04.02-Mean-Median-Imputation.ipynb

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   "source": [
    "## Mean / Median imputation\n",
    "\n",
    "Imputation is the act of replacing missing data with statistical estimates of the missing values. The goal of any imputation technique is to produce a **complete dataset** that can be used to train machine learning models.\n",
    "\n",
    "Mean / median imputation consists of replacing all occurrences of missing values (NA) within a variable by the mean (if the variable has a Gaussian distribution) or median (if the variable has a skewed distribution).\n",
    "\n",
    "**Note the following**:\n",
    "\n",
    "- If a variable is normally distributed, the mean, median and mode, are approximately the same. Therefore, replacing missing values by the mean and the median are equivalent. Replacing missing data by the mode is not common practice for  numerical variables.\n",
    "- If the variable is skewed, the mean is biased by the values at the far end of the distribution. Therefore, the median is a better representation of the majority of the values in the variable.\n",
    "- For discrete variables casted as 'int' (to save memory), the mean may not be an integer, therefore the whole variable will be re-casted as 'float'. In order to avoid this behaviour, we can replace NA with the median instead. The median will inevitably be an integer / discrete value as well.\n",
    "\n",
    "\n",
    "### Which variables can I impute with Mean / Median Imputation?\n",
    "\n",
    "The mean and median can only be calculated on numerical variables, therefore these methods are suitable for continuous and discrete numerical variables only.\n",
    "\n",
    "\n",
    "### Assumptions\n",
    "\n",
    "- Data is missing completely at random (MCAR)\n",
    "- The missing observations, most likely look like the majority of the observations in the variable (aka, the mean / median)\n",
    "\n",
    "If data is missing completely at random, then it is fair to assume that the missing values, are most likely very close to the value of the mean or the median of the distribution, as these represent the most frequent / average observation.\n",
    "\n",
    "\n",
    "### Advantages\n",
    "\n",
    "- Easy to implement\n",
    "- Fast way of obtaining complete datasets\n",
    "- Can be integrated in production (during model deployment)\n",
    "\n",
    "### Limitations\n",
    "\n",
    "- Distortion of the original variable distribution\n",
    "- Distortion of the original variance\n",
    "- Distortion of the covariance with the remaining variables of the dataset\n",
    "\n",
    "When replacing NA with the mean or median, the variance of the variable will be distorted if the number of NA is big respect to the total number of observations, leading to underestimation of the variance.\n",
    "\n",
    "In addition, estimates of covariance and correlations with other variables in the dataset may also be affected. Mean / median imputation may alter intrinsic correlations since the mean / median value that now replaces the missing data will not necessarily preserve the relation with the remaining variables.\n",
    "\n",
    "Finally, concentrating all missing values at the mean / median value, may lead to observations that are common occurrences in the distribution, to be picked up as outliers.\n",
    "\n",
    "\n",
    "### When to use mean / median imputation?\n",
    "\n",
    "- Data is missing completely at random\n",
    "- No more than 5% of the variable contains missing data\n",
    "\n",
    "Although in theory, the above conditions should be met to minimise the impact of this imputation technique, in practice, mean / median imputation is very commonly used, even in those cases when data is not MCAR and there are a lot of missing values. The reason behind this, is the simplicity of the technique.\n",
    "\n",
    "\n",
    "### Final note\n",
    "\n",
    "Replacement of NA with mean / median is widely used in the data science community and in various data science competitions. See for example the winning solution of the KDD 2009 cup: [\"Winning the KDD Cup Orange Challenge with Ensemble Selection\"]( http://www.mtome.com/Publications/CiML/CiML-v3-book.pdf).\n",
    "\n",
    "Typically, mean / median imputation is done together with adding a binary \"missing indicator\" variable to capture those observations where the data was missing (see lecture \"Missing Indicator\"), thus covering 2 angles: if the data was missing completely at random, this would be captured by the mean /median imputation, and if it wasn't this would be captured by the additional \"missing indicator\" variable. Both methods are extremely straight forward to implement, and therefore are a top choice in data science competitions.\n",
    "\n",
    "## In this demo:\n",
    "\n",
    "We will learn how to perform mean and median imputation using pandas on the Ames House Price and Titanic Datasets.\n",
    "\n",
    "- To download the datasets please refer to the lecture **Datasets** in **Section 1** of this course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# to split the datasets\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Titanic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>survived</th>\n",
       "      <th>age</th>\n",
       "      <th>fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>29.0000</td>\n",
       "      <td>211.3375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.9167</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2.0000</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>30.0000</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>25.0000</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   survived      age      fare\n",
       "0         1  29.0000  211.3375\n",
       "1         1   0.9167  151.5500\n",
       "2         0   2.0000  151.5500\n",
       "3         0  30.0000  151.5500\n",
       "4         0  25.0000  151.5500"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the Titanic Dataset with a few variables for demonstration\n",
    "\n",
    "data = pd.read_csv('../titanic.csv', usecols=['age', 'fare', 'survived'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "survived    0.000000\n",
       "age         0.200917\n",
       "fare        0.000764\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's look at the percentage of NA\n",
    "\n",
    "data.isnull().mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The only variable with missing data is Age, with ~20% of missing observations.\n",
    "\n",
    "### Imputation important\n",
    "\n",
    "Imputation should be done over the training set, and then propagated to the test set. This means that the mean / median to be used to fill missing values both in train and test set, should be extracted from the train set only. And this is to avoid overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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     "execution_count": 4,
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   "source": [
    "# let's separate into training and testing set\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    data[['age', 'fare']],  # predictors\n",
    "    data['survived'],  # target\n",
    "    test_size=0.3,  # percentage of obs in test set\n",
    "    random_state=0)  # seed to ensure reproducibility\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age     0.191048\n",
