01 Introduction to Statistical Learning.ipynb

{
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   "source": [
    "<img align=\"center\" src=\"http://sydney.edu.au/images/content/about/logo-mono.jpg\">\n",
    "<h1 align=\"center\" style=\"margin-top:10px\">Statistical Learning with Python</h1>\n",
    "<h2 align=\"center\" style=\"margin-top:20px\">Lecture 1: Introduction to Statistical Learning</h2>\n",
    "<br>\n",
    "\n",
    "In this lesson we use a simple dataset to illustrate some basic steps of a supervised learning project: loading and processing the dataset, creating training and test sets, learning a simple model, making predictions, and evaluating predictive performance. We will also illustrate other important practical aspects of modelling, such as exploratory data analysis (EDA).\n",
    "\n",
    "\n",
    "<a href=\"#1.-Credit-Card-Data\">Credit Card Data</a> <br>\n",
    "<a href=\"#2.-Training-and-Test-Sets\">Training and Test Sets</a> <br>\n",
    "<a href=\"#3.-Exploratory-Data-Analysis\">Exploratory Data Analysis</a> <br>\n",
    "<a href=\"#4.-Feature-Engineering\">Feature Engineering</a> <br>\n",
    "<a href=\"#5.-Linear-Regression\">Linear Regression</a> <br>\n",
    "<a href=\"#6.-Model-Evaluation\">Model Evaluation</a> <br>\n",
    "<a href=\"#7.-Saving-the-Data\">Saving the Data</a> <br>\n",
    "\n",
    "\n",
    "This notebook relies on the following imports and settings. We will load new functions and libraries in context to make clear what we are using them for. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Packages\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore') \n",
    "# this is to clear the warnings from this page, usually we should leave this on"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot settings\n",
    "sns.set_context('notebook') # optimises figures for notebook display\n",
    "sns.set_style('ticks') # set default plot style\n",
    "crayon = ['#4E79A7','#F28E2C','#E15759','#76B7B2','#59A14F', \n",
    "          '#EDC949','#AF7AA1','#FF9DA7','#9C755F','#BAB0AB']\n",
    "sns.set_palette(crayon) # set custom color scheme\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (9, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Credit Card Data\n",
    "\n",
    "In this lesson we will use the `Credit` dataset taken from the  <a href=\"http://www-bcf.usc.edu/~gareth/ISL/index.html\" target=\"_blank\">Introduction to Statistical Learning</a> texbook by James, Witten, Hastie and Tibshirani. The dataset records the average credit card balace at end of the month for customers of a financial services company, as well as other individual characteristics such age, education, gender, marital status, number of cards, and credit rating.\n",
    "\n",
    "The business objective to predict the average monthly credit card balance of customers based on the available information about them.  \n",
    "\n",
    "We start by loading the data. First, we need to load the pandas package. Since the dataset is in the `csv` format, we use the <a href=\"http://pandas.pydata.org/pandas-docs/stable/generated/pandas.read_csv.html\" target=\"_blank\"><TT>read_csv</TT></a> function to import the file. The package will automatically read the column names and infer the variable types.  We assign the data variable to a variable called <TT>data</TT>, which will store the dataset as an object called a `DataFrame`."
   ]
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  {
   "cell_type": "code",
   "execution_count": 3,
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Student</th>\n",
       "      <th>Married</th>\n",
       "      <th>Ethnicity</th>\n",
       "      <th>Balance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Obs</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14.891</td>\n",
       "      <td>3606</td>\n",
       "      <td>283</td>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>11</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Caucasian</td>\n",
       "      <td>333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>106.025</td>\n",
       "      <td>6645</td>\n",
       "      <td>483</td>\n",
       "      <td>3</td>\n",
       "      <td>82</td>\n",
       "      <td>15</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Asian</td>\n",
       "      <td>903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>104.593</td>\n",
       "      <td>7075</td>\n",
       "      <td>514</td>\n",
       "      <td>4</td>\n",
       "      <td>71</td>\n",
       "      <td>11</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Asian</td>\n",
       "      <td>580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>148.924</td>\n",
       "      <td>9504</td>\n",
       "      <td>681</td>\n",
       "      <td>3</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Asian</td>\n",
       "      <td>964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>55.882</td>\n",
       "      <td>4897</td>\n",
       "      <td>357</td>\n",
       "      <td>2</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Caucasian</td>\n",
       "      <td>331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>80.180</td>\n",
       "      <td>8047</td>\n",
       "      <td>569</td>\n",
       "      <td>4</td>\n",
       "      <td>77</td>\n",
       "      <td>10</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Caucasian</td>\n",
       "      <td>1151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>20.996</td>\n",
       "      <td>3388</td>\n",
       "      <td>259</td>\n",
       "      <td>2</td>\n",
       "      <td>37</td>\n",
       "      <td>12</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>African American</td>\n",
