmF9/AKY3jIWFh8vXmxlQ7bRlflaTWiL37z+a5rPmUXYw0sSaz5jDVfZaTRTTloNsKm2x3pkgrvhdecN6xamel4+rRAVd/LVeTJar1QlLW6Ys1nrPkqK9UkctCsGafZjnRG5YuxZc+hxCuotML7pfkFjt59fWbvo5UaT7M8DYraK98VZizWDRiJca2uWNcUizVfZaUgkZNWti6t35GuPmCkNeX0a8JYUsd2fUDL6txFbl6ob/6rDxBVsQXSWGenx5qvslJzUwFUJ9qNjY601JTTrwljSUtCfHjzWzM/d9GbF5KufJPENus71jXFYs1XWakmUSCtXkH1c8JYUo1o/G0XZnruojcvtHKFG+Os71i3+4w1X2WlIFEgjZqRkppj6ie89avJJut5CkVvXkj7uw2Z8Zp7tM1nsc5OjzVfZaUZ1znppMBOm6n9G1eO8fCR2YZbWBZ5m8tWZn7H3GdR5M9eBodmXEek09VV066gWmmOKVKTTX2B/57LVycGwWrzwl0Tx6Kem6ErXykyBYkcdFNgJzXlfHz/0cRja5tjitJkkxRAHz4yy29cOZY4i3tienZJgKiKLQBqqRApKgWJHGRdYLcy5DXtmNHzhzs6Z6+kBdDHv3c6cVHBvZMziUNuoT8BMOZmLimXvP7XNAQ2B1kP4du5dQPDK2xJ2vAKWzLaY+fWDQwPWf1T+el/vBrVUNJ2A2ijQNDrIZFFH5orxZHn/5qCRA6azWPoaMvQ+vK/7v72TWO8YdXyiuPCax7VkhntBtC0dIOeD4lstilTr7Z+lcGT597sChI5aLQvcSdXDHsnZ5Ys3AewsLi88H9pfvkqsJB9s0w3hWO7EwGTjjfgw5vf2vOqeKPajWoZkqU8+xTVJ5GTtI7MTjq1W/0H6sdyHd3ui93uSKA8Rw41+jy7HU2mvg6plefe7KpJRCbLtvf6TuleLddRW3O488BTXVeLq8uQ7LtpI1AZvdWoRtKP/cGTNPo8u7nya6UWoqaswZLn3uwKEpHppFO71U7pRs1cnaov0LJavC6poPzY/qNs+uQ/RVMgNvo8uxmc0EpfR6+ashR84tSL726r1NwUmU7Wpdm+aYw/Pvg0c3V9DtVO6dp/pKzH6/dq8bq01z378kJ0E+WS8tHN+kLNaiG9mhjZbVOh9FZec21Uk4hMp1cM/eqU7uT1O6kWN3rdImxi1M2VX7NaSK86MfMcQSPxUk0iQp1cMeTVsdWrxeuabWgU20zxJJ1e+TWrhWTxt07qGC/KrHzpL9UkSiKvjq20rVbfOLKSfTdt7LgjudkWrmXeO6BZLaTbv3Van8abRpJn35f5s5bmmtYkzOx+4P3AKXd/Z0i7ENgPrAWeA37T3c+amQH3AO8FXgZ+292/HZ6zA7grvOyn3P2BkH4l8HlgBPgqcIe7e9o5un7HOevV0Ma8hoJu3zTG1A/P8MXDz1PbZ91t30H1OUl9LYOwd0CjWki3f+u0ZqXzhlcwMjykfRpkiaZLhZvZrwA/Bb5QEyT+HDjj7nvMbBdwgbt/wszeC/welSBxNXCPu18dCvwpYJzK7pZHgCtDYHkSuAP4JpUg8Zfu/rW0czR7QzEvFV7GJaOT3lOt2uW8O3XXxDEePPwCi+4MmXHL1Zfxqe3v6uo1B9m6XV9JXO/KgH03bdT8jAHV8VLh7v6/zWxtXfKNwDXh9gPAE8AnQvoXvBJ5vmlmo2Z2STj2MXc/EzLzGLDNzJ4A3uju/xzSvwBsB77W4ByFVYTlutut6TQb3dRte/bE9CwPH5k9N7R20Z2Hj8wy/rYL+/KZlXFSW6M+Da1WK/U67ZN4i7v/CCD8fnNIHwNeqDnuREhrlH4iIb3ROZYxs9vMbMrMpk6fPt3hW+q9vDsGm42B72T8fbO817dntzsOv9cjbhrlp6xLa6QtZTI7N6+5EbJM1h3Xy2d0VZqX2k1vi7vf6+7j7j6+evXqdp/eN73cwD2LANBJgdwo7/Xt2VkGoSwCa7P8lHVIaG3HOFS+hPUbNilQSFWnQeLF0IxE+H0qpJ8ALqs5bg1wskn6moT0RucorF4ui5FFAOikQE4bhTQ6MrysryXLIFTd17ub2cHN8pN3za+XqkuZjI2OpG7YJAKdB4mDwI5wewfwaE36R6xiM/BSaCqaBK43swvM7ALgemAyPPbvZrY5jIz6SN1rJZ2jsHo1tT6rANBJTSfpPX3mpo0cvfv6Ze8rqyA