taxi_fare_predictor_walkthrough.ipynb

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    "# Implementing Linear Regression from Scratch\n",
    "\n",
    "## Introduction\n",
    "This project arose from a desire to practice and implement my newly acquired skills in Machine Learning. My understanding of these skills was honed through **Andrew Ng's acclaimed Supervised Learning course on Coursera**. With a solid grasp of the underlying calculus and newfound knowledge about different algorithms and concepts, I felt equipped and ready to put these principles into action by implementing a classic Machine Learning algorithm -- **linear regression**.\n",
    "\n",
    "The objective was straightforward yet challenging, to build a linear regression model entirely from scratch, implementing foundational algorithms such as **gradient descent** along the way. The project served as a fun playground to test out my theoretical knowledge in a practical setting, and to enjoy the thrill of seeing a mathematical model come alive.\n",
    "\n",
    "Keep in mind that contrary to the usual approach of identifying a problem first and then choosing an appropriate algorithm to solve it, the goal of this project was to practice implementing a pre-selected algorithm, linear regression, as a learning experience. With that in mind, I worked backwards and looked for a very large dataset that should work well with linear regression algorithm. The data set chosen for this project is a comprehensive collection of taxi rides in New York City, [available on Kaggle here](https://www.kaggle.com/competitions/new-york-city-taxi-fare-prediction/data).\n",
    "\n",
    "In the following sections, I will guide you through the different stages I undertook in the developing of this model, from pre-processing the data and implementing the algorithms to training the model and evaluating its performance.\n",
    "\n",
    "Join me on this exciting journey as I build my **first machine learning model from scratch**, and witness the beauty and magic where calculus meets computer science."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd  # data handling\n",
    "import numpy as np  # math (linear algebra)\n",
    "import matplotlib.pyplot as plt  # plotting data\n",
    "\n",
    "# machine learning workflow\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Loading and Inspection\n",
    "We're using a data set of taxi rides in New York City and we're trying to predict the cost of the trips. The dataset is originally nearly 55.5 million rows, which is massive 😳 So to make things much easier to handle, I picked a random sample of 1.3 million rows to work with; 1mil for training and 0.3mil for testing. Below I import the data and perform important inspection of the data where I see what features we have, the ranges of some of these features, etc.\n",
    "\n",
    "You should be able to view this notebook with its outputs (which is the recommended use), but if you'd like to try running it yourself, you can download the exact chunk of data I used from the link below. NOTE that the link in the intro is for the original dataset, not for the dataset I used, as was described in the previous paragraph. The dataset I used, which was a random sample of the original dataset is on [Google Drive at this link](https://drive.google.com/file/d/1IcIW1HZeTyrL-76U2Y_wOVH9c1kHNaNT/view?usp=sharing). Simply download it to the same folder you are storing this notebook and you should be good to go!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape:\n",
      "(1300000, 8)\n",
      "\n",
      "Columns:\n",
      "key, fare_amount, pickup_datetime, pickup_longitude, pickup_latitude, dropoff_longitude, dropoff_latitude, passenger_count\n",
      "\n",
      "Head:\n",
      "                             key  fare_amount          pickup_datetime   \n",
      "0  2010-09-15 20:03:00.000000195         12.5  2010-09-15 20:03:00 UTC  \\\n",
      "1    2010-02-19 13:32:37.0000003          5.7  2010-02-19 13:32:37 UTC   \n",
      "2    2015-05-24 13:21:59.0000007         11.0  2015-05-24 13:21:59 UTC   \n",
      "3    2013-07-15 19:48:38.0000001         12.5  2013-07-15 19:48:38 UTC   \n",
      "4    2014-06-18 22:12:13.0000002         10.5  2014-06-18 22:12:13 UTC   \n",
      "\n",
      "   pickup_longitude  pickup_latitude  dropoff_longitude  dropoff_latitude   \n",
      "0        -74.005988        40.741215         -74.015480         40.714537  \\\n",
      "1        -74.013270        40.715096         -74.012666         40.702455   \n",
