explore-nyc-taxi.ipynb

explore-nyc-taxi.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# New York Taxi Trip Dataset\n",
    "\n",
    "The [New York City Taxi & Limousine Commission Trip Record Data](https://www1.nyc.gov/site/tlc/about/tlc-trip-record-data.page) is a really nice dataset to get started with Data Engineering or teaching it. It has several nice properties that make it quite useful that we will show in this notebook. We will look at this data using only `pandas`, not introducing any other tooling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext lab_black"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To better handle the data, we convert one of the files to Apache Parquet. This enables us to get started much faster when starting the notebook a second time. For a more in-depth reasoning on why to use Parquet, I've made [a write-up on efficient DataFrame storage at one of my former employments](https://tech.jda.com/efficient-dataframe-storage-with-apache-parquet/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "if not os.path.exists(\"yellow_tripdata_2016-01.parquet\"):\n",
    "    df = pd.read_csv(\n",
    "        \"../data/yellow_tripdata_2016-01.csv\",\n",
    "        dtype={\"store_and_fwd_flag\": \"bool\"},\n",
    "        parse_dates=[\"tpep_pickup_datetime\", \"tpep_dropoff_datetime\"],\n",
    "        index_col=False,\n",
    "        infer_datetime_format=True,\n",
    "        true_values=[\"Y\"],\n",
    "        false_values=[\"N\"],\n",
    "    )\n",
    "    df.to_parquet(\"yellow_tripdata_2016-01.parquet\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While a single month of the data still fits easily into the main memory of a laptop, the whole dataset is so large that you won't be able to fit it into main memory of a consumer device. As you can see below, just the yellow cabs from 2009 until today need 225 GB of storage in CSV and the whole dataset using all available vehicle types add up to 267 GB.\n",
    "\n",
    "This makes it very well suited to use it in excerises where you don't want someone to be able to compute the result easily in main memory using just `pandas` but actually show the needs for additional tooling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the size is already a nice property, we can have a look at the data itself. For that, we load a single month into memory and have a brief look into it with `pandas`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_parquet(\"yellow_tripdata_2016-01.parquet\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first nice property one doesn't realise anymore is that the data fits into a table and thus is well-suited for a `pandas.DataFrame`. Other types of data, e.g. emails can surely be loaded into a `DataFrame` but is not as straight forward as the taxi data. While we may want to also look at how to transform such data into tabular format, we slowly want to introduce people to it. By using a dataset that is already tabular, we can gradually introduce new concepts instead of requiring them before we even have the data in `pandas`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>VendorID</th>\n",
       "      <th>tpep_pickup_datetime</th>\n",
       "      <th>tpep_dropoff_datetime</th>\n",
       "      <th>passenger_count</th>\n",
       "      <th>trip_distance</th>\n",
       "      <th>pickup_longitude</th>\n",
       "      <th>pickup_latitude</th>\n",
       "      <th>RatecodeID</th>\n",
       "      <th>store_and_fwd_flag</th>\n",
       "      <th>dropoff_longitude</th>\n",
       "      <th>dropoff_latitude</th>\n",
       "      <th>payment_type</th>\n",
       "      <th>fare_amount</th>\n",
       "      <th>extra</th>\n",
       "      <th>mta_tax</th>\n",
       "      <th>tip_amount</th>\n",
       "      <th>tolls_amount</th>\n",
       "      <th>improvement_surcharge</th>\n",
       "      <th>total_amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2</td>\n",
       "      <td>1.10</td>\n",
       "      <td>-73.990372</td>\n",
       "      <td>40.734695</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.981842</td>\n",
       "      <td>40.732407</td>\n",
       "      <td>2</td>\n",
       "      <td>7.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>8.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>5</td>\n",
       "      <td>4.90</td>\n",
       "      <td>-73.980782</td>\n",
       "      <td>40.729912</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.944473</td>\n",
       "      <td>40.716679</td>\n",
       "      <td>1</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>19.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>10.54</td>\n",
       "      <td>-73.984550</td>\n",
       "      <td>40.679565</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.950272</td>\n",
       "      <td>40.788925</td>\n",
       "      <td>1</td>\n",