0MjzEey5f3XVTULP89LLmF4syB0LJRitDYB+k0oF8sZmdAO4G9gAHzOxW4HngQ+Hwr1IZ2XScyhDYjwK4+xkz+1PgW+G4T1Y7sYHf4fUhsF8LPzQ4R6H1omOw1QDQbAJWp0tJtPqeOpkE1s2+3t3mp5ulNYoiz9VFpRhaGd10S8pD1yUc68DtKa9zP3B/QvoU8M6E9H9LOocsl1UA6PVciyyDUCv7enebnzyXIe+XQQiE0h0ty1ECWQaAXg6BzLLQzeIKuJX8lH1IaL8CYRmHEg+KppPpiibmyXS9NGhfwiwmJg7aZ9ZPtZ/t6PnD/PQ/XmXhtdfLmqJPIi2jtMl0ChKyTKyFZ32+3nP5ah7/3umO8lnG2e+xaDYLvyqL2fiSnY5nXMtgiXVPgaR8PXxktuNCvQiz34uq1T1GNIIqG72+qNMqsLJEWuF554Gnct2tLOuJbRr62TutfoYaQdW9fqwKoCAhS6R9wRfdc12aIutCfRDmQOSllc9QI6iy0Y9VARQkZIlWvuB5zMjNulDPc2P5skv6bIeHjNGR4b7vz1x2/agRq09ClkgaTpuk380yWY/nH4Q5EHnRZ9s//ZgMqSAhS9R/wVeYnVumu1a/m2V6UfCUfQ5Et7rpENVn2x/9mAypIbDSkIaKFktWI130d08W4/DwrPKkeRLSsRi/GLJclgX7lj2HEpsxBnluQ9kDp+ZJSMfUdFAMWc790BDh5QZ1bo1GN4mURJYFu4YILzeogVNBQqQksizYNUR4uUENnAoSIiWRZcHeqw2yimxQA6f6JERKIuthwuqLWmpQ539odJOIiGh0k0jZaahyccX8t1OQECmBGJd4Tyv4Yi4Q8xDj366WOq5FSqAfq4G2I20J67smjvV8aeuiie1vV09BQqQEYhvDn1bwPXj4hagLxDzE9rerpyAhUgKxjeFvtC9JO8cPgtj+dvUUJERKILYx/GkF3JBZW8cPgtj+dvUUJEQKbGJ6li17DvHx/Uc5b3hFNBv7pBV8t1x9WdQFYh5in7io0U0iBVU/KubsywuMDA+x76aNuRcwjSaejb/tQo1uqhPzxEVNphMpKC3nLVlKm0yn5iaRgop9VIyUg4KESEHFPipGykFBQqSgYh8VI+WgjmuRghrUVUmlvxQkRAos5lExUg5qbhIRkVQKEiIikkpBQkREUilIiIhIKgUJERFJVbplOczsNPDDnE5/MfDjnM7dqSLmGYqZ7yLmGZTvfsozz29z99X1iaULEnkys6mktU9iVsQ8QzHzXcQ8g/LdTzHmWc1NIiKSSkFCRERSKUhk6968M9CBIuYZipnvIuYZlO9+ii7P6pMQEZFUqkmIiEgqBQkREUmlINEBM7vfzE6Z2Xdq0i40s8fM7Pvh9wV55jGJmV1mZo+b2TNm9rSZ3RHSo827mZ1nZk+a2VMhz38S0teZ2eGQ5/1mtirvvCYxsyEzmzazL4f70efbzJ4zs2NmdtTMpkJatP8jAGY2amZfMrPvhf/vXy5AnjeEz7j68xMz+1hs+VaQ6MzngW11abuAr7v7euDr4X5sXgXudPd3AJuB283sCuLO+yvAte7+bmAjsM3MNgOfBvaFPJ8Fbs0xj43cATxTc78o+X6Pu2+sGbMf8/8IwD3AP7r75cC7qXzmUefZ3WfCZ7wRuBJ4GfgHYsu3u+ungx9gLfCdmvszwCXh9iXATN55bOE9PAr8WlHyDpwPfBu4msqs1JUh/ZeBybzzl5DfNVS+5NcCXwasIPl+Dri4Li3a/xHgjcCzhIE4Rchzwnu4HvhGjPlWTSI7b3H3HwGE32/OOT8NmdlaYBNwmMjzHppsjgKngMeAfwHm3P3VcMgJIMaddz4D/CHwWrh/EcXItwP/ZGZHzOy2kBbz/8jbgdPA34Wmvc+Z2RuIO8/1bgYeDLejyreCxAAys58FHgY+5u4/yTs/zbj7oleq5GuAq4B3JB3W31w1ZmbvB065+5Ha5IRDo8p3sMXdfwm4gUqT5K/knaEmVgK/BHzW3TcB/4+8m2jaEPqlPgD8fd55SaIgkZ0XzewSgPD7VM75SWRmw1QCxBfd/ZGQXIi8u/sc8ASV/pRRM6tuv7sGOJlXvlJsAT5gZs8BD1FpcvoM8ecbdz8Zfp+i0kZ+FXH/j5wATrj74XD/S1SCRsx5rnUD8G13fzHcjyrfChLZOQjsCLd3UGnvj4qZGXAf8Iy7/0XNQ9Hm3cxWm9louD0C/CqVTsnHgQ+Gw6LKM4C773b3Ne6+lkpTwiF3/zCR59vM3mBmP1e9TaWt/DtE/D/i7v8KvGBmG0LSdcB3iTjPdW7h9aYmiCzfmnHdATN7ELiGyrK+LwJ3AxPAAeCtwPPAh9z9TF55TGJm/xX4P8AxXm8n/yMq/RJR5t3M/gvwADBE5aLmgLt/0szeTuUK/UJgGvhv7v5KfjlNZ2bXAH/g7u+PPd8hf/8Q7q4E/pe7/w8zu4hI/0cAzGwj8DlgFfAD4KOE/xcizTOAmZ0PvAC83d1fCmlRfdYKEiIikkrNTSIikkpBQkREUilIiIhIKgUJERFJpSAhIiKpFCRERCSVgoSIiKT6/58NiVk4DcJ1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter( x=sales_noCC[\"CrimeRate\"], y=sales_noCC[\"HousePrice\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Refit our simple regression model on this modified dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target_noCC = sales_noCC['HousePrice']\n",
    "features_noCC = sales_noCC['CrimeRate']\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(features_noCC,target_noCC, test_size = 0.20, random_state=2)\n",
    "\n",
    "crime_noCC_model = LinearRegression()\n",
    "crime_noCC_model.fit(x_train.values.reshape(-1,1),y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot is of new model which is trained and tested on data after removing the house with high price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales_noCC['CrimeRate'],sales_noCC['HousePrice'],'.',\n",
    "        sales_noCC['CrimeRate'],crime_noCC_model.predict(sales_noCC['CrimeRate'].values.reshape(-1,1)),'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Look at the fit on data after removing the house:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAD4CAYAAAAZ1BptAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAbfUlEQVR4nO3deZAc5XnH8e+zuxKHbYwQsi1rhYQKhTPh2DWsg+PiMgibMg4GB0xihUBwueQqCE5ssFMmxkfZf3DYsUys4rQLEIQjojAEMEhxDiTYBWwkQGYtWLQBIyEWcEKMtNonf8w7MIym5+ye7p75faqmduadnulnZ2ffp9+j+zV3R0REpJKetAMQEZHsUpIQEZFIShIiIhJJSUJERCIpSYiISKS+tAOI25577unz589POwwRkVwZGRl52d1nlZd3XJKYP38+w8PDaYchIpIrZjZWqVzdTSIiEklJQkREIilJiIhIJCUJERGJpCQhIiKRlCRERCSSkoRk0sjYBEtXjjIyNpF2KCJdrePOk5D8Gxmb4MyrVrN1corpfT3ccM4QA/NmpB2WSFdSS0IyZ/WGLWydnGLKYdvkFKs3bEk7JJGupSQhmTO0YCbT+3roNZjW18PQgplphyTStdTdJJkzMG8GN5wzxOoNWxhaMFNdTSIpUpKQTBqYN0PJQSQD1N0kIiKRlCRERCSSkoSIiERSkhARkUhKEiIiEklJQkREIilJiIhIJCUJERGJpCQhIiKRlCRERCSSkoSIiERSksixdi3MowWARLqXLvCXU+1amEcLAIl0N7UkcqpdC/NoASCR7qYkkVPtWphHCwCJdDdz