      "2        -73.948174        40.782948         -73.975395         40.752914   \n",
      "3        -73.985779        40.758557         -73.974966         40.790157   \n",
      "4        -73.968955        40.754464         -73.997979         40.729139   \n",
      "\n",
      "   passenger_count  \n",
      "0                1  \n",
      "1                1  \n",
      "2                1  \n",
      "3                1  \n",
      "4                1  \n",
      "\n",
      "Info:\n",
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1300000 entries, 0 to 1299999\n",
      "Data columns (total 8 columns):\n",
      " #   Column             Non-Null Count    Dtype  \n",
      "---  ------             --------------    -----  \n",
      " 0   key                1300000 non-null  object \n",
      " 1   fare_amount        1300000 non-null  float64\n",
      " 2   pickup_datetime    1300000 non-null  object \n",
      " 3   pickup_longitude   1300000 non-null  float64\n",
      " 4   pickup_latitude    1300000 non-null  float64\n",
      " 5   dropoff_longitude  1300000 non-null  float64\n",
      " 6   dropoff_latitude   1300000 non-null  float64\n",
      " 7   passenger_count    1300000 non-null  int64  \n",
      "dtypes: float64(5), int64(1), object(2)\n",
      "memory usage: 79.3+ MB\n",
      "None\n",
      "\n",
      "Describe:\n",
      "        fare_amount  pickup_longitude  pickup_latitude  dropoff_longitude   \n",
      "count  1.300000e+06      1.300000e+06     1.300000e+06       1.300000e+06  \\\n",
      "mean   1.133598e+01     -7.250823e+01     3.991408e+01      -7.250711e+01   \n",
      "std    9.760992e+00      1.268129e+01     1.082634e+01       1.300699e+01   \n",
      "min   -4.500000e+01     -2.972263e+03    -3.441914e+03      -2.989027e+03   \n",
      "25%    6.000000e+00     -7.399206e+01     4.073497e+01      -7.399137e+01   \n",
      "50%    8.500000e+00     -7.398180e+01     4.075263e+01      -7.398012e+01   \n",
      "75%    1.250000e+01     -7.396706e+01     4.076717e+01      -7.396368e+01   \n",
      "max    5.000000e+02      2.848038e+03     3.361255e+03       3.426851e+03   \n",
      "\n",
      "       dropoff_latitude  passenger_count  \n",
      "count      1.300000e+06     1.300000e+06  \n",
      "mean       3.991949e+01     1.685017e+00  \n",
      "std        9.981196e+00     1.321247e+00  \n",
      "min       -3.441914e+03     0.000000e+00  \n",
      "25%        4.073403e+01     1.000000e+00  \n",
      "50%        4.075315e+01     1.000000e+00  \n",
      "75%        4.076812e+01     2.000000e+00  \n",
      "max        3.210356e+03     2.080000e+02  \n",
      "\n",
      "Null Count: key                  0\n",
      "fare_amount          0\n",
      "pickup_datetime      0\n",
      "pickup_longitude     0\n",
      "pickup_latitude      0\n",
      "dropoff_longitude    0\n",
      "dropoff_latitude     0\n",
      "passenger_count      0\n",
      "dtype: int64\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# load dataset and explore it\n",
    "dataset = pd.read_csv('ny_taxi_fares_dataset_chunk.csv')\n",
    "\n",
    "# analyze the dataset's shape, first few rows, features, means/summary, and more.\n",
    "print('Shape:')\n",
    "print(dataset.shape, end='\\n\\n')\n",
    "\n",
    "print('Columns:')\n",
    "print(', '.join(dataset.columns), end='\\n\\n')\n",
    "\n",
    "print('Head:')\n",
    "print(dataset.head(), end='\\n\\n')\n",
    "\n",
    "print('Info:')\n",
    "print(dataset.info(), end='\\n\\n')\n",
    "\n",
    "print('Describe:')\n",
    "print(dataset.describe(), end='\\n\\n')\n",
    "\n",
    "print('Null Count:', dataset.isnull().sum(), end='\\n\\n')"
   ]
  },
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   "attachments": {},
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   "source": [
    "The dataset analysis above allows us to actually get a grasp of the data we're looking at and understand how some of the datapoints may look. We also get to see the **features**, or inputs we're working with. The `describe` method revealed to me the wide variety of ranges of the different features, with the passenger count ranging from 0 to 20, while the pickup latitude ranging from -3442 to 3361. This tells us we're going to need to scale the features, otherwise the difference in ranges will have a terrible impact on gradient descent in terms of performance, and will make it difficult to even reach an acceptable minimum. We'll also have to deal with outliers and possible false values, because for example, the passenger count goes up to 20 and last I checked, taxis can't carry 20 people.\n",