       "fare    0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's explore the missing data in the train set\n",
    "# the percentages should be fairly similar to those\n",
    "# of the whole dataset\n",
    "\n",
    "X_train.isnull().mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's make a function to fill missing values with the mean or median:\n",
    "# the variable takes the dataframe, the variable, and the value of the\n",
    "# mean or median\n",
    "# and returns the variable with the filled na\n",
    "\n",
    "\n",
    "def impute_na(df, variable, mean_median):\n",
    "\n",
    "    return df[variable].fillna(mean_median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate the median Age\n",
    "\n",
    "median = X_train.age.median()\n",
    "median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.23144399460189"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate the mean Age\n",
    "\n",
    "mean = X_train.age.mean()\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>fare</th>\n",
       "      <th>Age_median</th>\n",
       "      <th>Age_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "    <tr>\n",
       "      <th>501</th>\n",
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       "      <td>22.0</td>\n",
       "      <td>22.0</td>\n",
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       "      <th>971</th>\n",
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       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>30.0</td>\n",
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       "      <td>30.0</td>\n",
       "      <td>30.0</td>\n",
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       "      <th>540</th>\n",
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       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
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       "      <th>294</th>\n",
       "      <td>49.0</td>\n",
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       "      <td>49.0</td>\n",
       "      <td>49.0</td>\n",
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       "    <tr>\n",
       "      <th>261</th>\n",
       "      <td>35.0</td>\n",
       "      <td>26.2875</td>\n",
       "      <td>35.0</td>\n",
       "      <td>35.0</td>\n",
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       "      <td>42.0</td>\n",
       "      <td>42.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>151.5500</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
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       "      <td>18.0</td>\n",
       "      <td>18.0</td>\n",
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       "      <th>1284</th>\n",
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      "text/plain": [
       "       age      fare  Age_median  Age_mean\n",
       "501   13.0   19.5000        13.0      13.0\n",
       "588    4.0   23.0000         4.0       4.0\n",
       "402   30.0   13.8583        30.0      30.0\n",
       "1193   NaN    7.7250        28.0      30.2\n",
       "686   22.0    7.7250        22.0      22.0\n",
       "971    NaN    7.8792        28.0      30.2\n",
       "117   30.0   56.9292        30.0      30.0\n",
       "540    2.0   26.0000         2.0       2.0\n",
       "294   49.0  110.8833        49.0      49.0\n",
       "261   35.0   26.2875        35.0      35.0\n",
       "587    2.0   23.0000         2.0       2.0\n",
       "489   42.0   26.0000        42.0      42.0\n",
       "2      2.0  151.5500         2.0       2.0\n",
       "405   18.0   13.0000        18.0      18.0\n",
       "1284   NaN    8.0500        28.0      30.2"
      ]
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     "execution_count": 9,
     "metadata": {},
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   "source": [
    "# create a new variable with the missing values replaced\n",
    "# using the function we created above\n",
    "\n",
    "# first replace with the median\n",
    "X_train['Age_median'] = impute_na(X_train, 'age', median)\n",
    "\n",
    "# now replace with the mean\n",
    "X_train['Age_mean'] = impute_na(X_train, 'age', mean)\n",
    "\n",
    "# the mean contains many decimals, so I round to 1\n",
    "# using the round function from numpy\n",
    "X_train['Age_mean'] = np.round(X_train['Age_mean'], 1)\n",
    "\n",
    "X_train.head(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the rows with missing data (NaN) in Age, and see how in the new variables those were replaced by either 28 (median) or 30 (mean)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original variable variance:  194.16304666581854\n",
      "Variance after median imputation:  157.7984295760209\n",
      "Variance after mean imputation:  157.02170735199397\n"
     ]
    }
   ],
   "source": [
    "# we can see a change in the variance after mean / median imputation\n",
    "# this is expected, because the percentage of missing data is quite\n",
    "# high in Age, ~20%\n",
    "\n",
    "print('Original variable variance: ', X_train['age'].var())\n",
    "print('Variance after median imputation: ', X_train['Age_median'].var())\n",
    "print('Variance after mean imputation: ', X_train['Age_mean'].var())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the variance is underestimated, because now many values are the same ==> either the mean or the median value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<matplotlib.legend.Legend at 0x1177d91ef0>"
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     "execution_count": 11,
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we can see that the distribution has changed \n",
    "# with now more values accumulating towards the median\n",
    "# or median\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "# original variable distribution\n",
    "X_train['age'].plot(kind='kde', ax=ax)\n",
    "\n",
    "# variable imputed with the median\n",
    "X_train['Age_median'].plot(kind='kde', ax=ax, color='red')\n",
    "\n",
    "# variable imputed with the mean\n",
    "X_train['Age_mean'].plot(kind='kde', ax=ax, color='green')\n",
    "\n",
    "# add legends\n",
    "lines, labels = ax.get_legend_handles_labels()\n",
    "ax.legend(lines, labels, loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As mentioned above, the mean / median imputation distorts the original distribution of the variable Age. The transformed variable shows more values around the mean / median values.\n",
    "\n",
    "**Is this important?**\n",
    "\n",
    "It depends on the machine learning model you want to build. Linear models assume that the variables are normally distributed. Mean / median imputation may distort the original normal distribution if the % of missing data is high. Therefore the final imputed variable will no longer be normally distributed, which in turn may affect the linear model performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>fare</th>\n",
       "      <th>age</th>\n",
       "      <th>Age_median</th>\n",
       "      <th>Age_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fare</th>\n",
       "      <td>2248.326729</td>\n",
       "      <td>136.176223</td>\n",
       "      <td>114.961682</td>\n",
       "      <td>110.198311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>136.176223</td>\n",
       "      <td>194.163047</td>\n",
       "      <td>194.163047</td>\n",