97RjiNXg4KAPDw+nHUZbjIxNtGVhnnbtR0TSY2Yj7j5YXq4xiRxr18I8WgBIpHupu0lERCIpSYiISCQlCRERiaQkISIikZQkREQkkpKEiIhEUpIQEZFIShIiIhJJSUJERCLVnSTMrNfMHjOzu8Ljvc1sjZk9Y2Y3m9n0UL5TeDwanp9f8h4XhfL1ZnZCSfmiUDZqZheWlFfch4iItEcjLYnzgKdKHn8PuNzdFwITwNmh/Gxgwt33AS4P22FmBwCnAwcCi4AfhcTTCywFTgQOAM4I21bbh4iItEFdScLM+oFPAFeFxwYcA9waNrke+FS4f3J4THj+2LD9ycByd3/T3Z8FRoHDw23U3Te4+1ZgOXByjX2IiEgb1NuSuAL4MjAVHs8EXnX3yfB4HJgT7s8BNgKE518L279VXvaaqPJq+3gHMzvXzIbNbHjz5s11/koiIlJLzSRhZicBm9x9pLS4wqZe47m4yncsdF/m7oPuPjhr1qxKm4iISBPquVT4kcAnzezjwM7AbhRaFrubWV840u8HXgjbjwNzgXEz6wPeC7xSUl5U+ppK5S9X2YeIiLRBzZaEu1/k7v3uPp/CwPOD7n4msBI4NWy2GFgR7t8ZHhOef9ALKxvdCZweZj/tDSwEHgYeARaGmUzTwz7uDK+J2odUMTI2wdKVo4yMTaQdiojkXCuLDn0FWG5m3wIeA64O5VcDPzWzUQotiNMB3H2dmd0CPAlMAkvcfTuAmX0RuBfoBa5x93U19iERRsYmOPOq1WydnGJ6Xw83nDOkBYNEpGkNJQl3XwWsCvc3UJiZVL7N74HTIl7/beDbFcrvBu6uUF5xHxJt9YYtbJ2cYsph2+QUqzdsUZIQkabpjOsOM7RgJtP7eug1mNbXw9CCmWmHJCI5pjWuO8zAvBnccM4QqzdsYWjBTLUiRKQlShIdaGDeDCUHEYmFuptERCSSkoSIiERSkhARkUhKEiIiEklJQkREIilJiIhIJCUJERGJpCQhIiKRlCRaoKutikin0xnXTdLVVkWkG6gl0aRKV1sVEek0ShJN0tVWRaQbqLupSbraqoh0AyWJFuhqqyLS6dTdJCIikZQkREQkkpKEiIhEUpIQEZFIShIiIhJJSUJERCIpSYiISCQlCRERiaQkISIikZQkREQkkpKEiIhEUpIQEZFIShIiIhJJSUJERCIpSYiISCQlCRERiaQkISIikZQkREQkkpKEiIhEqpkkzGxnM3vYzH5pZuvM7BuhfG8zW2Nmz5jZzWY2PZTvFB6Phufnl7zXRaF8vZmdUFK+KJSNmtmFJeUV9yEiIu1RT0viTeAYdz8YOARYZGZDwPeAy919ITABnB22PxuYcPd9gMvDdpjZAcDpwIHAIuBHZtZrZr3AUuBE4ADgjLAtVfYhHW5kbIKlK0cZGZtIOxSRrlYzSXjB/4SH08LNgWOAW0P59cCnwv2Tw2PC88eamYXy5e7+prs/C4wCh4fbqLtvcPetwHLg5PCaqH1ITLJYGY+MTXDmVau59L71nHnV6kzFJtJt6hqTCEf8jwObgPuB3wCvuvtk2GQcmBPuzwE2AoTnXwNmlpaXvSaqfGaVfZTHd66ZDZvZ8ObNm+v5lYTsVsarN2xh6+QUUw7bJqdYvWFL2iGJdK26koS7b3f3Q4B+Ckf++1faLPy0iOfiKq8U3zJ3H3T3wVmzZlXaRCrIamU8tGAm0/t66DWY1tfD0IKZaYck0rX6GtnY3V81s1XAELC7mfWFI/1+4IWw2TgwFxg3sz7gvcArJeVFpa+pVP5ylX1IDIqV8bbJqUxVxgPzZnDDOUOs3rCFoQUzGZg3I+2QRLpWzSRhZrOAbSFB7AIcR2FAeSVwKoUxhMXAivCSO8Pjh8LzD7q7m9mdwI1mdhnwQWAh8DCFFsNCM9sb+G8Kg9ufDa+J2ofEIMuV8cC8GZmKR6Rb1dOSmA1cH2Yh9QC3uPtdZvYksNzMvgU8Blwdtr8a+KmZjVJoQZwO4O7rzOwW4ElgElji7tsBzOyLwL1AL3CNu68L7/WViH1ITFQZi0g15l6xmz+3BgcHfXh4OO0wRERyxcxG3H2wvFxnXHegLE5rFZF8amjgWrKvOK116+QU0/t6uOGcIXUniUjT1JLoMFmd1ioi+aQk0WF0joGIxEndTRk1Mjaxw9TUSmXlsjytVUTyR0kigyqNKwB1jzVoWquIxEVJIoOixhXKy5QIRCRpShIZFHW5jKQuoVFPN5aIdCcliQyKGldIYqxBU2ZFpBoliYyqNK6QxFhDpa4tJQkRKdIU2Aq66YxlTZkVkWrUkijTbd0vmjIrItUoSZTpxu4XTZkVkSjqbiqj7hcRkbepJVFG3S8iIm9TkqhA3S8iIgXqbpK6ddOsLxEpUEsi0FnH1XXbrC8RKVCSQBVgPbpx1peIqLsJ0EI99dCsL5HupJYE0RfUk7dp1pdIdzJ3TzuGWA0ODvrw8HDDr2tlTELjGSKSd2Y24u6D5eVqSQTNTnvVeIaIdDKNSbSodDxjq8YzRKTDKEm0aMau05kKPXZTXngsItIplCRaNPHGVizc7wmPRUQ6hZJEi4YWzGSnaYWpodOnaWaUiHQWDVy3SFNDRaSTKUnEQBcEFJFOpe4m2YEu5CeSTWn8b6olIe+g8z5Esimt/021JOQtI2MTXPHzX+s6ViIZlNY15tSSEODto5Q3t03hQI8u5CeSKWldY05JIkHtvqZTK/srHqU4heblkfvsyfnH/YG6mkQyIq2ZlEoSCWl3/2Gr+ys/SlGCEMmeNGZS1hyTMLO5ZrbSzJ4ys3Vmdl4o38PM7jezZ8LPGaHczOwHZjZqZr8ys8NK3mtx2P4ZM1tcUj5gZk+E1/zAzKzaPvKg3f2Hre6veJRywfH7arBaRN5Sz8D1JPAld98fGAKWmNkBwIXAA+6+EHggPAY4EVgYbucCV0KhwgcuBo4ADgcuLqn0rwzbFl+3KJRH7SPz6l2kJ64pbbX2V89+BubNYMnR+yhBiMhbGl5PwsxWAD8Mt6Pc/UUzmw2scvd9zezH4f5NYfv1wFHFm7t/PpT/GFgVbivdfb9QfkZxu+Jry/dRLb5m15NIQq0xgnq7iOoda4jarpOmtWrtDpFkxLKehJnNBw4F1gDvd/cXAUIl/r6w2RxgY8nLxkNZtfLxCuVU2Ud5XOdSaImw1157NfIrJaK0Ilty9D6R29WzbnR5Bf/1kw5k4o2tFSvJqP7KTlmfupOSnUhe1J0kzOzdwG3A+e7+ehg2qLhphTJvorxu7r4MWAaFlkQjr41bIxVZPVPayter+PqKtUy5N1RJdsryrJ2S7ETypK4kYWbTKCSIG9z99lD8kpnNLukK2hTKx4G5JS/vB14I5UeVla8K5f0Vtq+2j8xqpCKrZ0pbaQVvZmyfcpzGKsnS/czYdfpbg9p5q2A7JdlJutRl2ZiaSSLMNLoaeMrdLyt56k5gMfDd8HNFSfkXzWw5hUHq10Ilfy/wnZLB6uOBi9z9FTP7nZkNUejG+hzwjzX2kVmNVmS1prSVV/CX3LWuqUqyuI88d9foirvSKnVZNq6elsSRwF8AT5jZ46HsqxQq7lvM7GzgeeC08NzdwMeBUeAN4CyAkAy+CTwStrvE3V8J978AXAfsAtwTblTZR2YlUZGVJpJ9P/Celk+YS6K7pl1HZ7rirrRCXZaNq5kk3P0/qDxuAHBshe0dWBLxXtcA11QoHwYOqlC+pdI+si7JiqyV906qu0ZHZ5IX6rJsnM647iJJddfo6EzyQl2WjVOS6DJJtHJ0dCZ5oi7LxihJSMt0dJY+zdiRpChJZEie/9F1dJYejQlJkpQkMkL/6NIsjQlJkrQyXZm01ndOa9WptKX1eXfSOt71XkxSpBlqSZRI82i+Gwd/k/q847qwYl5oTEiSpCRRtPFhBq79GE/3Ar2h7NoK2/VOh70/WrjN/wjMPgR6eits2Jhu/EdPopukngTQid0zGhOSpChJFG1cU99227fC6M8Lt5gNhBv/Fgr+eiXMOSz6BW2S1IB6Eq2nehJAN7baRJrV8HoSWdfqehIjz23h12uH+ejUw8yZeBie/UWM0WXIBw+Fc1fV3Czprpm4E1Ax3mICaHWNDpFuEbWehJJEuz1xK9x2dtpRJO+Cp2C3D6ayayUAkcYpSWRQPQOsDVV2a2+DW/8qgUgz5k+XwcF/lnYUIh1FSSJjanXjNLIiXb2Wrhzl0vvWM+XQa3DB8ftWXTmvNJZfPb2esx46oan95speH4az7oHoRbVEOlIsy5dKfGoNsL5jRbptza1IV67ZAdvCzJkhOOG1is/H0r2z9AjY/HRzr43T8w/BN3ZP7v1T7IYTaYaSREpqVdjlK9JNuTc8ZbO88k5imm1Ui6jhxLGkztllzdj4CFx9XHLv34jL9k/uvU+/Efb7RHLvL11JSSIltSrsVleki