    "\n",
    "Below are the columns/features we pulled from the dataset.\n",
    "\n",
    "### Features\n",
    "- fare_amount **(target value)**: float dollar amount of the cost of the taxi ride.\n",
    "- pickup_datetime: timestamp value indicating when the taxi ride started.\n",
    "- pickup_longitude: float for longitude coordinate of where the taxi ride started.\n",
    "- pickup_latitude: float for latitude coordinate of where the taxi ride started.\n",
    "- dropoff_longitude: float for longitude coordinate of where the taxi ride ended.\n",
    "- dropoff_latitude: float for latitude coordinate of where the taxi ride ended.\n",
    "- passenger_count: integer indicating the number of passengers in the taxi ride."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Preprocessing\n",
    "This is where a lot of work is going to be before we can get to any fun math. During the **data inspection** stage, we revealed many odd values like negative coordinates and trips with 20 passenger, which is what we aim to fix in this stage.\n",
    "\n",
    "First as a more general step, we cut off the key column and drop the rows with null values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "# drop \"key ID\" column, then drop null rows\n",
    "dataset = dataset.drop('key', axis=1)\n",
    "dataset.dropna(inplace=True)"
   ]
  },
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   "attachments": {},
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   "metadata": {},
   "source": [
    "### Preprocessing the Target Values\n",
    "To preprocess the target values we're going filter the target `fare_amount` to remove extreme outliers. This involves setting a maximum acceptable value (high threshold) and a minimum threshold based on the 1st percentile of fare data (low threshold). We then filter the dataset to remove rows outside of this range and only include fares within this range.\n",
    "\n",
    "This helps make our model more robust by limiting the influence of extreme fare values, as well as removing clearly false negative prices. After this filtering process, we check the new minimum and maximum fare_amount values to confirm that our filtering operation was successful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min fare_amount before filtering: -45.0\n",
      "Max fare_amount before filtering: 500.0\n",
      "High threshold:  100\n",
      "1st percentile:  3.3\n",
      "Min fare_amount after filtering: 3.3\n",
      "Max fare_amount after filtering: 100.0\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check the min and max before filtering\n",
    "print('Min fare_amount before filtering:', dataset['fare_amount'].min())\n",
    "print('Max fare_amount before filtering:', dataset['fare_amount'].max())\n",
    "\n",
    "# set a fixed high threshold\n",
    "high_threshold = 100\n",
    "print('High threshold: ', high_threshold)\n",
    "\n",
    "# calculate 1st percentile-based low threshold\n",
    "low_threshold = dataset['fare_amount'].quantile(0.01)\n",
    "print('1st percentile: ', low_threshold)\n",
    "\n",
    "# filter based on the thresholds\n",
    "dataset = dataset[dataset['fare_amount'] <= high_threshold]\n",
    "dataset = dataset[dataset['fare_amount'] >= low_threshold]\n",
    "\n",
    "# check the min and max after filtering\n",
    "print('Min fare_amount after filtering:', dataset['fare_amount'].min())\n",
    "print('Max fare_amount after filtering:', dataset['fare_amount'].max())\n",
    "\n",
    "# plot the distribution of fare_amount to see how the shape has improved\n",
    "plt.hist(dataset['fare_amount'], bins=30, edgecolor='black')\n",
    "plt.title('Distribution of Fare Amount')\n",
    "plt.xlabel('Fare Amount')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preprocessing the Features\n",
    "To preprocess the features, we'll visualize each feature using both histograms and boxplots. These plots provide valuable insight into the distribution of each feature and allow us to identify any potential outliers. This allows us to evaluate what outlier treatment might be necessary to better prepare our data for model training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x2000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we plot each feature's data in a histogram and boxplot\n",
    "# to analyze the features for outlier treatment\n",