       "      <td>194.159033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age_median</th>\n",
       "      <td>114.961682</td>\n",
       "      <td>194.163047</td>\n",
       "      <td>157.798430</td>\n",
       "      <td>157.035694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age_mean</th>\n",
       "      <td>110.198311</td>\n",
       "      <td>194.159033</td>\n",
       "      <td>157.035694</td>\n",
       "      <td>157.021707</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   fare         age  Age_median    Age_mean\n",
       "fare        2248.326729  136.176223  114.961682  110.198311\n",
       "age          136.176223  194.163047  194.163047  194.159033\n",
       "Age_median   114.961682  194.163047  157.798430  157.035694\n",
       "Age_mean     110.198311  194.159033  157.035694  157.021707"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we also said that mean / median imputation may affect the relationship \n",
    "# with the other variables in the dataset, let's have a look\n",
    "\n",
    "X_train[['fare', 'age', 'Age_median', 'Age_mean']].cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see indeed that the covariance between Age and Fare is changed after the mean / median imputation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1177de08d0>"
      ]
     },
     "execution_count": 13,
     "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": [
    "# Finally, I mentioned that mean / median imputation may lead \n",
    "# to observations that are normal, to look like outliers\n",
    "\n",
    "# or in other words, mean / median imputation may lead to an increase\n",
    "# in the apparent number of  outliers\n",
    "\n",
    "# Let's find out using a boxplot\n",
    "X_train[['age', 'Age_median', 'Age_mean']].boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the boxplot above, we can see that after the imputation not only we have more outliers on the higher Age values, but we have now outliers as well for the lower values of Age.\n",
    "\n",
    "**Is this important?**\n",
    "\n",
    "If we are after true outliers, we need to keep this behaviour in mind, to make sure that we are neither masking nor creating artificial outliers with our imputation technique. In practice, we normally don't check for this behaviour at all. But I think it is important to know that is happening.\n",
    "\n",
    "## House Prices Dataset\n",
    "\n",
    "Let's repeat the exercise in the House Prices dataset from. In this dataset, there are variables with a lot or with few missing data. Therefore we can compare the effect of mean / median imputation in both scenarios."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we are going to use only the following variables,\n",
    "# 3 of which contain NA\n",
    "\n",
    "cols_to_use = [\n",
    "    'OverallQual', 'TotalBsmtSF', '1stFlrSF', 'GrLivArea', 'WoodDeckSF',\n",
    "    'BsmtUnfSF', 'LotFrontage', 'MasVnrArea', 'GarageYrBlt', 'SalePrice'\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1460, 10)\n"
     ]
    },
    {
     "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>LotFrontage</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <th>1stFlrSF</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>65.0</td>\n",
       "      <td>7</td>\n",
       "      <td>196.0</td>\n",
       "      <td>150</td>\n",
       "      <td>856</td>\n",
       "      <td>856</td>\n",
       "      <td>1710</td>\n",
       "      <td>2003.0</td>\n",
       "      <td>0</td>\n",
       "      <td>208500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>80.0</td>\n",
       "      <td>6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>284</td>\n",
       "      <td>1262</td>\n",
       "      <td>1262</td>\n",
       "      <td>1262</td>\n",
       "      <td>1976.0</td>\n",
       "      <td>298</td>\n",
       "      <td>181500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>68.0</td>\n",
       "      <td>7</td>\n",
       "      <td>162.0</td>\n",
       "      <td>434</td>\n",
       "      <td>920</td>\n",
       "      <td>920</td>\n",
       "      <td>1786</td>\n",
       "      <td>2001.0</td>\n",
       "      <td>0</td>\n",
       "      <td>223500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.0</td>\n",
       "      <td>7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>540</td>\n",
       "      <td>756</td>\n",
       "      <td>961</td>\n",
       "      <td>1717</td>\n",
       "      <td>1998.0</td>\n",
       "      <td>0</td>\n",
       "      <td>140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>84.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>490</td>\n",
       "      <td>1145</td>\n",
       "      <td>1145</td>\n",
       "      <td>2198</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>192</td>\n",
       "      <td>250000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   LotFrontage  OverallQual  MasVnrArea  BsmtUnfSF  TotalBsmtSF  1stFlrSF  \\\n",
       "0         65.0            7       196.0        150          856       856   \n",
       "1         80.0            6         0.0        284         1262      1262   \n",
       "2         68.0            7       162.0        434          920       920   \n",
       "3         60.0            7         0.0        540          756       961   \n",
       "4         84.0            8       350.0        490         1145      1145   \n",
       "\n",
       "   GrLivArea  GarageYrBlt  WoodDeckSF  SalePrice  \n",
       "0       1710       2003.0           0     208500  \n",
       "1       1262       1976.0         298     181500  \n",
       "2       1786       2001.0           0     223500  \n",
       "3       1717       1998.0           0     140000  \n",
       "4       2198       2000.0         192     250000  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's load the House Prices dataset\n",
    "\n",
    "data = pd.read_csv('../houseprice.csv', usecols=cols_to_use)\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['LotFrontage', 'MasVnrArea', 'GarageYrBlt']"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the variables that contain missing data\n",
    "\n",
    "# in the next list comprehension, I loop over all the columns\n",
    "# of the dataset and select those that contain missing data\n",
    "\n",
    "[var for var in data.columns if data[var].isnull().sum() > 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LotFrontage    0.177397\n",
       "MasVnrArea     0.005479\n",
       "GarageYrBlt    0.055479\n",
       "dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find the percentage of missing data within those variables\n",
    "# same code as we learnt in section 3 on variable characteristics\n",
    "\n",
    "data[['LotFrontage', 'MasVnrArea', 'GarageYrBlt']].isnull().mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Remember that the mean and the median that we will use to replace the NA needs to be calculated in the train set and propagated to the test set.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1022, 10), (438, 10))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's separate into training and testing set\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(data,\n",
    "                                                    data['SalePrice'],\n",
    "                                                    test_size=0.3,\n",