6q8455PH3WmeKZOVpv7IfiHyq2glm37PfxwEF7bmMz7N2L5ZxN765G5Z8ExX2Ng71mJ7aNRmqDQHkoSKapn6dJmV6Rr1wljlVpEnXiyWqRpO8PfrG34ZXVPLc7IbLiBjdfC9ZXOLo3BgafACd+B3WbX/ZJOO2s+y5QkcqKYMIrXHKqVLNp1wlhUi0gnq+2o9Mi37kT6h6cWbkn43Uvwswvg6buSef96rbu9cGvAANS+OgLA3CE47mKY98ctBNjdNLspRxo9ekqzOZ7EvvPcvVBptlppF2JWj4TrPTlxB1NTMHIN/OxLyQeZBuuFgz5duO1zLPROSzuilml2UwdotBsnzev5xL3vvHcvlP/tJt7YmotrdTU92aGnBz50TuGWhN+u5fUVf8duL/5XMu9fi2+HJ24p3OI2a7+S68P9CeyS4Gy7OihJ5Eg3X3Mo7+Mclf52ebkoXybj/MBB7Pb5e5J5723/B+vugDX/BC/+Mpl9VLP56cLt4WWNvW6/k+AzP4nlgqOllCRypNZRXT3dMXntssl7guzGq/zm1rRd4JDPFm5JeOnJwtUR1t4GE8/G975P31W4AGnPLvG9JxqTSFWcFXY93TF577KJ/TImIvIWjUlkTNwVdj3dMXnqsqlU4Vfr9rhxzfN8fcVatk85O03LXwIUySotX5qSuJcrrWcJy7wsc1lMoJfet54zr1pdc4nRkbEJvr5iLZNTjlO4jEm3LP8qkjS1JFISdx97PX3exW1uf3ScLHcyNtriWb1hC1Ml3aY9PdbWBKhuLmmXNL5rShIpSXMg87ZHx9k6OcXtj45nslum0QRa3H7r5BQ9Zlxy8kFt+53yPs4j+ZHWd01JIkXV+tgbPWKo9wuUh3GJRhNomgm31uepVobEJa3/XSWJDGrmiKHeL1C7ppK2Wjk2Ojc/rbn81T5PtTIkTmlNA1eSyKBmjhjq/QK146i7myrHap9nq0d+aoVIqbRazEoSGdTMEUMjg9JJHHU3dfG6Bt83qxVl1OfZypFfvee9ZP2zkXil0WJWksigVo4Y0hiUrnTxujiaxaXv29djnDY4l1MO689NhdjK37GesY6kWmtKPlJKSSKjmjliSGtgK6mL171jCdftzo1rnue2jM7IitLskV+tVkhSf+tu6iqU+ihJdJC0BraSunhd8X3f3DaFA052Z2TFrVYrJKm/dR5mv0l76dpNHSatroKk9jsyNsFtj45z68g427dne+2Fdmv1M6/0+qbXj5Dci7p2U80kYWbXACcBm9z9oFC2B3AzMB94DviMu0+YmQHfBz4OvAH8pbs/Gl6zGPj78LbfcvfrQ/kAcB2wC3A3cJ67e9Q+av2i3Z4k0pZkslA/eXyqdSvps+5OUUminms3XQcsKiu7EHjA3RcCD4THACcCC8PtXODKsPM9gIuBI4DDgYvNrPjtuzJsW3zdohr7yL3iEqS1rkmUJyNjE3ztjic4Y9lDdV9zqRED82aw5Oh9VGnFpNq1w/RZS6maYxLu/gszm19WfDJwVLh/PbAK+Eoo/4kXmierzWx3M5sdtr3f3V8BMLP7gUVmtgrYzd0fCuU/AT4F3FNlH7nWiQODxd+pOHYA8fdn6+g2Xnlfn0Pap9mB6/e7+4sA7v6imb0vlM8BNpZsNx7KqpWPVyivto8dmNm5FFoj7LXXXk3+Su2Rh4HBRivk4u9UTBBGvFeZTTuxdmKC0iJIUq+4ZzdZhTJvorwh7r4MWAaFMYlGX99OaR/B1bNwT6MVcunv1Nvbw6kD/Xy6yvkMzSahpBJrtXjSTlBJKp2B1omJUOLRbJJ4ycxmhyP82cCmUD4OzC3Zrh94IZQfVVa+KpT3V9i+2j5yLckjuDgSQDMVciO/U6tJKO7EWiuePLT8WtXJiVBa1+yiQ3cCi8P9xcCKkvLPWcEQ8FroMroXON7MZoQB6+OBe8NzvzOzoTAz6nNl71VpH7mXxMBgPQv11LPQUbMLE9X7OzWz2FIxCV1w/L47VGCtTgKoFU9eFmpqRdwLYElnqdmSMLObKLQC9jSzcQqzlL4L3GJmZwPPA6eFze+mMP11lMIU2LMA3P0VM/sm8EjY7pLiIDbwBd6eAntPuFFlH1JBPUe89RyRJ91X3WyroNLJeXEcAdeKpxv67tPuApVs08l0HaLek6Cy0PccVwxLV45y6X3rmXLoNbjg+H1ZcvQ+qcWTZ/oMpOmT6fKmW5MEdN8/us