       "      <td>203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>71.408</td>\n",
       "      <td>7114</td>\n",
       "      <td>512</td>\n",
       "      <td>2</td>\n",
       "      <td>87</td>\n",
       "      <td>9</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Asian</td>\n",
       "      <td>872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>15.125</td>\n",
       "      <td>3300</td>\n",
       "      <td>266</td>\n",
       "      <td>5</td>\n",
       "      <td>66</td>\n",
       "      <td>13</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Caucasian</td>\n",
       "      <td>279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>71.061</td>\n",
       "      <td>6819</td>\n",
       "      <td>491</td>\n",
       "      <td>3</td>\n",
       "      <td>41</td>\n",
       "      <td>19</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "      <td>African American</td>\n",
       "      <td>1350</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Income  Limit  Rating  Cards  Age  Education  Gender Student Married  \\\n",
       "Obs                                                                          \n",
       "1     14.891   3606     283      2   34         11    Male      No     Yes   \n",
       "2    106.025   6645     483      3   82         15  Female     Yes     Yes   \n",
       "3    104.593   7075     514      4   71         11    Male      No      No   \n",
       "4    148.924   9504     681      3   36         11  Female      No      No   \n",
       "5     55.882   4897     357      2   68         16    Male      No     Yes   \n",
       "6     80.180   8047     569      4   77         10    Male      No      No   \n",
       "7     20.996   3388     259      2   37         12  Female      No      No   \n",
       "8     71.408   7114     512      2   87          9    Male      No      No   \n",
       "9     15.125   3300     266      5   66         13  Female      No      No   \n",
       "10    71.061   6819     491      3   41         19  Female     Yes     Yes   \n",
       "\n",
       "            Ethnicity  Balance  \n",
       "Obs                             \n",
       "1           Caucasian      333  \n",
       "2               Asian      903  \n",
       "3               Asian      580  \n",
       "4               Asian      964  \n",
       "5           Caucasian      331  \n",
       "6           Caucasian     1151  \n",
       "7    African American      203  \n",
       "8               Asian      872  \n",
       "9           Caucasian      279  \n",
       "10   African American     1350  "
      ]
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We will always assume that the data file is in a subdirectory called \"Data\"\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "data=pd.read_csv('Data/Credit.csv', index_col='Obs')\n",
    "data.head(10) # displays the first 10 rows of the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Training and Test Sets\n",
    "\n",
    "We use the Scikit-Learn <a href=\"http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html\" target=\"_blank\">train_test_split</a> method to split the data into training and test sets. \n",
    "\n",
    "Below, we specify that the training set will contain 70% of the data. The random state parameter is an arbitrary number. By  setting the random state we ensure that get the same training and test sets if we run the analysis again, even though the split is random. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Randomly split indexes\n",
    "index_train, index_test  = train_test_split(np.array(data.index), train_size=0.7, random_state=10)\n",
    "\n",
    "# Write training and test sets \n",
    "train = data.loc[index_train,:].copy()\n",
    "test =  data.loc[index_test,:].copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Exploratory Data Analysis\n",
    "\n",
    "Exploratory data analysis (EDA) is the initial process of examining the data and discovering patterns that can inform feature engineering and model building. EDA is also fundamental for identifying data problems that need to be fixed, if any. Here, we conduct a short EDA of the dataset. \n",
    "\n",
    "**We use only the training dataset for exploratory data analysis.**\n",
    "\n",
    "We start by computing the descriptive statistics and pairwise correlations for the numerical variables. When displaying the results, we chain a command to round the results to two decimal places to facilitate visual inspection.\n",
    "\n",
    "The count row in the first table shows the number available observations for each variable. In this case all variables have the same count, reassuring us that there are no missing values. The response has a large standard deviation relative to the mean : we should keep these magnitudes in mind when discussing coefficient sizes and prediction errors.  The first quartile of the response is 64, indicating that a substantial fraction of customers have low balance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "280\n"
     ]
    },
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Balance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>280.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>280.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>44.6</td>\n",
       "      <td>4731.4</td>\n",
       "      <td>354.5</td>\n",
       "      <td>2.9</td>\n",
       "      <td>55.3</td>\n",
       "      <td>13.4</td>\n",
       "      <td>521.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>34.8</td>\n",
       "      <td>2343.7</td>\n",
       "      <td>156.6</td>\n",
       "      <td>1.3</td>\n",
       "      <td>17.3</td>\n",
       "      <td>3.2</td>\n",
       "      <td>458.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>10.4</td>\n",