    "                                                    random_state=0)\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's plot the distributions of the variables\n",
    "# we learnt this code in section 3 on variable characteristics\n",
    "\n",
    "X_train.hist(bins=50, figsize=(10,10))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sole\\Anaconda3\\lib\\site-packages\\pandas\\core\\indexing.py:362: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  self.obj[key] = _infer_fill_value(value)\n",
      "C:\\Users\\Sole\\Anaconda3\\lib\\site-packages\\pandas\\core\\indexing.py:543: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  self.obj[item] = s\n"
     ]
    }
   ],
   "source": [
    "# create a new variable with the missing values replaced\n",
    "# by the median using the function we created above\n",
    "\n",
    "# I repeat the following lines for each of the variables with NA\n",
    "# over the next cells\n",
    "\n",
    "median = X_train['LotFrontage'].median()\n",
    "\n",
    "X_train.loc[:,'LotFrontage_median'] = impute_na(X_train, 'LotFrontage', median)\n",
    "X_test.loc[:,'LotFrontage_median'] = impute_na(X_test, 'LotFrontage', median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "median = X_train['MasVnrArea'].median()\n",
    "\n",
    "X_train.loc[:,'MasVnrArea_median'] = impute_na(X_train, 'MasVnrArea', median)\n",
    "X_test.loc[:,'MasVnrArea_median'] = impute_na(X_test, 'MasVnrArea', median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "median = X_train['GarageYrBlt'].median()\n",
    "\n",
    "X_train.loc[:, 'GarageYrBlt_median'] = impute_na(X_train, 'GarageYrBlt', median)\n",
    "X_test.loc[:,'GarageYrBlt_median'] = impute_na(X_test, 'GarageYrBlt', median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1178830588>"
      ]
     },
     "execution_count": 23,
     "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": [
    "# let's evaluate the effect of median imputation on the distribution\n",
    "\n",
    "# we can see that the distribution has changed for LotFrontAge\n",
    "# with now more values accumulating towards the median\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "# original variable distribution\n",
    "X_train['LotFrontage'].plot(kind='kde', ax=ax)\n",
    "\n",
    "# variable imputed with the median\n",
    "X_train['LotFrontage_median'].plot(kind='kde', ax=ax, color='red')\n",
    "\n",
    "# add legends\n",
    "lines, labels = ax.get_legend_handles_labels()\n",
    "ax.legend(lines, labels, loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11788464e0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0w5k2OFhVuUd7uqyccNxCxZhSY6FihkU7nVAJVe8ZKlpWRig+8Gx4xpjRx0LFDE9nJ0nx4A32mou+vBx/OkU6uvfER8aY0ctCxQyLRDqJ+kPQ+0647m1bIs12/y9jSomFihkWTyRCLBDcu929bUvUQsWYkmKhYobFCZW9b5vtcS+GjFmoGFNSLFTMsHiiEeJ9hIq3K1RsThVjSoqFihkWXzRCIrh3qPjcU4zjLXarFmNKiYWKGRZ/LNpnqPjdUEm22k0ljSklFipmWHyxCKlQeK/2gBsqCQsVY0qKhYoZlkAsSjK4d6gE3Ysh0222+8uYUmKhYoYlEI+SCu8dKqGaKgBSNlGXMSXFQsUMSzARI93H7q/gmGoA1ELFmJJioWKGJRSPomVle7WXVTunFKt7a3xjTGmwUDFDlk6lCSViaB+7v/x+H53+INjsj8aUlLyGiogsEJFNIrJFRK7u4/WgiCx3X18pIvU9XrvGbd8kIvN7recVkddE5OF81m8GFovE8Gka6WOkAhD1h/C4dzE2xpSGvIWKiHiBW4HTgWnAYhGZ1qvbxcBuVT0Y+Alwo7vuNGARMB1YAPzC3V6XK4CN+ardZCba4pwuLOV9h0okGLZQMabE5HOkMhvYoqpbVTUOLAMW9uqzELjHXb4fOFlExG1fpqoxVX0b2OJuDxGZBHweuCOPtZsMxFq7QqW879eDYbwRCxVjSkk+Q2Ui8F6P541uW599VDUJtAC1g6x7M3AVkM59ySYbsVbneImnn5FKPBjGF7ED9caUknyGivTRphn26bNdRM4EPlLV1YO+ucglIrJKRFbt2LFj8GpN1uLdodL3SCURCuOL2JTCxpSSfIZKI3Bgj+eTgG399RERH1AN7Bpg3eOAs0SkAWd32kki8n/7enNV/ZWqzlLVWXV1dcP/NGYvSfcaFJ87Idder4fLCMQsVIwpJfkMlVeAqSIyRUQCOAfeV/TqswK4wF0+B3hGVdVtX+SeHTYFmAq8rKrXqOokVa13t/eMqn41j5/BDCDR5uza8lX2PVKxUDGm9PjytWFVTYrIZcDjgBe4S1U3iMj1wCpVXQHcCfxGRLbgjFAWuetuEJH7gDeAJHCpqqbyVasZmqQbKv7Kvkcq6XAZIQsVY0pK3kIFQFUfBR7t1XZdj+UocG4/694A3DDAtp8Fns1FnWZoUh2DhEpZOaFYdF+WZIwpMLui3gxZ2g2VYHXfoaLl5YQTUdDe52cYY0YrCxUzZGn3vl7BfkYqlJfj1TTxDtsFZkypsFAxQ9fphEXInTulN6lwDuBHd7Xss5KMMYVloWKGTDu7Rip9n/3lcUcw0ZbWfVaTMaawLFTMkElnhJjXj8ff9/ke3oquULEphY0pFRYqZsgk0kk0EOz3dU+ls1ss3myhYkypsFAxQyaRCDF/qN/XA+6xlnir7f4yplRYqJgh80Y6iQ8wUvFVObu/kq02UjGmVFiomCHzRiPEA4OPVJKtNvujMaXCQsUMmS8WJRHsP1RCNdUApNotVIwpFRYqZsh80QjJ4N7z03cJuiMVtVAxpmRYqJgh88ejJAcYqYTHVAGQbrNQMaZUWKiYIQvEoqTC/Y9UQhXlpBHosNkfjSkVFipmyALxKKlQ/6Hi8XqIBEIWKsaUEAsVM2TBRIz0ACMVgEggjKfTQsWYUmGhYoYsFI+h4bIB+0SDYbydnfuoImNMoVmomCFJJ1OEkzEoGyRUwmV4baRiTMmwUDFDEnXnUhksVOKhMvwWKsaUDAsVMyRR9yaRMkioJMJlBKK2+8uYUmGhYoYk5l574invey6VLslwuYWKMSUko1ARkd+LyOdFxELIABB37+flqRg4VFJl5YRiNp2wMaUi05D4JfBlYLOI/JeIHJbHmswIkHBHKt5BQiVdXk7YQsWYkpFRqKjqU6r6FeAYoAF4UkReEJELRcSfzwJNcUq0OQffvRUDH1PRigrC8Qio7ouyjDEFlvHuLBGpBf4X8E/Aa8BPcULmybxUZopa0h2p+N0pg/sjFRX40ylinTZaMaYU9D25eC8i8gBwGPAb4B9Udbv70nIRWZWv4kzxSrqnFPsqB979hTulcKSphWD5wKMaY8zIl1GoAHeo6qM9G0QkqKoxVZ2Vh7pMkUu59/MKVA08Uumapz7S3ELN5PF5r8sYU1iZ7v76zz7aXsxlIWZkSbsjlYAbGv3xVjmvx3bbPPXGlIIBQ0VEDhCRmUBYRI4WkWPcxwnAoPsyRGSBiGwSkS0icnUfrwdFZLn7+koRqe/x2jVu+yYRme+2hUTkZRF5XUQ2iMi/Z/l5TY6kO5xrT0KDjFR81V2h0pz3mowxhTfY7q/5OAfnJwE/7tHeBlw70Ioi4gVuBU4FGoFXRGSFqr7Ro9vFwG5VPVhEFgE3AueJyDRgETAdmAA8JSKHADHgJFVtd886e05E/qSqL2X2cU2uqHuTyFDNwCMVf5UzUVfcvQLfGDO6DRgqqnoPcI+IfElVf5/ltmcDW1R1K4CILAMWAj1DZSGwxF2+H/i5iIjbvkxVY8DbIrIFmK2qLwJd0wj63Yedq1oA4oZKcJBTigNu6CRbbfeXMaVgwFARka+q6v8F6kXkyt6vq+qP+1ity0TgvR7PG4E5/fVR1aSItAC1bvtLvdad6NbkBVYDBwO3qurKfmq/BLgEYPLkyQOUaYaks5NOf5Ayz8CH5YI11QCkWm2kYkwpGOxAfdf5ohVAZR+PgUgfbb1HFf316XddVU2p6gycXXKzReTwvt5cVX+lqrNUdVZdXd0gpZpsSSRCzN///PRdwrUWKsaUksF2f93u/hzKAfFG4MAezycB2/rp0ygiPqAa2JXJuqraLCLPAguA9UOozwyDJ9JJLBActF94TA0A2t4+SE9jzGiQ6Q0lbxKRKhHxi8jTIrJTRL46yGqvAFNFZIqIBHAOvK/o1WcFcIG7fA7wjKqq277IPTtsCjAVeFlE6kSkxq0pDJwCvJnJZzC55Y1GiAUyGKm4Z39pm4WKMaUg0+tUTlPVVuBMnFHEIcD/O9AKqpoELgMeBzYC96nqBhG5XkTOcrvdCdS6B+KvBK52190A3IdzUP8x4FJVTQHjgT+LyFqc0HpSVR/O+NOanPFGIyQyCBWPz0unPwQ2UjGmJGR6RX3XTSPPAJaq6i7nJK2BuVfhP9qr7boey1Hg3H7WvQG4oVfbWuDoDGs2eeSLRkkEBw8VgEgwjMdmfzSmJGQ6UnlIRN4EZgFPi0gdEM1fWabY+WIREqFwRn2jwTDeDhupGFMKMr31/dXAXGCWqiaADpxrSUyJCsSipIKZhkoZXhupGFMSMt39BfApnOtVeq5zb47rMSNEIB4lleFIJREuw2+hYkxJyPTW978BPgmsAVJus2KhUrIC8RjpcGahEg+XE2qze38ZUwoyHanMAqa5p/saQzAezThUkmVlBHZsH7yjMWbEy/RA/XrggHwWYkaWUCLzkUqqrJxQrDPPFRljikGmI5VxwBsi8jLOnYIBUNWz+l/FjFapWJxAOgnlA9/2vku6vIJQzKYTNqYUZBoqS/JZhBlZIi1tVABSltlIRcvLKYtHUFUyub7JGDNyZRQqqvoXEfkEMFVVnxKRMsCb39JMsYo2tzihUpHZSIWKCgKpJLFIlGCGQWSMGZkyvffXP+PMd3K72zQR+GO+ijLFLdbiXMjoKS8fpKejK3wiu2xOFWNGu0wP1F8KHAe0AqjqZmC/fBVlilvcvY29ryKzUPFUO7M/djbtzltNxpjikGmoxFQ13vXEvQDSTi8uUfFWZ6Tircxs95fPvf19546mvNVkjCkOmYbKX0TkWiAsIqcCvwMeyl9Zppgl3VDxVWY2UgmMHQNAzEYqxox6mYbK1cAOYB3wv3HuPPyv+SrKFLdEm3PLlUDVYJN/OoK1YwGIW6gYM+plevZXWkT+CPxRVXfkuSZT5FLu3Cj+DHd/heuckUpil92qxZjRbsCRijiWiMhOnBkWN4nIDhG5bqD1zOiWbndGKsGazEYqZXW1AKR220jFmNFusN1f38I56+vTqlqrqmOBOcBxIvLtvFdnilLanRslmOFIpWJ/J1RotpGKMaPdYKHyNWCxqr7d1aCqW4Gvuq+ZEqQdzn28wmOqM+rvLy8j5vVDi12nYsxoN1io+FV1Z+9G97iKv4/+phR0dJBGCFaUZbxKe6gcaW3JY1HGmGIwWKjEh/iaGc06O4n4g3i8mZ48CJFwBb62tjwWZYwpBoOd/XWUiPS1z0KAUB7qMSOAp7OTWCBIZlepOCJlFfjbbfeXMaPdgKGiqnbTSLMXiXQSDWR3Y8hYeQWBzvY8VWSMKRaZ778wxuWNRogHshuoJiqqCHfYSMWY0c5CxWTNF4kQD2Y3UklVVhKOdOSpImNMsbBQMVnzxSIkgtmNVFJVNVRELVSMGe0sVEzW/NEIyQznp+9WXUV5PEIsGhu8rzFmxMprqIjIAhHZJCJbROTqPl4Pishy9/WVIlLf47Vr3PZNIjLfbTtQRP4sIhtFZIOIXJHP+k3fAvEoqVB2oSK1zlX1rds+ykdJxpgikbdQEREvcCtwOjANWCwi03p1uxjYraoHAz8BbnTXnQYsAqYDC4BfuNtLAv+iqp8CPgNc2sc2TZ4FYxGS4cwvfATw140DoP19CxVjRrN8jlRmA1tUdas7wdcyYGGvPguBe9zl+4GTRUTc9mWqGnNvEbMFmK2q21X1VQBVbQM24kxtbPahYDyGZrn7K7C/M1Fox/YP81GSMaZI5DNUJgLv9XjeyN4B0N1HVZNAC1CbybrurrKjgZU5rNlkIBSPki7L5tJHKJvghErsAwsVY0azfIaK9NHWewri/voMuK6IVAC/B76lqn1e/CAil4jIKhFZtWOHTQGTK+lkinAyBmXZ7f4qn3AAAPGP9rqVnDFmFMlnqDQCB/Z4PgnY1l8fd977amDXQOuKiB8nUH6rqg/09+aq+itVnaWqs+rq6ob5UUyXaJt7VXyWI5WqSU6oqAW8MaNaPkPlFWCqiEwRkQDOgfcVvfqsAC5wl88BnlFVddsXuWeHTQGmAi+7x1vuBDaq6o/zWLvpR7TZuSmkpzy7kUqopoq41wdNTfkoyxhTJDKaTngoVDUpIpcBjwNe4C5V3SAi1wOrVHUFTkD8RkS24IxQFrnrbhCR+4A3cM74ulRVUyIyDzgfWCcia9y3ulZVH83X5zB7irY4oSIVmU3Q1U2ElvJqvLssVIwZzfIWKgDuH/tHe7Vd12M5Cpzbz7o3ADf0anuOvo+3mH0k0ers/vJmMZdKl/aKavzNNqWwMaOZXVFvshJzZ2/0ZjiVcE+RyhpCLRYqxoxmFiomK/FmJ1T8NZlNJdxTrHos5e02+6Mxo5mFislKotkJhWCG89P3lBozhkoLFWNGNQsVk5WUu/srWFOV9brp/Q9gbGcLkY5orssyxhQJCxWTlWSrc/ZXeGxN1ut6D5wEwM7NDbksyRhTRCxUTHba3FCpHZP1qqHJTqi0vPVOTksyxhQPCxWTna6RSnVl1qtWHvwJADob3s1pScaY4mGhYrLT3kZHIIzH58161TEH1wOQeLcxx0UZY4qFhYrJiqejg84s56fvUjHxABIeH2zrfQs4Y8xoYaFisuLtaCcazP5qegDxemmqqsX3wfYcV2WMKRYWKiYrvs52YqGhhQpA69g6wjtsThVjRisLFZMVf6STWDi72973FBm3P9W7LFSMGa0sVExWApEOkllO0NVTYspBjG/aTjQaz2FVxphiYaFishKKdJIsy/5mkl28nzqMQDrJ+69vzGFVxphiYaFishKKRUiVDz1Uqo+cBsCu1etzVZIxpohYqJishGOdpMuHfkxl/08fBUD0DRupGDMaWaiYjKWSKcoTUajM/mr6LuUTD6A1VIFn8+YcVmaMKRYWKiZjnbvd29YPI1QQ4aMDJlPR8FZuijLGFBULFZOxSFMzAJ4hzPrYU9th06l/dxPxeDIXZRljioiFislY50dNAPjGjh3Wdrxz5lAdbeftl17PRVnGmCJioWIyFtnhhIq/dnihsv+pnwPgw8eeGXZNxpjiYqFiMhbf6YRKsG6YoTJ3Jrsqx+B/+slclGWMKSIWKiZjiabdAISHGSp4PLz36c8xbe0Z2tJdAAAREElEQVSLNO9uy0FlxphiYaFiMpba5YRK2f7jhr2tmovOpzrazqu33D3sbRljioeFislYercTKhU5CJVPLDqbD+omMum2m2ntiA57e8aY4mChYjLX0kLM6ydYMfQr6rt5vUT+/T855IOtvPCFi2iP2A0mjRkN8hoqIrJARDaJyBYRubqP14Mistx9faWI1Pd47Rq3fZOIzO/RfpeIfCQidvOofczT0kJ7eHjXqPQ05esXsPncr7HgyaW8efgcHvnxvTS1RnK2fWPMvpe3UBERL3ArcDowDVgsItN6dbsY2K2qBwM/AW50150GLAKmAwuAX7jbA7jbbTP7mK+1hfayYVxN35sIU5ffzTv/8QMO3vkun/+XC+icPIWHvnAJzz3xMslUOnfvZYzZJ/I5UpkNbFHVraoaB5YBC3v1WQjc4y7fD5wsIuK2L1PVmKq+DWxxt4eq/hXYlce6TT8C7a1Ey3MYKgAifOJfv0PNh++z/Zd3kjjok3z+wTuYN38Oa6bO5PHbfmfhYswIks9QmQi81+N5o9vWZx9VTQItQG2G65p9LNjeRqy8Kj8bD4UY//WLOOjV50ltfZvNl3+XKbvfZ/7/84+8OPMk3ly7JT/va4zJqXyGivTRphn2yWTdgd9c5BIRWSUiq3bs2JHNqqYf4c42EpV5CpUe/PWfYOot/8XYxrfZ/I3vMHvDC4yb+2keu+lOVLP6NTDG7GP5DJVG4MAezycB2/rrIyI+oBpn11Ym6w5IVX+lqrNUdVZdXV2WpZu+lEfaSFblP1S6SHk5U2/9AdHnVxKpreO07/4zj178XdsdZkwRy2eovAJMFZEpIhLAOfC+olefFcAF7vI5wDPq/FN0BbDIPTtsCjAVeDmPtZpBaDpNRaQDra7Z5+9dPftoJm5cw+ZjT+bzv/4BTy2+zEYsxhSpvIWKe4zkMuBxYCNwn6puEJHrReQst9udQK2IbAGuBK52190A3Ae8ATwGXKqqKQARWQq8CBwqIo0icnG+PoP5WPuuFgLpJDJm34cKgKe8jEP/+hhvnHo2C373S564fElB6jDGDMyXz42r6qPAo73aruuxHAXO7WfdG4Ab+mhfnOMyTQZa391GJeDZf//CFeH18qmHl/Pmcady8i/+k5VzZjLn/LMGX88Ys8/YFfUmI63vbQcgOL6AoQJIIMBBj/2RHWMPYPJl/8S2t98vaD3GmD1ZqJiMRLd9AEB44gEFrgQCtWPQpUsZ176LrV/7uh1fMaaIWKiYjCS2O6FSceCEAlfimHDq59iw+J+Z99zDvHLvHwtdjjHGZaFiMpL88CMAaiYXzzWo03/5Az4ccwDjrvo20Uis0OUYY7BQMZnasZOoL0B4zL67TmUw/soKmm+4kYM+eoeV1/2w0OUYY7BQMRnyN+2guaIGpK+bHRTOoV8/n80HH8mnbvsxzTt2F7ocY0qehYrJSGB3E+2VYwpdxt5E8P/wB+zXvos1/7Kk0NUYU/IsVExGws27idQMc276PKlfeBrrPn0is5b/N9u3vFvocowpaRYqJiOVbbuIjaktdBn92u/nPyaUiLHl8u8WuhRjSpqFihlUOpVmbNtuUnX7FbqUfu0/ewZrTz+XzzzxO/7+7CuFLseYkmWhYgbV9O77BFMJPAdOKnQpAzrkth8T8wdpu/xbdkGkMQVioWIGtXvjVgD8U+oLWsdgKg6cwN8v+TYz17/Ayl/+T6HLMaYkWaiYQbW91QBA5SfrC1pHJo666fu8t99k6q/9Nk3vf1TocowpORYqZlDxtxsAGHPYQYUtJAPeUBC9+27GtTax6byLbDeYMfuYhYoZlL7XSNzjY0x9cR9T6TL59BNZe8GlHPv8I/z569cUuhxjSoqFihlU8J23+bB2POL1FrqUjB393z9m3dxTOelXN/LMJVeTtimIjdknLFTMoKq3vcPu8ZMLXUZWxOfjU0/+kXWfOYWT/vtGVs08kYbX3ix0WcaMehYqZkDpVJrxHzUSrZ9S6FKy5isv4/DnHuP1y67hiA0r2W/ODP76lctobWoudGnGjFoWKmZAO956h/JEFA6eWuhShkS8Xo762f9H56tr2DLreD73P7cSnXIwLy75ie0SMyYPLFTMgLb/bRUAVUcfUeBKhqf2iMM48oXHeeuBx2iu3Z+5/34lr8ydT/MHOwtdmjGjioWKGVDny84tTyacdGyBK8mNT35hPlO3rOXVS69m5qpnaDtiBpv/8nKhyzJm1LBQMQPyr1vLBzX7UTVh/0KXkjPi9XLMz/8PW3/3MGXRTsafdgKv/OzeQpdlzKhgoWL6papMfPN1Pjh4eqFLyYtDvnQ6unIlHxwwmZnf/F/87cJv23EWY4bJQsX0673VG5iw+wMSnzu+0KXkzbhpUzlw/Spen7eAz959M69++iTeW2OnHhszVL5CF2CKV+PyB5kMHHD2GYUuJa+ClRXM+MvDrLri+xx+2w/xzDyCVcd8jviJJxM6+CC8ZWGSu5tJ7G5G29pIt7VDLIZnXC2BKfVMPuME6kbI3QaMyTcphXsjzZo1S1etWlXoMkac9YccTVXLLiZ/0FB0c9Pny84Nf6fhe//JQU89xNiOzK9n2Tr+ILafeiYT/ulr1M87BimR78uMXiKyWlVnZbteXkcqIrIA+CngBe5Q1f/q9XoQuBeYCTQB56lqg/vaNcDFQAr4pqo+nsk2TW5seuxvHL55DS//05VMLqE/kOOmH8K4P94Lquxc+yYtb79HorOT4NgaQmPHEK6tITSmGn84REvjdna89gYtT/+Fyj8/ydx7f4bn3lvYesAUPjjuRMo/v4BJJ8+jdvL4Qn8sY/aZvI1URMQL/B04FWgEXgEWq+obPfp8AzhSVb8uIouAL6jqeSIyDVgKzAYmAE8Bh7irDbjNvthIJTvxSIwtR8zmwPffQhoaqNh/XKFLGhGa/v42b91+LxWPrODgzWsJpJMA7KwYw85xE+ioO4D4ARNg0kR8n5hMxSfrqZ46hXGHTCEQDha4emP2VIwjldnAFlXdCiAiy4CFQM8AWAgscZfvB34uzn6DhcAyVY0Bb4vIFnd7ZLBNM0TxzihbHvsLyX/9Pke+tZY1N/yMGRYoGas9ZAq1P/o3+NG/EdnVwoYHH6d99et4Nr5B+INt1L2zmXFrnqcsEd1jvTRCWzBM3Bcg7g+Q8AWIB0MkgmGSwRDJUJhkeQWpyiq0qgqqqvBUVeGtqcYTDju7JkXAI4DzU0RAPM5eyx7P8XgQj9O/u4/7vKvNWx4mNKaG0NgawuPGUFFbg9c/+J8KTadJJZIkY3ES0RipaJxkPAaALxDEVxbCHw7iDwbx+Aa+Oamm0ySicWLtHSQjMZLJBBpPkkom0bTi8XnxBfx4/H68gQAevxdfIIA34HfavXYOUqHkM1QmAu/1eN4IzOmvj6omRaQFqHXbX+q17kR3ebBt5syWAw/Fn4iBO5qTrp9dHXqM8qR7uZ++Pfp//Jru2d6ja/f2evWVPQaWfW9vwD4DfIZwIsq0dIqOQJjV/3oTM6+9DDM04bHVTL/wH+HCf9zzBVXaPtzJ7k1badncQPTtd0i9+y7S2oJEY0g8hicaxRtzHr5YlLKW3YSjHYSjHVREO/CnU/v883T6g3QGy1ARPOk0HlVE03jSaXzpJL5UikA6iQ/nj0pokO0lPF6SHh8Jr4+kz0fS6wfAn4wTTMQIJhMENE1giPWmxOM8PF5SHven10tanJ8pj5e0x0va40E9HpTRuYu3s7KaaZvX7NP3zGeo9PVfqfe+tv769Nfe1z8/+tx/JyKXAJcATJ48tDvsNn/ik3gSCedNuo4r9PrZ1S49+3QX4XH77FFY39tBupsU6d6eiPPc+UY+fk/ptb3u9xDp7ofs2aernm6ej98bgPJyAjOO5JALz2PmfrV9fSVmuESoPKCOygPq4Pjs/z2k6TTR9k46du6ic8cukp1R0DSaVjStgLOMAmlFNe1MVKaKptMf/0xrH+0K6TTJaJRkcwupllbSLa1oWxvS1oa0tyOqqMcZ8eD+QcbvR/1+xOdHA37w+xG/+zPghIXGE5BIoPE4uA+JxyGRQBJxJJ5wagiH0KDzoCyMhEIQCCB+H3h9eHw+ENBkCk0mIZn8+GcqBe6yuD9x28RdlmQSSaUg5fyUZBLR0XttUrKyep+/Zz5DpRE4sMfzScC2fvo0iogPqAZ2DbLuYNsEQFV/BfwKnGMqQ/kAs557dCirGZM34vEQqqogVFVB7UEjazoCUxryuePxFWCqiEwRkQCwCFjRq88K4AJ3+RzgGXXOHFgBLBKRoIhMAaYCL2e4TWOMMQWSt5GKe4zkMuBxnNN/71LVDSJyPbBKVVcAdwK/cQ/E78IJCdx+9+EcgE8Cl6pqCqCvbebrMxhjjMmOXfxojDFmL0M9pdjOuzPGGJMzFirGGGNyxkLFGGNMzlioGGOMyRkLFWOMMTlTEmd/icgO4J1C15GhccDOQhcxDCO5/pFcO1j9hTSSa4e+6/+EqtZlu6GSCJWRRERWDeU0vmIxkusfybWD1V9II7l2yG39tvvLGGNMzlioGGOMyRkLleLzq0IXMEwjuf6RXDtY/YU0kmuHHNZvx1SMMcbkjI1UjDHG5IyFSgGJyBIReV9E1riPM3q8do2IbBGRTSIyv0f7Ardti4hcXZjK91asdfUmIg0iss79vle5bWNF5EkR2ez+HOO2i4jc4n6mtSJyTAHqvUtEPhKR9T3asq5XRC5w+28WkQv6eq99VPuI+J0XkQNF5M8islFENojIFW77SPnu+6s//9+/qtqjQA9gCfCdPtqnAa8DQWAK8BbOrf697vJBQMDtM60IPkdR1tVPrQ3AuF5tNwFXu8tXAze6y2cAf8KZQ/MzwMoC1Ps54Bhg/VDrBcYCW92fY9zlMQWqfUT8zgPjgWPc5Urg726NI+W776/+vH//NlIpTguBZaoaU9W3gS3AbPexRVW3qmocWOb2LbRirStTC4F73OV7gLN7tN+rjpeAGhEZvy8LU9W/4sw11FO29c4HnlTVXaq6G3gSWFCg2vtTVL/zqrpdVV91l9uAjcBERs5331/9/cnZ92+hUniXucPlu7qG0jj/8d/r0afRbeuvvdCKta6+KPCEiKwWkUvctv1VdTs4/zMC+7ntxfq5sq232D7HiPqdF5F64GhgJSPwu+9VP+T5+7dQyTMReUpE1vfxWAj8EvgkMAPYDvyoa7U+NqUDtBdasdbVl+NU9RjgdOBSEfncAH1H0ueCkfF7M6J+50WkAvg98C1VbR2oax9txVh/3r//vE0nbByqekom/UTkv4GH3aeNwIE9Xp4EbHOX+2svpIHqLSqqus39+ZGI/AFneP+hiIxX1e3uLouP3O7F+rmyrbcROKFX+7P7oM69qOqHXcvF/jsvIn6cP8i/VdUH3OYR8933Vf+++P5tpFJAvfbPfwHoOktmBbBIRIIiMgWYCrwMvAJMFZEpIhIAFrl9C61Y69qDiJSLSGXXMnAazne+Aug6K+cC4EF3eQXwNffMns8ALV27Pgos23ofB04TkTHu7o7T3LZ9bqT8zouIAHcCG1X1xz1eGhHffX/175PvP99nIdhjwDM0fgOsA9a6/6HG93jtezhnXWwCTu/RfgbOmRxvAd8r9Gco9rp61XgQztkrrwMbuuoEaoGngc3uz7FuuwC3up9pHTCrADUvxdlNkcD51+TFQ6kXuAjn4OsW4MIC1j4ifueBeTi7edYCa9zHGSPou++v/rx//3ZFvTHGmJyx3V/GGGNyxkLFGGNMzlioGGOMyRkLFWOMMTljoWKMMSZnLFSMMcbkjIWKMcaYnLFQMcYYkzP/P74Bc0RXyyv/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For MasVnrArea, because the percentage of missing data\n",
    "# was low, we don't expect and won't see a dramatic change in the\n",
    "# original distribution of the variable\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "# original variable distribution\n",
    "X_train['MasVnrArea'].plot(kind='kde', ax=ax)\n",
    "\n",
    "# variable imputed with the median\n",