    "\n",
    "feature_names = ['pickup_longitude', 'pickup_latitude', 'dropoff_longitude', 'dropoff_latitude', 'passenger_count']\n",
    "\n",
    "fig, axs = plt.subplots(len(feature_names), 2, figsize=(15, 4*len(feature_names)))\n",
    "\n",
    "# iterate through every feature and plot their data\n",
    "for i, feature in enumerate(feature_names):\n",
    "    # histogram\n",
    "    axs[i][0].hist(dataset[feature], bins=30, edgecolor='black', alpha=0.7)\n",
    "    axs[i][0].set_title(f'Histogram: {feature}')\n",
    "\n",
    "    # boxplot\n",
    "    axs[i][1].boxplot(dataset[feature].dropna(), vert=False)  # dropna() is used in case there are any NaN values\n",
    "    axs[i][1].set_title(f'Boxplot: {feature}')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on what we've seen in the boxplots and histograms, we filter the passenger count and pickup longitude & latitude to cut off the extreme values. We also convert the pickup_datetime from a string to a datetime object, because it wouldn't mean anything as a string."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "# filter out passenger counts higher than 10\n",
    "dataset = dataset[dataset['passenger_count'] <= 10]\n",
    "\n",
    "# filter the pickup longitudes and latitudes using fixed thresholds\n",
    "dataset = dataset[(dataset['pickup_longitude'] >= -750) & (dataset['pickup_longitude'] <= 200)]\n",
    "dataset = dataset[(dataset['pickup_latitude'] >= -500) & (dataset['pickup_latitude'] <= 550)]\n",
    "\n",
    "# convert pickup_datetime from string to datetime\n",
    "dataset['pickup_datetime'] = pd.to_datetime(dataset['pickup_datetime'])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Engineering!\n",
    "Feature engineering is one of my most favorite parts, as the idea of combining distinct features to generate more meaningful data is quite intriguing.\n",
    "\n",
    "First, we're going to turn the datetime column into more useful features, because the linear regression model needs values in the form of numbers. Out of all the information in a datetime, the day_of_week and the hour_of_day seem the most useful as they should have the most influence on taxi fares (ex. more taxis on a Friday night).\n",
    "\n",
    "On another note, this dataset unfortunately doesn't contain trip distances, which I believe would be most strongly correlated with the taxi price. What we do have is the pickup and dropoff coordinates in longitude and latitude, so we can calculate the Euclidean distance and add that as a feature. The problem is that the Euclidean distance is essentially a straight line between two points, which is not an accurate reflection of the actual trip distance for a taxi ride. This is due to the realities of city navigation - taxis must follow roads and traffic patterns, which can lead to routes that deviate considerably from a straight-line path. Nevertheless, this is the best we can do without the true trip distance, and maybe Euclidean distance will have at least some small influence towards a more accurate prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create day_of_week and hour_of_day features (0 is Monday, 6 is Sunday)\n",
    "dataset['day_of_week'] = dataset['pickup_datetime'].dt.dayofweek\n",
    "dataset['hour_of_day'] = dataset['pickup_datetime'].dt.hour\n",
    "dataset = dataset.drop('pickup_datetime', axis=1)  # drop the original pickup_datetime feature\n",
    "\n",
    "# add the Euclidean distance as a feature\n",
    "dataset['euclidean_distance'] = np.abs(np.sqrt((dataset['pickup_longitude'] - dataset['dropoff_longitude'])**2 \n",
    "                               + (dataset['pickup_latitude'] - dataset['dropoff_latitude'])**2))\n",
    "\n",
    "# add new features\n",
    "feature_names.extend(['day_of_week', 'hour_of_day', 'euclidean_distance'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first few rows of the data after feature engineering\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>fare_amount</th>\n",
       "      <th>pickup_longitude</th>\n",
       "      <th>pickup_latitude</th>\n",
       "      <th>dropoff_longitude</th>\n",
       "      <th>dropoff_latitude</th>\n",
       "      <th>passenger_count</th>\n",
       "      <th>day_of_week</th>\n",
       "      <th>hour_of_day</th>\n",
       "      <th>euclidean_distance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.5</td>\n",
       "      <td>-74.005988</td>\n",
       "      <td>40.741215</td>\n",
       "      <td>-74.015480</td>\n",