       "      <td>33.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>34.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>4.75</td>\n",
       "      <td>-73.993469</td>\n",
       "      <td>40.718990</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.962242</td>\n",
       "      <td>40.657333</td>\n",
       "      <td>2</td>\n",
       "      <td>16.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>17.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>3</td>\n",
       "      <td>1.76</td>\n",
       "      <td>-73.960625</td>\n",
       "      <td>40.781330</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.977264</td>\n",
       "      <td>40.758514</td>\n",
       "      <td>2</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>8.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   VendorID tpep_pickup_datetime tpep_dropoff_datetime  passenger_count  \\\n",
       "0         2           2016-01-01            2016-01-01                2   \n",
       "1         2           2016-01-01            2016-01-01                5   \n",
       "2         2           2016-01-01            2016-01-01                1   \n",
       "3         2           2016-01-01            2016-01-01                1   \n",
       "4         2           2016-01-01            2016-01-01                3   \n",
       "\n",
       "   trip_distance  pickup_longitude  pickup_latitude  RatecodeID  \\\n",
       "0           1.10        -73.990372        40.734695           1   \n",
       "1           4.90        -73.980782        40.729912           1   \n",
       "2          10.54        -73.984550        40.679565           1   \n",
       "3           4.75        -73.993469        40.718990           1   \n",
       "4           1.76        -73.960625        40.781330           1   \n",
       "\n",
       "   store_and_fwd_flag  dropoff_longitude  dropoff_latitude  payment_type  \\\n",
       "0               False         -73.981842         40.732407             2   \n",
       "1               False         -73.944473         40.716679             1   \n",
       "2               False         -73.950272         40.788925             1   \n",
       "3               False         -73.962242         40.657333             2   \n",
       "4               False         -73.977264         40.758514             2   \n",
       "\n",
       "   fare_amount  extra  mta_tax  tip_amount  tolls_amount  \\\n",
       "0          7.5    0.5      0.5         0.0           0.0   \n",
       "1         18.0    0.5      0.5         0.0           0.0   \n",
       "2         33.0    0.5      0.5         0.0           0.0   \n",
       "3         16.5    0.0      0.5         0.0           0.0   \n",
       "4          8.0    0.0      0.5         0.0           0.0   \n",
       "\n",
       "   improvement_surcharge  total_amount  \n",
       "0                    0.3           8.8  \n",
       "1                    0.3          19.3  \n",
       "2                    0.3          34.3  \n",
       "3                    0.3          17.3  \n",
       "4                    0.3           8.8  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "About half of all columns are floating point but we also have integers, booleans and even datetime types. This gives us a wide range of types we can work on but still omits the types where the handling with Pandas isn't as good as with those included. For the types in the dataset, `pandas` and `numpy` provide highly optimized routines and we can use their plain-and-simple APIs and get decent performance. This is really good to start with the basics and not need to dive into more low-level techniques to efficiently handle the data eventhough one has a datatype that is not supported by them.\n",
    "\n",
    "Strings would be a typical datatype that will occur quite often in real-life datasets but currently `pandas` doesn't have good native support for it. It is represented as `object` datatype which basically means that all routines on it fall back to pure Python and cannot make use of the highly optimised `numpy` algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 10906858 entries, 0 to 10906857\n",
      "Data columns (total 19 columns):\n",
      "VendorID                 int64\n",
      "tpep_pickup_datetime     datetime64[ns]\n",
      "tpep_dropoff_datetime    datetime64[ns]\n",
      "passenger_count          int64\n",
      "trip_distance            float64\n",
      "pickup_longitude         float64\n",
      "pickup_latitude          float64\n",
      "RatecodeID               int64\n",
      "store_and_fwd_flag       bool\n",
      "dropoff_longitude        float64\n",
      "dropoff_latitude         float64\n",
      "payment_type             int64\n",
      "fare_amount              float64\n",
      "extra                    float64\n",
      "mta_tax                  float64\n",
      "tip_amount               float64\n",
      "tolls_amount             float64\n",
      "improvement_surcharge    float64\n",