       "      <td>855.0</td>\n",
       "      <td>93.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>19.7</td>\n",
       "      <td>3082.5</td>\n",
       "      <td>247.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>41.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>64.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>33.0</td>\n",
       "      <td>4636.0</td>\n",
       "      <td>344.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>459.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>57.5</td>\n",
       "      <td>6034.8</td>\n",
       "      <td>443.5</td>\n",
       "      <td>4.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>864.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>186.6</td>\n",
       "      <td>13913.0</td>\n",
       "      <td>982.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>98.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1999.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Income    Limit  Rating  Cards    Age  Education  Balance\n",
       "count   280.0    280.0   280.0  280.0  280.0      280.0    280.0\n",
       "mean     44.6   4731.4   354.5    2.9   55.3       13.4    521.1\n",
       "std      34.8   2343.7   156.6    1.3   17.3        3.2    458.2\n",
       "min      10.4    855.0    93.0    1.0   23.0        5.0      0.0\n",
       "25%      19.7   3082.5   247.2    2.0   41.0       11.0     64.0\n",
       "50%      33.0   4636.0   344.0    3.0   54.0       14.0    459.5\n",
       "75%      57.5   6034.8   443.5    4.0   69.0       16.0    864.2\n",
       "max     186.6  13913.0   982.0    9.0   98.0       20.0   1999.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(len(train)) #  number of observations in the training data frame\n",
    "train.describe().round(1) # rounding the table to one decimal digit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pairwise correlations reveal that the predictors that are most correlated with the response are limit, rating, and income. The remaining predictors have very low correlation with th credit card balance. Another important finding is that limit and rating have nearly perfect positive correlation. Therefore, we should work with only one of these variables to avoid multicollinearity problems. Also note that income is highly correlated with limit and rating. Limit seems to be the key linear predictor in data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Balance</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Income</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.80</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Limit</th>\n",
       "      <td>0.80</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rating</th>\n",
       "      <td>0.80</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cards</th>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.11</td>\n",
       "      <td>-0.11</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.11</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Education</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.11</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Balance</th>\n",
       "      <td>0.49</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0.88</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Income  Limit  Rating  Cards   Age  Education  Balance\n",
       "Income       1.00   0.80    0.80  -0.01  0.17       0.02     0.49\n",
       "Limit        0.80   1.00    1.00  -0.01  0.10       0.00     0.87\n",
       "Rating       0.80   1.00    1.00   0.03  0.10      -0.01     0.88\n",
       "Cards       -0.01  -0.01    0.03   1.00  0.11      -0.11     0.04\n",
       "Age          0.17   0.10    0.10   0.11  1.00      -0.05     0.02\n",
       "Education    0.02   0.00   -0.01  -0.11 -0.05       1.00     0.01\n",
       "Balance      0.49   0.87    0.88   0.04  0.02       0.01     1.00"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.corr().round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now investigate the (unconditional) distribution of the response by plotting a histogram. We find that the response has a pronouncedly right skewed distribution. A substantial number of customers has zero or low credit card balance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statlearning import plot_dist\n",
    "\n",
    "# The statlearning.py has file auxiliary Python functionality for this course  \n",
    "# You have download and place it in the same directory as you are running this notebook from\n",
    "\n",
    "fig, ax = plot_dist(train['Balance'])\n",
    "ax.set_title('Distribution plot for customer credit card balance', fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.225"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(train['Balance']==0).sum()/len(train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We should also plot the distribution of the predictors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plot_dist(train['Income'])\n",
    "ax.set_title('Distribution plot for customer credit card balance', fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A scatter plot of credit limit with credit balance reveals that there is a nonlinear relationship between these two variables. Furthermore, there are several customers with a response value of zero, which is likely to affect model fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "plt.scatter(train['Limit'], train['Balance'], s=25) # the s option is the size of the dot\n",
    "ax.set_xlabel('Credit card limit')\n",
    "ax.set_ylabel('Balance')\n",