    "X_train['MasVnrArea_median'].plot(kind='kde', ax=ax, color='red')\n",
    "\n",
    "# add legends\n",
    "lines, labels = ax.get_legend_handles_labels()\n",
    "ax.legend(lines, labels, loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11780a56d8>"
      ]
     },
     "execution_count": 25,
     "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": [
    "# similarly, for GarageBlt, because the percentage of missing data\n",
    "# was low, we don't expect a massive change in the\n",
    "# original distribution of the variable, however we see more values\n",
    "# at around the median\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "# original variable distribution\n",
    "X_train['GarageYrBlt'].plot(kind='kde', ax=ax)\n",
    "\n",
    "# variable imputed with the median\n",
    "X_train['GarageYrBlt_median'].plot(kind='kde', ax=ax, color='red')\n",
    "\n",
    "# add legends\n",
    "lines, labels = ax.get_legend_handles_labels()\n",
    "ax.legend(lines, labels, loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Variance:  532.5872021885676\n",
      "Variance after median imputation:  434.06604265416564\n"
     ]
    }
   ],
   "source": [
    "# similarly we can explore the effect of the imputation technique on \n",
    "# the variance\n",
    "\n",
    "# we can see a change in the variance after imputation for LotFrontAge\n",
    "# this is expected, because the percentage of missing data is quite\n",
    "# high ~20%\n",
    "\n",
    "print('Original Variance: ', X_train['LotFrontage'].var())\n",
    "print('Variance after median imputation: ', X_train['LotFrontage_median'].var())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Variance:  32983.538710039466\n",
      "Variance after median imputation:  32874.27007404175\n"
     ]
    }
   ],
   "source": [
    "# this is not the case for MasnVnrArea, because the % of missing data was small\n",
    "print('Original Variance: ', X_train['MasVnrArea'].var())\n",
    "print('Variance after median imputation: ', X_train['MasVnrArea_median'].var())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Variance:  624.3059475074134\n",
      "Variance after median imputation:  591.3356883144767\n"
     ]
    }
   ],
   "source": [
    "# for GarageBlt, the % of missing data was small so the effect\n",
    "# on the variance will also be small\n",
    "\n",
    "print('Original Variance: ', X_train['GarageYrBlt'].var())\n",
    "print('Variance after median imputation: ', X_train['GarageYrBlt_median'].var())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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>LotFrontage</th>\n",
       "      <th>OverallQual</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <th>1stFlrSF</th>\n",
       "      <th>GrLivArea</th>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <th>SalePrice</th>\n",
       "      <th>LotFrontage_median</th>\n",
       "      <th>MasVnrArea_median</th>\n",
       "      <th>GarageYrBlt_median</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>532.587202</td>\n",
       "      <td>6.587119</td>\n",
       "      <td>6.805603e+02</td>\n",
       "      <td>9.496573e+02</td>\n",
       "      <td>2.908856e+03</td>\n",
       "      <td>3.379794e+03</td>\n",
       "      <td>3.919952e+03</td>\n",
       "      <td>30.611717</td>\n",
       "      <td>1.347414e+02</td>\n",
       "      <td>6.689645e+05</td>\n",
       "      <td>532.587202</td>\n",
       "      <td>6.744233e+02</td>\n",
       "      <td>28.095264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OverallQual</th>\n",
       "      <td>6.587119</td>\n",
       "      <td>1.843859</td>\n",
       "      <td>1.014970e+02</td>\n",
       "      <td>1.746147e+02</td>\n",
       "      <td>2.886241e+02</td>\n",
       "      <td>2.242973e+02</td>\n",
       "      <td>4.091242e+02</td>\n",
       "      <td>17.902809</td>\n",
       "      <td>3.168557e+01</td>\n",
       "      <td>8.320132e+04</td>\n",
       "      <td>5.384774</td>\n",
       "      <td>1.005330e+02</td>\n",
       "      <td>16.875386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>680.560330</td>\n",
       "      <td>101.496976</td>\n",
       "      <td>3.298354e+04</td>\n",
       "      <td>7.540788e+03</td>\n",
       "      <td>2.478877e+04</td>\n",
       "      <td>2.086595e+04</td>\n",
       "      <td>3.520785e+04</td>\n",
       "      <td>1203.583792</td>\n",
       "      <td>3.208924e+03</td>\n",
       "      <td>6.836439e+06</td>\n",
       "      <td>553.921303</td>\n",
       "      <td>3.298354e+04</td>\n",
       "      <td>1134.380889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>949.657293</td>\n",
       "      <td>174.614725</td>\n",
       "      <td>7.540788e+03</td>\n",
       "      <td>1.875241e+05</td>\n",
       "      <td>7.513307e+04</td>\n",
       "      <td>4.987449e+04</td>\n",
       "      <td>5.203392e+04</td>\n",
       "      <td>1823.065167</td>\n",
       "      <td>-1.833201e+03</td>\n",
       "      <td>6.833028e+06</td>\n",
       "      <td>788.095358</td>\n",
       "      <td>7.472110e+03</td>\n",
       "      <td>1724.141544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>2908.855504</td>\n",
       "      <td>288.624075</td>\n",
       "      <td>2.478877e+04</td>\n",
       "      <td>7.513307e+04</td>\n",
       "      <td>1.682931e+05</td>\n",
       "      <td>1.212079e+05</td>\n",
       "      <td>8.615192e+04</td>\n",
       "      <td>3173.042442</td>\n",
       "      <td>1.227966e+04</td>\n",
       "      <td>2.003928e+07</td>\n",
       "      <td>2370.929189</td>\n",
       "      <td>2.465436e+04</td>\n",
       "      <td>2989.473391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>3379.793504</td>\n",
       "      <td>224.297266</td>\n",
       "      <td>2.086595e+04</td>\n",
       "      <td>4.987449e+04</td>\n",
       "      <td>1.212079e+05</td>\n",
       "      <td>1.398656e+05</td>\n",
       "      <td>1.044401e+05</td>\n",
       "      <td>2009.195552</td>\n",
       "      <td>1.109406e+04</td>\n",
       "      <td>1.783631e+07</td>\n",
       "      <td>2750.747094</td>\n",
       "      <td>2.080136e+04</td>\n",
       "      <td>1890.271636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>3919.951834</td>\n",
       "      <td>409.124216</td>\n",
       "      <td>3.520785e+04</td>\n",
       "      <td>5.203392e+04</td>\n",
       "      <td>8.615192e+04</td>\n",
       "      <td>1.044401e+05</td>\n",
       "      <td>2.681277e+05</td>\n",
       "      <td>2738.982988</td>\n",
       "      <td>1.558395e+04</td>\n",
       "      <td>2.934477e+07</td>\n",
       "      <td>3189.685753</td>\n",
       "      <td>3.496714e+04</td>\n",
       "      <td>2576.345636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageYrBlt</th>\n",
       "      <td>30.611717</td>\n",
       "      <td>17.902809</td>\n",
       "      <td>1.203584e+03</td>\n",
       "      <td>1.823065e+03</td>\n",
       "      <td>3.173042e+03</td>\n",
       "      <td>2.009196e+03</td>\n",
       "      <td>2.738983e+03</td>\n",
       "      <td>624.305948</td>\n",
       "      <td>6.658911e+02</td>\n",
       "      <td>9.309355e+05</td>\n",
       "      <td>24.755173</td>\n",
       "      <td>1.182673e+03</td>\n",
       "      <td>624.305948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <td>134.741376</td>\n",
       "      <td>31.685571</td>\n",