      "total_amount             float64\n",
      "dtypes: bool(1), datetime64[ns](2), float64(12), int64(4)\n",
      "memory usage: 1.5 GB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the different values a column has, we see that we have some high entropy columns, some medium entropy and some low entropy columns. This gives us a good mix of column values for aggregation operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2h 5min 24s, sys: 41.9 s, total: 2h 6min 6s\n",
      "Wall time: 2h 6min 9s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "VendorID                       2\n",
       "tpep_pickup_datetime     2368616\n",
       "tpep_dropoff_datetime    2372528\n",
       "passenger_count               10\n",
       "trip_distance               4513\n",
       "pickup_longitude           35075\n",
       "pickup_latitude            62184\n",
       "RatecodeID                     7\n",
       "store_and_fwd_flag             2\n",
       "dropoff_longitude          53813\n",
       "dropoff_latitude           87358\n",
       "payment_type                   5\n",
       "fare_amount                 1878\n",
       "extra                         35\n",
       "mta_tax                       16\n",
       "tip_amount                  3551\n",
       "tolls_amount                 940\n",
       "improvement_surcharge          7\n",
       "total_amount               11166\n",
       "dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "# This takes quite some time to compute as the high entropy columns have expensive set operations.\n",
    "df.nunique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is even so dense that we can also use it to do simple streaming application tests. With on average 4 reqs/s, this doesn't relate to real streaming applications but already gives a good start for the engineering challenges of such applications. And as the dataset is quite large, one can increase the pressure in streaming situations by supplying e.g. data for 10s in the actual timespan of only 1s. This increases the load tenfold while still being able to test your streaming application for a year under this load."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.36 s, sys: 363 ms, total: 1.72 s\n",
      "Wall time: 1.84 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0022222222222222222,\n",
       " 4.072154271206691,\n",
       " 4.694444444444445,\n",
       " 7.919722222222222)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "events_per_minute = (\n",
    "    df.iloc[:, 0]\n",
    "    .groupby(\n",
    "        by=[df[\"tpep_pickup_datetime\"].dt.dayofyear, df[\"tpep_pickup_datetime\"].dt.hour]\n",
    "    )\n",
    "    .count()\n",
    "    / 60\n",
    "    / 60\n",
    ")\n",
    "events_per_minute.min(), events_per_minute.mean(), events_per_minute.median(), events_per_minute.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 104 ms, sys: 50.6 ms, total: 155 ms\n",
      "Wall time: 229 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x127928860>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "events_per_minute.hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally, we can also use the data to do the most basic form of machine learning: linear regression. We can train a simple estimator that takes the trip distance and estimates the price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x127bb7320>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.sample(10000).plot.scatter(x=\"trip_distance\", y=\"fare_amount\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we only want to do a very basic estimation, we do a [simple linear regression estimation](https://en.wikipedia.org/wiki/Ordinary_least_squares#Simple_linear_regression_model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 342 ms, sys: 168 ms, total: 510 ms\n",
      "Wall time: 510 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(12.486907739140417, 4.6752084884145456e-06)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "cov_xy = (df[\"trip_distance\"] * df[\"fare_amount\"]).sum() - (\n",
    "    df[\"trip_distance\"].sum() * df[\"fare_amount\"].sum()\n",
    ") / len(df)\n",
    "var_xy = (df[\"trip_distance\"] ** 2).sum() - df[\"trip_distance\"].sum() ** 2 / len(df)\n",
    "beta = cov_xy / var_xy\n",
    "alpha = df[\"fare_amount\"].mean() - beta * df[\"trip_distance\"].mean()\n",
    "alpha, beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x127d23550>"
      ]
     },
     "execution_count": 12,
     "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": [
    "sample = df.sample(10000)\n",
    "sample[\"price\"] = alpha + beta * sample[\"trip_distance\"]\n",
    "ax = sample.plot.scatter(x=\"trip_distance\", y=\"fare_amount\")\n",