       "      <td>40.714537</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>20</td>\n",
       "      <td>0.028316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.7</td>\n",
       "      <td>-74.013270</td>\n",
       "      <td>40.715096</td>\n",
       "      <td>-74.012666</td>\n",
       "      <td>40.702455</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>13</td>\n",
       "      <td>0.012655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11.0</td>\n",
       "      <td>-73.948174</td>\n",
       "      <td>40.782948</td>\n",
       "      <td>-73.975395</td>\n",
       "      <td>40.752914</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>13</td>\n",
       "      <td>0.040534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12.5</td>\n",
       "      <td>-73.985779</td>\n",
       "      <td>40.758557</td>\n",
       "      <td>-73.974966</td>\n",
       "      <td>40.790157</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0.033399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.5</td>\n",
       "      <td>-73.968955</td>\n",
       "      <td>40.754464</td>\n",
       "      <td>-73.997979</td>\n",
       "      <td>40.729139</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>22</td>\n",
       "      <td>0.038519</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fare_amount  pickup_longitude  pickup_latitude  dropoff_longitude   \n",
       "0         12.5        -74.005988        40.741215         -74.015480  \\\n",
       "1          5.7        -74.013270        40.715096         -74.012666   \n",
       "2         11.0        -73.948174        40.782948         -73.975395   \n",
       "3         12.5        -73.985779        40.758557         -73.974966   \n",
       "4         10.5        -73.968955        40.754464         -73.997979   \n",
       "\n",
       "   dropoff_latitude  passenger_count  day_of_week  hour_of_day   \n",
       "0         40.714537                1            2           20  \\\n",
       "1         40.702455                1            4           13   \n",
       "2         40.752914                1            6           13   \n",
       "3         40.790157                1            0           19   \n",
       "4         40.729139                1            2           22   \n",
       "\n",
       "   euclidean_distance  \n",
       "0            0.028316  \n",
       "1            0.012655  \n",
       "2            0.040534  \n",
       "3            0.033399  \n",
       "4            0.038519  "
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('first few rows of the data after feature engineering')\n",
    "dataset.head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Preparation\n",
    "Now that our raw data has undergone various stages of data processing, we can prepare it for modeling. The most important data preparation step is splitting the dataset into training and testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split data\n",
    "y = dataset['fare_amount']\n",
    "X = dataset.drop('fare_amount', axis=1)\n",
    "\n",
    "                    # ~0.3 million rows / ~1.3 million total rows = 0.233\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.233, random_state=42)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature Scaling\n",
    "One processing step we couldn't perform earlier is **feature scaling**, because it needs to be applied after we've split our dataset into training and testing data.\n",
    "\n",
    "The reason behind this order is to prevent **information leakage** from the test set into training set. When we calculate scaling parameters using the entire dataset, we run the risk of incorporating knowledge from the test set. This could lead to overoptimistic performance and a skewed model evaluation.\n",
    "\n",
    "Hence, it's crucial to perform the train-test split before undertaking any feature scaling. By doing so, we ensure that our scaling parameters are derived solely from the training data, thereby preserving the integrity of our testing process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       pickup_longitude  pickup_latitude  dropoff_longitude  dropoff_latitude   \n",
      "count     988376.000000    988376.000000      988376.000000     988376.000000  \\\n",
      "mean           0.854487         0.523703           0.469758          0.113507   \n",
      "std            0.013524         0.007946           0.003591          0.001944   \n",