       "      <td>3.208924e+03</td>\n",
       "      <td>-1.833201e+03</td>\n",
       "      <td>1.227966e+04</td>\n",
       "      <td>1.109406e+04</td>\n",
       "      <td>1.558395e+04</td>\n",
       "      <td>665.891118</td>\n",
       "      <td>1.648582e+04</td>\n",
       "      <td>3.029981e+06</td>\n",
       "      <td>106.009105</td>\n",
       "      <td>3.212101e+03</td>\n",
       "      <td>627.624634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>668964.454191</td>\n",
       "      <td>83201.317781</td>\n",
       "      <td>6.836439e+06</td>\n",
       "      <td>6.833028e+06</td>\n",
       "      <td>2.003928e+07</td>\n",
       "      <td>1.783631e+07</td>\n",
       "      <td>2.934477e+07</td>\n",
       "      <td>930935.489321</td>\n",
       "      <td>3.029981e+06</td>\n",
       "      <td>6.105731e+09</td>\n",
       "      <td>544838.836893</td>\n",
       "      <td>6.790442e+06</td>\n",
       "      <td>877485.418108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotFrontage_median</th>\n",
       "      <td>532.587202</td>\n",
       "      <td>5.384774</td>\n",
       "      <td>5.539213e+02</td>\n",
       "      <td>7.880954e+02</td>\n",
       "      <td>2.370929e+03</td>\n",
       "      <td>2.750747e+03</td>\n",
       "      <td>3.189686e+03</td>\n",
       "      <td>24.755173</td>\n",
       "      <td>1.060091e+02</td>\n",
       "      <td>5.448388e+05</td>\n",
       "      <td>434.066043</td>\n",
       "      <td>5.488480e+02</td>\n",
       "      <td>22.883476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea_median</th>\n",
       "      <td>674.423263</td>\n",
       "      <td>100.533003</td>\n",
       "      <td>3.298354e+04</td>\n",
       "      <td>7.472110e+03</td>\n",
       "      <td>2.465436e+04</td>\n",
       "      <td>2.080136e+04</td>\n",
       "      <td>3.496714e+04</td>\n",
       "      <td>1182.673336</td>\n",
       "      <td>3.212101e+03</td>\n",
       "      <td>6.790442e+06</td>\n",
       "      <td>548.848031</td>\n",
       "      <td>3.287427e+04</td>\n",
       "      <td>1115.571890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageYrBlt_median</th>\n",
       "      <td>28.095264</td>\n",
       "      <td>16.875386</td>\n",
       "      <td>1.134381e+03</td>\n",
       "      <td>1.724142e+03</td>\n",
       "      <td>2.989473e+03</td>\n",
       "      <td>1.890272e+03</td>\n",
       "      <td>2.576346e+03</td>\n",
       "      <td>624.305948</td>\n",
       "      <td>6.276246e+02</td>\n",
       "      <td>8.774854e+05</td>\n",
       "      <td>22.883476</td>\n",
       "      <td>1.115572e+03</td>\n",
       "      <td>591.335688</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      LotFrontage   OverallQual    MasVnrArea     BsmtUnfSF  \\\n",
       "LotFrontage            532.587202      6.587119  6.805603e+02  9.496573e+02   \n",
       "OverallQual              6.587119      1.843859  1.014970e+02  1.746147e+02   \n",
       "MasVnrArea             680.560330    101.496976  3.298354e+04  7.540788e+03   \n",
       "BsmtUnfSF              949.657293    174.614725  7.540788e+03  1.875241e+05   \n",
       "TotalBsmtSF           2908.855504    288.624075  2.478877e+04  7.513307e+04   \n",
       "1stFlrSF              3379.793504    224.297266  2.086595e+04  4.987449e+04   \n",
       "GrLivArea             3919.951834    409.124216  3.520785e+04  5.203392e+04   \n",
       "GarageYrBlt             30.611717     17.902809  1.203584e+03  1.823065e+03   \n",
       "WoodDeckSF             134.741376     31.685571  3.208924e+03 -1.833201e+03   \n",
       "SalePrice           668964.454191  83201.317781  6.836439e+06  6.833028e+06   \n",
       "LotFrontage_median     532.587202      5.384774  5.539213e+02  7.880954e+02   \n",
       "MasVnrArea_median      674.423263    100.533003  3.298354e+04  7.472110e+03   \n",
       "GarageYrBlt_median      28.095264     16.875386  1.134381e+03  1.724142e+03   \n",
       "\n",
       "                     TotalBsmtSF      1stFlrSF     GrLivArea    GarageYrBlt  \\\n",
       "LotFrontage         2.908856e+03  3.379794e+03  3.919952e+03      30.611717   \n",
       "OverallQual         2.886241e+02  2.242973e+02  4.091242e+02      17.902809   \n",
       "MasVnrArea          2.478877e+04  2.086595e+04  3.520785e+04    1203.583792   \n",
       "BsmtUnfSF           7.513307e+04  4.987449e+04  5.203392e+04    1823.065167   \n",
       "TotalBsmtSF         1.682931e+05  1.212079e+05  8.615192e+04    3173.042442   \n",
       "1stFlrSF            1.212079e+05  1.398656e+05  1.044401e+05    2009.195552   \n",
       "GrLivArea           8.615192e+04  1.044401e+05  2.681277e+05    2738.982988   \n",
       "GarageYrBlt         3.173042e+03  2.009196e+03  2.738983e+03     624.305948   \n",
       "WoodDeckSF          1.227966e+04  1.109406e+04  1.558395e+04     665.891118   \n",
       "SalePrice           2.003928e+07  1.783631e+07  2.934477e+07  930935.489321   \n",
       "LotFrontage_median  2.370929e+03  2.750747e+03  3.189686e+03      24.755173   \n",
       "MasVnrArea_median   2.465436e+04  2.080136e+04  3.496714e+04    1182.673336   \n",
       "GarageYrBlt_median  2.989473e+03  1.890272e+03  2.576346e+03     624.305948   \n",
       "\n",
       "                      WoodDeckSF     SalePrice  LotFrontage_median  \\\n",
       "LotFrontage         1.347414e+02  6.689645e+05          532.587202   \n",
       "OverallQual         3.168557e+01  8.320132e+04            5.384774   \n",
       "MasVnrArea          3.208924e+03  6.836439e+06          553.921303   \n",
       "BsmtUnfSF          -1.833201e+03  6.833028e+06          788.095358   \n",
       "TotalBsmtSF         1.227966e+04  2.003928e+07         2370.929189   \n",
       "1stFlrSF            1.109406e+04  1.783631e+07         2750.747094   \n",
       "GrLivArea           1.558395e+04  2.934477e+07         3189.685753   \n",
       "GarageYrBlt         6.658911e+02  9.309355e+05           24.755173   \n",
       "WoodDeckSF          1.648582e+04  3.029981e+06          106.009105   \n",
       "SalePrice           3.029981e+06  6.105731e+09       544838.836893   \n",
       "LotFrontage_median  1.060091e+02  5.448388e+05          434.066043   \n",
       "MasVnrArea_median   3.212101e+03  6.790442e+06          548.848031   \n",
       "GarageYrBlt_median  6.276246e+02  8.774854e+05           22.883476   \n",
       "\n",
       "                    MasVnrArea_median  GarageYrBlt_median  \n",
       "LotFrontage              6.744233e+02           28.095264  \n",
       "OverallQual              1.005330e+02           16.875386  \n",
       "MasVnrArea               3.298354e+04         1134.380889  \n",
       "BsmtUnfSF                7.472110e+03         1724.141544  \n",
       "TotalBsmtSF              2.465436e+04         2989.473391  \n",
       "1stFlrSF                 2.080136e+04         1890.271636  \n",
       "GrLivArea                3.496714e+04         2576.345636  \n",
       "GarageYrBlt              1.182673e+03          624.305948  \n",
       "WoodDeckSF               3.212101e+03          627.624634  \n",
       "SalePrice                6.790442e+06       877485.418108  \n",
       "LotFrontage_median       5.488480e+02           22.883476  \n",
       "MasVnrArea_median        3.287427e+04         1115.571890  \n",
       "GarageYrBlt_median       1.115572e+03          591.335688  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# finally, let's explore the covariance:\n",