    "sns.despine()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell illustrates how we can create a figure to explore the relationship between a nominal variable and the response. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = train['Cards']<=7 # too few observations for more than 7 cards\n",
    "sns.boxplot(x=train.loc[rows,'Cards'], y=train.loc[rows,'Balance'], boxprops=dict(alpha=.9))\n",
    "sns.despine()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Feature Engineering\n",
    "\n",
    "In machine learning and data science, feature engineering is the process of preparing the dataset for the learning algorithm. It may sound a bit too fancy for what we'll do in this lesson, but this is usually a critical step for predictive modelling, as we will discuss in more detail later.   \n",
    "\n",
    "It is good practice to write a function that performs the full feature engineering process. There are a few reasons for this: \n",
    "\n",
    "<ol>\n",
    "<li style=\"margin-top: 12px;\">You need to process the test data in the same way. </li>\n",
    "    \n",
    "<li style=\"margin-top: 12px;\">It allows you to easily reproduce the analysis. </li>\n",
    "\n",
    "<li style=\"margin-top: 12px;\">It helps you to build a library of data processing steps, which can save you a lot of time in the future.  </li>\n",
    "\n",
    "<li style=\"margin-top: 12px;\">You can use the function to continuously process new data in a live system. </li>\n",
    "\n",
    "<li style=\"margin-top: 12px;\">It makes it simple for you to try different feature engineering pipelines. </li>\n",
    "</ol>\n",
    "\n",
    "We do as follows for our dataset. "
   ]
  },
  {
   "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>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Student</th>\n",
       "      <th>Married</th>\n",
       "      <th>Balance</th>\n",
       "      <th>Male</th>\n",
       "      <th>Caucasian</th>\n",
       "      <th>Asian</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Obs</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>400</th>\n",
       "      <td>18.701</td>\n",
       "      <td>5524</td>\n",
       "      <td>5</td>\n",
       "      <td>64</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>966</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>14.090</td>\n",
       "      <td>4323</td>\n",
       "      <td>5</td>\n",
       "      <td>25</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>671</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>280</th>\n",
       "      <td>54.319</td>\n",
       "      <td>3063</td>\n",
       "      <td>3</td>\n",
       "      <td>59</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>269</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>261</th>\n",
       "      <td>67.937</td>\n",
       "      <td>5184</td>\n",
       "      <td>4</td>\n",
       "      <td>63</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>345</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131</th>\n",
       "      <td>23.793</td>\n",
       "      <td>3821</td>\n",
       "      <td>4</td>\n",
       "      <td>56</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>868</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Income  Limit  Cards  Age  Education  Student  Married  Balance  Male  \\\n",
       "Obs                                                                          \n",
       "400  18.701   5524      5   64          7        0        0      966     0   \n",
       "26   14.090   4323      5   25         16        0        1      671     0   \n",
       "280  54.319   3063      3   59          8        1        0      269     0   \n",
       "261  67.937   5184      4   63         12        0        1      345     1   \n",
       "131  23.793   3821      4   56         12        1        1      868     0   \n",
       "\n",
       "     Caucasian  Asian  \n",
       "Obs                    \n",
       "400          0      1  \n",
       "26           0      0  \n",
       "280          1      0  \n",
       "261          0      1  \n",
       "131          0      0  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def prepare_data(df):\n",
    "    df['Male']=(df['Gender'] ==' Male').astype(int) # create dummy variable for gender\n",
    "    df['Student']=(df['Student'] =='Yes').astype(int)\n",
    "    df['Married']=(df['Married'] =='Yes').astype(int)\n",
    "    df['Caucasian']=(df['Ethnicity'] =='Caucasian').astype(int)\n",
    "    df['Asian']=(df['Ethnicity'] =='Asian').astype(int)\n",
    "    df=df.loc[:, df.dtypes!='object'] # discards the columns that are not numerical\n",
    "    df=df.drop(columns='Rating') # because of collinearity with limit\n",
    "    return df\n",
    "\n",
    "train = prepare_data(train)\n",
    "test = prepare_data(test)\n",
    "\n",
    "train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we need to create the reponse vector and the design matrix that we will provide to the learning algorithm. What I like to do here is to create Python variables that identify the response and the predictors, referring to the column names in the pandas `DataFrame`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Response label\n",
    "response = 'Balance'\n",
    "\n",
    "# Creates a list with the names of all variables which are not the respose\n",
    "predictors = [variable for variable in train.columns if variable!=response] \n",
    "\n",
    "# Here we convert the data to NumPy arrays. This is not strictly necessary, but generally better.\n",
    "y_train = train[response].to_numpy() \n",
    "X_train = train[predictors].to_numpy() \n",
    "\n",
    "y_test = train[response].to_numpy()\n",
    "X_test = train[predictors].to_numpy() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Income',\n",
       " 'Limit',\n",