4OFomPkoR0pG5LjHmmv1W2RSUJXeBPcq3VCwmq4kpO6WcLaAZVTilJSEVZrTzjjEtTP5NT/tmeclh/x08l7lRKErKDrFaeccfVDedApKX8szXQDKoEJXlQpyQhO4iaN592yyLuSl1TP5NT/tmeclg/pxzWn/p3qBMlfVCnJCE7KP8Hn7Hr9Ey0LOKu1LvhHIi0RH22+ozjl3SLWElCdlD+D56VbpkkKvU0FpbvFvps2yPpFrGShFRU/g+elW4ZVTwi75R0i1jnSUhdsjrbSZKlv3v30HkS0hIdwedHXBV7Vme5pa3bEqeShEgHibNiz8pYVJZ0Y+Js9lLhIpJBcV72uxsuk96obrysuloSIh0kzpkumiK8o248t0YD1yIdptv6zNutUz9fDVyLdAlNMkhWt32+GpMQEZFIShIiIhJJSUKkg4yMTbB05SgjYxNphyINyurfTmMSIh0ii3P4owZ5O3Xwt1lZ/NsVKUmIdIisnfwWVfFluUJMS9b+dqXU3STSIbJ28lu1dUm67YS0WrL2tyulloRIh8jayW9RJ5514wlptWTtb1dKJ9OJSGI0JpEfOplOpENlucKNOvGs205IyzMlCZEc0yCwJE0D1yI5pkFgSZqShEiOZXlWjHQGdTeJ5FiWZ8VIZ1CSEMk5DQJLktTdJCIikZQkREQkkpKEiIhEUpIQEZFIShIiIhJJSUJERCJ13AX+zGwzMJbS7vcEXk5p383KY8yQz7jzGDMo7nZKM+Z57j6rvLDjkkSazGy40lUUsyyPMUM+485jzKC42ymLMau7SUREIilJiIhIJCWJeC1LO4Am5DFmyGfceYwZFHc7ZS5mjUmIiEgktSRERCSSkoSIiERSkmiCmV1jZpvMbG1J2R5mdr+ZPRN+Zu7azWY218xWmtlTZrbOzM4L5ZmN3cx2NrOHzeyXIeZvhPK9zWxNiPlmM5uedqyVmFmvmT1mZneFx5mP28yeM7MnzOxxMxsOZZn9jgCY2e5mdquZPR2+3x/OQcz7hs+4eHvdzM7PWtxKEs25DlhUVnYh8IC7LwQeCI+zZhL4krvvDwwBS8zsALId+5vAMe5+MHAIsMjMhoDvAZeHmCeAs1OMsZrzgKdKHucl7qPd/ZCSOftZ/o4AfB/4V3ffDziYwmee6ZjdfX34jA8BBoA3gDvIWtzurlsTN2A+sLbk8Xpgdrg/G1ifdox1/A4rgI/lJXZgV+BR4AgKZ6X2hfIPA/emHV+FePsp/JMfA9wFWE7ifg7Ys6wss98RYDfgWcJEnDzEXOF3OB74zyzGrZZEfN7v7i8ChJ/vSzmeqsxsPnAosIaMxx66bB4HNgH3A78BXnX3ybDJODAnrfiquAL4MjAVHs8kH3E7cJ+ZjZjZuaEsy9+RBcBm4NrQtXeVmb2LbMdc7nTgpnA/U3ErSXQhM3s3cBtwvru/nnY8tbj7di80yfuBw4H9K23W3qiqM7OTgE3uPlJaXGHTTMUdHOnuhwEnUuiS/GjaAdXQBxwGXOnuhwL/S9pdNA0I41KfBP457VgqUZKIz0tmNhsg/NyUcjwVmdk0CgniBne/PRTnInZ3fxVYRWE8ZXczK67R3g+8kFZcEY4EPmlmzwHLKXQ5XUH248bdXwg/N1HoIz+cbH9HxoFxd18THt9KIWlkOeZSJwKPuvtL4XGm4laSiM+dwOJwfzGF/v5MMTMDrgaecvfLSp7KbOxmNsvMdg/3dwGOozAouRI4NWyWqZgB3P0id+939/kUuhIedPczyXjcZvYuM3tP8T6FvvK1ZPg74u6/BTaa2b6h6FjgSTIcc5kzeLurCTIWt864boKZ3QQcReGyvi8BFwP/AtwC7AU8D5zm7q+kFWMlZvYR4N+BJ3i7n/yrFMYlMhm7mf0RcD3QS+Gg5hZ3v8TMFlA4Qt8DeAz4c3d/M71Io5nZUcDfuvtJWY87xHdHeNgH3Oju3zazmWT0OwJgZocAVwHTgQ3AWYTvCxmNGcDMdgU2Agvc/bVQlqnPWklCREQiqbtJREQiKUmIiEgkJQkREYmkJCEiIpGUJEREJJKShIiIRFKSEBGRSP8PJw+UnDhcP0YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sales_noCC['CrimeRate'],sales_noCC['HousePrice'],'.',\n",