    "# take your time to compare the values in the table below.\n",
    "# see how the covariance is affected for LotFrontAge but not\n",
    "# so much for the other 2 variables\n",
    "\n",
    "X_train.cov()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11781acd68>"
      ]
     },
     "execution_count": 30,
     "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": [
    "# Finally, let's explore the knock-on effect on outliers\n",
    "\n",
    "# there is a decrease in the outlier boundaries for LotFrontage\n",
    "# (look at the height of the top whisker)\n",
    "# but not a visible effect for the other 2 variables\n",
    "\n",
    "X_train[['LotFrontage', 'LotFrontage_median']].boxplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11784e50b8>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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88ghLlx4yrLPZlHJ8ZquSYwDnAmdERGuafx/wBuBc4HciolfSG4BPRMTbJN2Vpn+Quox+ARwfwzTAxwAqt2jRIs455xy+9a1vDQy51z+/cePGrJtnOef4nBxTcRroVuB0SS8GngeWAhuALuDdwE3ABcAtqf6taf4HaXnncD/+NjEeeeQRfvnLXzJr1iwigl27dvHFL36RZ555JuummTk+MzbuBBAR90n6GvAjoBf4MbAGuA24SdL/SGVr00vWAl+RtAXYDpxXScNtdGpqaujr66O9vX3gQpt3vetd1NTUZN00M8dnxnwl8DQnidmzZzN79uyBC2127NjBjh07qOb/veWD43Ny+G6gNqD/i9R/1q2/WFZNHJ/ZcQKY5mpra+ntLZ6V2//F6u3tpbbWdwGx7Dk+s+VPeZrr6+tj9+7d7NmzB0ns2bPH91q3quH4zJb3AKa5I488kuXLlzN3bvGau7lz57J8+XKOPPLIjFtm5vjMmhPANLdv3z7uvvtudu3aBcCuXbu4++672bdvX8YtM3N8Zs0JYJqbN28e+/fvBw72se7fv5958+YN9zKzKeH4zJaPAeTAzJkzB51nvXz58qybZDbA8ZkdJ4Bp7sknn+Taa69l5cqVA5far169mgsvvDDrppk5PjPmLqBprrGxkc2bNw8q27x5M42NjRm1yOwgx2e2nACmuSVLlnDFFVfw9NNPc+DAAZ5++mmuuOIKD7xtVcHxmS3fCmKaq6+v55lnnqG3t5f9+/dzxBFHUFtby9y5cz3otmXO8Tk5PCi8AdDT08MRRxwxcKZF/3NPT0+WzTIDHJ9ZcxdQDuzfv585c+YwY8YM5syZM/AlM6sGjs/sOAHkxHPPPceBAwd47rnnsm6K2SEcn9lwAsiJ/mM91XzMx/LL8ZkNJ4Cc6L/Vbv+zWTVxfGajogQgabakr0n6qaRuSW+QdKykeyQ9mp7npLqSdLWkLZIeknTKxPwJNhrewrJq5vjMRqV7AFcBd0bEq4HXAd3A5cC6iFgArEvzAGcCC9JjBXBNheu2MThw4MCgZ7Nq4vjMxrgTgKSXAn9EGvM3IvZFxA7gbOC6VO064Jw0fTbw5Si6F5gt6YRxt9zGZMaMGYOezaqJ4zMblXzarwB+DfwfST+W9C+SjgbqIuIpgPT8slR/HlB6ZUdPKrMp4C0sq2aOz2xUciFYLXAKsDIi7pN0FQe7e8opd3TnkA4/SSsodhFRV1dHoVCooInWb8aMGRw4cGDgGfBna1XD8ZmNcd8KQtLvAPdGREOa/0OKCeD3gJaIeCp18RQi4mRJX0zTHan+5v56h1uHbwVRueHOqvABN8ua43NyjPZWEOPuAoqIXwDbJJ2cipYCjwC3AheksguAW9L0rcD70tlApwPPDvfjbxNrzpw5g57NqonjMxuV3gtoJXCDpCOBx4CLKCaVmyW1AluBc1Pd24G3A1uA3amuTYHa2lp27twJwM6dO6mtraW3tzfjVpkVOT6zU1ECiIifAOV2M5aWqRvAJZWsz8anr69v4OyKAwcO+ECbVRXHZ3Z8zlUORATHH388M2bM4Pjjj3ffqlUVx2d2fDvonPjFL34x6Nmsmjg+s+E9gJyoqakZ9GxWTRyf2XACyIGZM2dSX1/PjBkzqK+vZ+bMmVk3yWyA4zM7TgA5sG/fPp5//nkigueff559+/Zl3SSzAY7P7DgBTHOSaGxsZMeOHUQEO3bsoLGx0bfdtarg+MyWE8A0FxFs2rSJiy++mG9/+9tcfPHFbNq0yWdaWFVwfGZr3LeCmAq+FUTlZs6cycyZM3n22WcHyo455hj27NnDnj17MmyZmeNzsoz2VhA+DXSa27t3L3v37h1UVvplM8uS4zNb7gLKCQ+5Z9XM8ZkNJ4Cc8JB7Vs0cn9lwAjAzyyknADOznHICMDPLKScAM7OccgLIiVmzZiGJWbNmZd0Us0M4PrNRcQKQVCPpx5K+k+ZPknSfpEclfTWNFoako9L8lrS8odJ12+jt3LmTiBgYecmsmjg+szERewAfBLpL5v8R+ExELAB+A7Sm8lbgNxHxe8BnUj2bBJIGHhNRz2yilMac4zN7FSUASfOBs4B/SfMC3gR8LVW5DjgnTZ+d5knLl8r/2UkREQOPSy+9FEmD7rcuiUsvvXRQPbOpUBpzjs/sVXoriM8ClwEvSfNzgR0R0T+icw8wL03PA7YBRESvpGdT/acrbIMN43Of+xwAX/rSl+jr66O2tpb3v//9A+VmWXJ8ZmvcN4OT9A7g7RHxAUktwEeBi4AfpG4eJNUDt0fEayRtAt4WET1p2f8DTouIZ4a87wpgBUBdXd2pN9100/j+MjvEhXfu4tozjs66GWZlOT4nzpIlSyb9ZnB/ALxT0tuBmcBLKe4RzJZUm/YC5gNPpvo9QD3QI6kWOAbYPvRNI2INsAaKdwNtaWmpoIk2yJ234c/Tqpbjc8qN+xhARHwsIuZHRANwHtAZEe8FuoB3p2oXALek6VvTPGl5Z7hzz8wsM5NxHcDfAB+WtIViH//aVL4WmJvKPwxcPgnrNjOzUZqQ8QAiogAU0vRjwGll6uwBzp2I9ZmZWeV8JbCZWU45AZiZ5ZQTgJlZTjkBmJnllBOAmVlOOQGYmeWUE4CZWU45AZiZ5ZQTgJlZTjkBmJnllBOAmVlOOQGYmeWUE4CZWU45AZiZ5ZQTgJlZTjkBmJnl1LgTgKR6SV2SuiVtkvTBVH6spHskPZqe56RySbpa0hZJD0k6ZaL+CDMzG7tK9gB6gY9ERCNwOnCJpIUUh3pcFxELgHUcHPrxTGBBeqwArqlg3WZmVqFKBoV/KiJ+lKZ/C3QD84CzgetSteuAc9L02cCXo+heYLakE8bdcjMzq8iEjAksqQH4T8B9QF1EPAXFJCHpZanaPGBbyct6UtlTQ95rBcU9BOrq6igUChPRREv8eVo1c3xOrYoTgKRZwNeBD0XEc5IOW7VMWRxSELEGWAPQ3NwcLS0tlTbR+t15G/48rWo5PqdcRWcBSTqC4o//DRHxjVT8y/6unfT8q1TeA9SXvHw+8GQl6zczs/Gr5CwgAWuB7oi4smTRrcAFafoC4JaS8vels4FOB57t7yoyM7Opp4hDemFG90JpMfA94GHgQCr+bxSPA9wMnAhsBc6NiO0pYXweOAPYDVwUERuGW0dzc3Ns2DBslVx73d/fzbPP75/UdRzzoiN48ONvndR12PTj2MyWpAcionmkeuM+BhAR6ynfrw+wtEz9AC4Z7/rsUM8+v58n/uGsUdcvFApj7mNtuPy2MbbKbOyxCWOPT8dm5XwlsJlZTjkBmJnllBOAmVlOOQGYmeWUE4CZWU45AZiZ5ZQTgJlZTjkBmJnllBOAmVlOOQGYmeWUE4CZWU45AZiZ5ZQTgJlZTjkBmJnllBOAmVlOTXkCkHSGpM2Stki6fKrXb2ZmRVOaACTVAF8AzgQWAsskLZzKNpiZWdFU7wGcBmyJiMciYh9wE3D2FLfBzMyY+gQwD9hWMt+TyszMbIqNe0zgcSo3hvCgUeklrQBWANTV1VEoFKagWS9ML2m8nNdcN8bDKNeNdR1QKBw9thdZ7o0rNmFM8enYrNxUJ4AeoL5kfj7wZGmFiFgDrAFobm6OsQ5inicP8/CY6o9nUHiz8RhrbILjMwtT3QX0Q2CBpJMkHQmcB9w6xW0wMzOmeA8gInolXQrcBdQA7RGxaSrbYGZmRVPdBURE3A7cPtXrNTOzwXwlsJlZTjkBmJnllBOAmVlOOQGYmeWUE4CZWU4pIkaulRFJvwZ+lnU7ppHjgKezboTZYTg+J87LI+L4kSpVdQKwiSVpQ0Q0Z90Os3Icn1PPXUBmZjnlBGBmllNOAPmyJusGmA3D8TnFfAzAzCynvAdgZpZTTgAZkRSSvlIyXyvp15K+M473Kkh625CyD0n653G8V62kpyVdMdbXmtkLixNAdnYBiyS9KM2/Bfj5ON+rg+LYCqXOS+WjIqkmTb4V2Az8maRyI7iV1rWMeUNiYklqkLQxTTdLujrrNk0mJ4Bs3QGclaaXUfKDLek0Sd+X9OP0fHIqb5J0v6SfSHpI0gLga8A7JB2V6jQAvwusl9SSvthfk/RTSTf0/7BLekLS30laD5xb0o6rgK3A6SXtGVRX0isl3SnpAUnfk/TqVO+PJd2X2v1dSXWT9NlZkTckJklEbIiI/5p1OyZVRPiRwQPYCbyW4o/3TOAnQAvwnbT8pUBtmn4z8PU0/TngvWn6SOBFafo24Ow0fTnw6TTdAjxLcfjNGcAPgMVp2RPAZSVtehHFITpfTHFc5qtLlg2tuw5YkKZfD3Sm6TkcPLngz4H/lfVnPZ0fKY7+J/DuNP9l4G9K4ug04PvAj9Pzyam8Cbg/xd1DwAJgLvBr4KhUp4HihoBSHBVSvP4UuKHk//wE8HfAeuC8VPYV4M+ALuANQ+JooC7wSuBO4AHge8CrU70/Bu5L7f4uUDfMZ/AJiqMJ353e/0+B1cDD6b2PSPVOBf4tresu4ISS8gfTd+PTwMaS785In+OFwDfSeh4FVmcdE2OKn6wbkNcHsDM9bwAuSl/i0oCrB74JbEyB/NNUvhzYlL7kC0re73ygI03/BDglTbcA95TUuwY4P00/QfGS8f5l5wI3pOm5wDagZmhdYBbwfFpP/6M7LXtN+iI+THEL8M6sP+vp/MAbElBMAOuBI4DXAbuBM9OybwLnpGXfB45P5e+hOCIhFBPgf0nTh0sAh/scLwQeA45Jn//PgPqs42K0jykfEcwOcSvwTxSDbW5J+aeAroj4k9SlUwCIiBsl3Uex6+guSX8eEZ3At4ArJZ1C8cv8o5L32lsy3cfgkeB2lUwvA/5A0hNpfi6whOIWWGndGcCOiPj9Mn/P54ArI+JWSS0Uv5w2iSLioRQjyzh0tL1jgOtSV2FQ/CGE4g94m6T5wDci4tFU3t8NdEt6vrjkve6PiB4AST+huIewPi37akm9d1CM3d2Svg78raS/ioi+0rqSZgFvBP61pJfoqPQ8H/iqpBMoJqjHR/gY7oiI/ZIepjjc7J2p/OHUzpOBRcA9aV01wFOSjgFmR8S/pfpfAc4s8/6H+xwB1kXEs+lvegR4OcWNp6rnYwDZawc+GREPDyk/hoN9uRf2F0p6BfBYRFxNMXm8FiAidlJMEu2Moc+25H1fCiwGToyIhohoAC6h+KMySEQ8Bzwu6dz0Wkl6XZl2XzDWdti49W9IDP3f929ILKLYrTITihsSwDsp7sndJelNqf63gKUTsCHx5rQh8QAHNySG1h3YkCh5NKZlnwM+HxGvAf6iv93D2Jv+rgPA/kib58CB1E4Bm0rW85qIeGsqH83FUGU/x9J1J0M/l6rmBJCxiOiJiKvKLFoNXCHpPyhurfR7D7AxbYG9mmKfb78OirvAN42jKX9Kcfe7NJhvAd7Zf3B5iPcCrZIepNgldXYq/wTFLbrv4Ts7TiVvSAxvM3C8pDekdR0hqSkidgDPSlqc6r33MK8v+zm+0L1gMtV0ExGzypQVONjV8wPgVSWL/zaVXwGUPbUuIr5JcYum7Hum+UtLphtKpq8Frh3y2u1A/y1lG4Ysexw4o0wbbqGYOGwKpa6Zw21IXCfpw0BnSfl7gPMl7Qd+AXyyZFkHxQObQ88IGo3DbUisHmZD4hpJ/51it8pNFA/IfoLihsTPgXuBk8bRlgERsU/Su4GrU7dPLfBZihsvFwHtknZTPDhczuE+xxc03wrCzCyn3AVkZpZT7gIysxcESRcBHxxS/B8RcUkW7ZkO3AVkZpZT7gIyM8spJwAzs5xyAjAzyyknADOznHICMDPLqf8P6+JLrSW9vnwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train[['MasVnrArea', 'MasVnrArea_median']].boxplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11780f1588>"
      ]
     },
     "execution_count": 32,
     "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": [
    "X_train[['GarageYrBlt', 'GarageYrBlt_median']].boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**That is all for this demonstration**.\n",
    "\n",
    "Towards the end of this section, I will show you how to do mean / median imputation with open source Python packages, as part of a machine learning model pipeline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  }
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