    "sample.plot.line(x=\"trip_distance\", y=\"price\", ax=ax, color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also, as with every real life dataset, the New York City trip dataset also contains outliers that we need to clean to get a good regression. With the goal just showing the nice properties of the dataset, we aren't doing any sophiscated cleaning here but simply get rid of the noisy data that disturbs our basic regression example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>VendorID</th>\n",
       "      <th>tpep_pickup_datetime</th>\n",
       "      <th>tpep_dropoff_datetime</th>\n",
       "      <th>passenger_count</th>\n",
       "      <th>trip_distance</th>\n",
       "      <th>pickup_longitude</th>\n",
       "      <th>pickup_latitude</th>\n",
       "      <th>RatecodeID</th>\n",
       "      <th>store_and_fwd_flag</th>\n",
       "      <th>dropoff_longitude</th>\n",
       "      <th>dropoff_latitude</th>\n",
       "      <th>payment_type</th>\n",
       "      <th>fare_amount</th>\n",
       "      <th>extra</th>\n",
       "      <th>mta_tax</th>\n",
       "      <th>tip_amount</th>\n",
       "      <th>tolls_amount</th>\n",
       "      <th>improvement_surcharge</th>\n",
       "      <th>total_amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2</td>\n",
       "      <td>1.10</td>\n",
       "      <td>-73.990372</td>\n",
       "      <td>40.734695</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.981842</td>\n",
       "      <td>40.732407</td>\n",
       "      <td>2</td>\n",
       "      <td>7.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>8.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>5</td>\n",
       "      <td>4.90</td>\n",
       "      <td>-73.980782</td>\n",
       "      <td>40.729912</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.944473</td>\n",
       "      <td>40.716679</td>\n",
       "      <td>1</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>19.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>10.54</td>\n",
       "      <td>-73.984550</td>\n",
       "      <td>40.679565</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.950272</td>\n",
       "      <td>40.788925</td>\n",
       "      <td>1</td>\n",
       "      <td>33.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>34.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>4.75</td>\n",
       "      <td>-73.993469</td>\n",
       "      <td>40.718990</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.962242</td>\n",
       "      <td>40.657333</td>\n",
       "      <td>2</td>\n",
       "      <td>16.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>17.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>3</td>\n",
       "      <td>1.76</td>\n",
       "      <td>-73.960625</td>\n",
       "      <td>40.781330</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>-73.977264</td>\n",
       "      <td>40.758514</td>\n",
       "      <td>2</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>8.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   VendorID tpep_pickup_datetime tpep_dropoff_datetime  passenger_count  \\\n",
       "0         2           2016-01-01            2016-01-01                2   \n",
       "1         2           2016-01-01            2016-01-01                5   \n",
       "2         2           2016-01-01            2016-01-01                1   \n",
       "3         2           2016-01-01            2016-01-01                1   \n",
       "4         2           2016-01-01            2016-01-01                3   \n",
       "\n",
       "   trip_distance  pickup_longitude  pickup_latitude  RatecodeID  \\\n",
       "0           1.10        -73.990372        40.734695           1   \n",
       "1           4.90        -73.980782        40.729912           1   \n",
       "2          10.54        -73.984550        40.679565           1   \n",
       "3           4.75        -73.993469        40.718990           1   \n",
       "4           1.76        -73.960625        40.781330           1   \n",
       "\n",
       "   store_and_fwd_flag  dropoff_longitude  dropoff_latitude  payment_type  \\\n",
       "0               False         -73.981842         40.732407             2   \n",
       "1               False         -73.944473         40.716679             1   \n",
       "2               False         -73.950272         40.788925             1   \n",
       "3               False         -73.962242         40.657333             2   \n",
       "4               False         -73.977264         40.758514             2   \n",
       "\n",
       "   fare_amount  extra  mta_tax  tip_amount  tolls_amount  \\\n",
       "0          7.5    0.5      0.5         0.0           0.0   \n",
       "1         18.0    0.5      0.5         0.0           0.0   \n",
       "2         33.0    0.5      0.5         0.0           0.0   \n",
       "3         16.5    0.0      0.5         0.0           0.0   \n",
       "4          8.0    0.0      0.5         0.0           0.0   \n",
       "\n",
       "   improvement_surcharge  total_amount  \n",
       "0                    0.3           8.8  \n",