       " 'Cards',\n",
       " 'Age',\n",
       " 'Education',\n",
       " 'Student',\n",
       " 'Married',\n",
       " 'Male',\n",
       " 'Caucasian',\n",
       " 'Asian']"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Linear Regression\n",
    "\n",
    "Scikit-Learn allows us to learn and use a wide range of machine learning algorithms using a simple and consistent recipe: \n",
    "\n",
    "1. Import the learning algorithm.<br>\n",
    "2. Specify the model and options.<br>\n",
    "3. Learn the model.<br>\n",
    "4. Use the estimated model to make predictions. \n",
    "\n",
    "Here, we use the <a href=\"http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html\" target=\"_blank\">LinearRegression</a> class from Scikit-Learn.\n",
    "\n",
    "We start by training a model with only one predictor, the credit card limit (the second column in the design matrix `X_train`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "slr = LinearRegression()\n",
    "slr.fit(X_train[: , 1].reshape(-1, 1), y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some explanation is helpful here. When we select one column through `X_train[: ,1]`, NumPy returns a flat array (that is, a 1D array). However, Scikit-Learn expects the argument to be a matrix (a 2D array). Therefore, we use `.reshape(-1, 1)` to reconfigure the array such that it becomes a matrix with one column (the `-1` part means that the number is rows is whatever it needs to be for the total number of elements to be same as in the original array).\n",
    "\n",
    "Suppose that we want to predict the credit card balance of a customer that has a limit of 5000 dollars."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([566.97270565])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slr.predict(np.array([[5000]])) # again, the function only accepts a 2D array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualise the estimated model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here, we generate a grid of 500 values ranging from the minimum to the maximum value of the\n",
    "# variable in the training data\n",
    "x = np.linspace(X_train[: , 1].min(), X_train[: , 1].max(), 2).reshape((-1,1))\n",
    "\n",
    "# Compute the predicted values for each of these input points\n",
    "y_pred = slr.predict(x)\n",
    "\n",
    "# Figure\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X_train[: , 1], y_train, s=25) # the s option is the size of the dot\n",
    "ax.set_title(\"Linear Regression Fit\", fontsize=14)\n",
    "ax.set_xlabel('Credit card limit')\n",
    "ax.set_ylabel('Balance')\n",
    "ax.plot(x, y_pred, color='black', alpha = 0.7)\n",
    "sns.despine()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's fit a model with all the available predictors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr = LinearRegression()\n",
    "mlr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Model evaluation\n",
    "\n",
    "The final step in our analysis is model evaluation. Let's compare the two models from the previous section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "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>RMSE</th>\n",
       "      <th>R-Squared</th>\n",
       "      <th>MAE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>One predictor</th>\n",
       "      <td>223.02</td>\n",
       "      <td>0.76</td>\n",
       "      <td>168.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All predictors</th>\n",
       "      <td>99.11</td>\n",
       "      <td>0.95</td>\n",
       "      <td>79.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  RMSE  R-Squared     MAE\n",
       "One predictor   223.02       0.76  168.91\n",
       "All predictors   99.11       0.95   79.02"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score,  mean_absolute_error\n",
    "\n",
    "# Initialise table\n",
    "columns=['RMSE', 'R-Squared', 'MAE']\n",
    "rows=['One predictor', 'All predictors']\n",
    "results =pd.DataFrame(0.0, columns=columns, index=rows)\n",
    "\n",
    "# Computer test predictions and metrics\n",
    "y_pred = slr.predict(X_test[:,1].reshape((-1,1))) \n",
    "results.iloc[0, 0] = np.sqrt(mean_squared_error(y_test, y_pred))\n",
    "results.iloc[0, 1] = r2_score(y_test, y_pred)\n",
    "results.iloc[0, 2] = mean_absolute_error(y_test, y_pred) \n",
    "\n",
    "y_pred =  mlr.predict(X_test)\n",
    "results.iloc[1, 0] = np.sqrt(mean_squared_error(y_test, y_pred))\n",
    "results.iloc[1, 1] = r2_score(y_test, y_pred)\n",
    "results.iloc[1, 2] = mean_absolute_error(y_test, y_pred) \n",
    "\n",
    "results.round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7. Saving the Data\n",
    "\n",
    "We'll continue working with this dataset in the next session. A good option here is to store the training and test dataframes in a [HDF5](https://en.wikipedia.org/wiki/Hierarchical_Data_Format) file. The Hierarchical Data Format (HDF) is very useful for data science because it provides a solution for managing large and heterogeneous datasets, unlike text formats such as csv.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "train.to_hdf('Data/Credit.h5', 'train')\n",
    "test.to_hdf('Data/Credit.h5', 'test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to save the model. Refer to the [Scikit-Learn documentation](https://scikit-learn.org/stable/modules/model_persistence.html) if you wish to learn how to do that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": [
     "removecell"
    ]
   },
   "outputs": [
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    "# This cells formats the notebook for display online.  Please omit it from your work.  \n",
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