    "        sales_noCC['CrimeRate'],crime_model.predict(sales_noCC['CrimeRate'].values.reshape(-1,1)),'-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare coefficients for full-data fit versus no-Center-City fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visually, the fit seems different, but let's quantify this by examining the estimated coefficients of our original fit and that of the modified dataset with Center City removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-441.71052831]\n"
     ]
    }
   ],
   "source": [
    "print(crime_model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2002.58015335]\n"
     ]
    }
   ],
   "source": [
    "print(crime_noCC_model.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: We see that for the \"no Center City\" version, per unit increase in crime, the predicted decrease in house prices is 2002.  In contrast, for the original dataset, the drop is only 441 per unit increase in crime.  This is significantly different!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### High leverage points: \n",
    "Center City is said to be a \"high leverage\" point because it is at an extreme x value where there are not other observations.  As a result, recalling the closed-form solution for simple regression, this point has the *potential* to dramatically change the least squares line since the center of x mass is heavily influenced by this one point and the least squares line will try to fit close to that outlying (in x) point.  If a high leverage point follows the trend of the other data, this might not have much effect.  On the other hand, if this point somehow differs, it can be strongly influential in the resulting fit.\n",
    "\n",
    "### Influential observations:  \n",
    "An influential observation is one where the removal of the point significantly changes the fit.  As discussed above, high leverage points are good candidates for being influential observations, but need not be.  Other observations that are *not* leverage points can also be influential observations (e.g., strongly outlying in y even if x is a typical value)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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