       "1                    0.3          19.3  \n",
       "2                    0.3          34.3  \n",
       "3                    0.3          17.3  \n",
       "4                    0.3           8.8  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# As with every dataset, we need to first clean the data a bit\n",
    "cap_fare = df[\"fare_amount\"].mean() + 3 * df[\"fare_amount\"].std()\n",
    "cap_distance = df[\"trip_distance\"].mean() + 3 * df[\"trip_distance\"].std()\n",
    "df_filtered = df.query(\n",
    "    f\"trip_distance > 0 and trip_distance < {cap_distance} and fare_amount > 0 and fare_amount < {cap_fare}\"\n",
    ")\n",
    "df_filtered.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 364 ms, sys: 70.1 ms, total: 434 ms\n",
      "Wall time: 434 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(4.651606864471554, 2.661444816924383)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "cov_xy = (df_filtered[\"trip_distance\"] * df_filtered[\"fare_amount\"]).sum() - (\n",
    "    df_filtered[\"trip_distance\"].sum() * df_filtered[\"fare_amount\"].sum()\n",
    ") / len(df_filtered)\n",
    "var_xy = (df_filtered[\"trip_distance\"] ** 2).sum() - df_filtered[\n",
    "    \"trip_distance\"\n",
    "].sum() ** 2 / len(df_filtered)\n",
    "beta = cov_xy / var_xy\n",
    "alpha = df_filtered[\"fare_amount\"].mean() - beta * df_filtered[\"trip_distance\"].mean()\n",
    "alpha, beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x126d7c4e0>"
      ]
     },
     "execution_count": 15,
     "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": [
    "sample[\"price\"] = alpha + beta * sample[\"trip_distance\"]\n",
    "ax = sample.plot.scatter(x=\"trip_distance\", y=\"fare_amount\")\n",
    "sample.plot.line(x=\"trip_distance\", y=\"price\", ax=ax, color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Schema changes\n",
    "\n",
    "Another thing that represents real life issues is that the dataset has a small schema change throughout its history. The columns used in 2015 and in 2018 aren't exactly the same. They have changed the location columns from providing coordinates for pickup and dropoff to using location IDs in later datasets\n",
    "\n",
    "This is nice as you can use the dataset to explain schema migrations and write methods handling that. Still, the schema change is so small, that you can easily work around it when you aren't interested in dealing with it explicitly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'DOLocationID',\n",
       " 'PULocationID',\n",
       " 'RatecodeID',\n",
       " 'VendorID',\n",
       " 'extra',\n",
       " 'fare_amount',\n",
       " 'improvement_surcharge',\n",
       " 'mta_tax',\n",
       " 'passenger_count',\n",
       " 'payment_type',\n",
       " 'store_and_fwd_flag',\n",
       " 'tip_amount',\n",
       " 'tolls_amount',\n",
       " 'total_amount',\n",
       " 'tpep_dropoff_datetime',\n",
       " 'tpep_pickup_datetime',\n",
       " 'trip_distance'}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First line of yellow_tripdata_2018-08.csv\n",
    "columns_2018 = \"VendorID,tpep_pickup_datetime,tpep_dropoff_datetime,passenger_count,trip_distance,RatecodeID,store_and_fwd_flag,PULocationID,DOLocationID,payment_type,fare_amount,extra,mta_tax,tip_amount,tolls_amount,improvement_surcharge,total_amount\"\n",
    "columns_2018 = set(columns_2018.split(\",\"))\n",
    "columns_2018"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'RatecodeID',\n",
       " 'VendorID',\n",
       " 'dropoff_latitude',\n",
       " 'dropoff_longitude',\n",
       " 'extra',\n",
       " 'fare_amount',\n",
       " 'improvement_surcharge',\n",
       " 'mta_tax',\n",
       " 'passenger_count',\n",
       " 'payment_type',\n",
       " 'pickup_latitude',\n",
       " 'pickup_longitude',\n",
       " 'store_and_fwd_flag',\n",
       " 'tip_amount',\n",
       " 'tolls_amount',\n",
       " 'total_amount',\n",
       " 'tpep_dropoff_datetime',\n",
       " 'tpep_pickup_datetime',\n",
       " 'trip_distance'}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First line of yellow_tripdata_2015-08.csv\n",
    "columns_2016 = \"VendorID,tpep_pickup_datetime,tpep_dropoff_datetime,passenger_count,trip_distance,pickup_longitude,pickup_latitude,RatecodeID,store_and_fwd_flag,dropoff_longitude,dropoff_latitude,payment_type,fare_amount,extra,mta_tax,tip_amount,tolls_amount,improvement_surcharge,total_amount\"\n",
    "columns_2016 = set(columns_2016.split(\",\"))\n",
    "columns_2016"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Removed columns: {'pickup_latitude', 'dropoff_longitude', 'pickup_longitude', 'dropoff_latitude'}\n",
      "Added columns: {'DOLocationID', 'PULocationID'}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    f\"\"\"\n",
    "Removed columns: {columns_2016 - columns_2018}\n",
    "Added columns: {columns_2018 - columns_2016}\n",
    "\"\"\"\n",
    ")"
   ]
  }
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