      "min            0.000000         0.000000           0.000000          0.000000   \n",
      "25%            0.852609         0.524740           0.469280          0.113728   \n",
      "50%            0.852622         0.524763           0.469284          0.113734   \n",
      "75%            0.852641         0.524781           0.469289          0.113738   \n",
      "max            1.000000         1.000000           1.000000          1.000000   \n",
      "\n",
      "       passenger_count    day_of_week    hour_of_day  euclidean_distance  \n",
      "count    988376.000000  988376.000000  988376.000000       988376.000000  \n",
      "mean          0.280980       0.506659       0.587568            0.000063  \n",
      "std           0.218229       0.324814       0.283248            0.001933  \n",
      "min           0.000000       0.000000       0.000000            0.000000  \n",
      "25%           0.166667       0.166667       0.391304            0.000004  \n",
      "50%           0.166667       0.500000       0.608696            0.000007  \n",
      "75%           0.333333       0.833333       0.826087            0.000012  \n",
      "max           1.000000       1.000000       1.000000            1.000000  \n"
     ]
    }
   ],
   "source": [
    "# feature scaling\n",
    "scaler = MinMaxScaler()\n",
    "\n",
    "# fit the scale based on the training data (avoids leakage)\n",
    "# then transform both the train and testing data\n",
    "X_train_scaled = scaler.fit_transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "\n",
    "# replace the feature data with the scaled data\n",
    "X_train = X_train_scaled\n",
    "X_test = X_test_scaled\n",
    "\n",
    "# convert scaled training data to pandas dataframe for analysis\n",
    "scaled_df = pd.DataFrame(X_train_scaled, columns=feature_names)\n",
    "print(scaled_df.describe())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After feature scaling, we can see that our ranges are significantly smaller and more similar to each other. This normalization improves the efficiency of the gradient descent optimization process in our linear regression model. With features on a similar scale, the path of gradient descent is more direct and less likely to oscillate, allowing it to converge to the minimum more quickly and accurately. Essentially, feature scaling enhances the algorithm's performance and speed, providing a more reliable and efficient learning process."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Building\n",
    "At last we've reached the model building stage, there won't be any more data preprocessing/preparation. This is the stage where we put the machine learning concepts we've been discussing into practice. The objective of this stage is to implement a linear regression model using gradient descent from scratch. We will use mini-batch gradient descent, because unfortunately we have far too many rows to use regular batch gradient descent.\n",
    "\n",
    "### Linear Regression\n",
    "Linear regression is a fundamental algorithm in supervised learning that predicts a target variable (fare_amount) by fitting the best linear relationship between the target and feature variables (hour_of_day, pickup_longitude, etc.). Linear regression achieves this \"best fit\" by minimizing a measure of the error (sum of the squared differences) between the actual and predicted values; the measure of the error is called the cost, calculated using the **cost function**.\n",
    "\n",
    "The iterative process used to minimize the cost function is called **gradient descent**. We start with random values for the coefficients (parameters), and then iteratively update these values, moving them down the gradient of the cost function. The process continues until we converge to the minimum of the function, hence achieving the optimal parameters for our linear regression model.\n",
    "\n",
    "### The Math Behind It\n",
    "While I won't delve into nitty-gritty, it's important to note that these equations are key to this implementation. Therefore, I'll present them below for your reference, as they form the mathematical foundation of the work ahead.\n",
    "\n",
    "Linear model: $ f_{\\mathbf{w},b}(\\mathbf{x}) =  w_0x_0 + w_1x_1 +... + w_{n-1}x_{n-1} + b$\n",
    "\n",
    "or in vector notation (which is what we will be using): $ f_{\\mathbf{w},b}(\\mathbf{x}) = \\mathbf{w} \\cdot \\mathbf{x} + b$\n",
    "\n",
    "Note that $\\mathbf{w}$ (parameters) and $\\mathbf{x}^{(i)}$ (one row's features) are vectors\n",
    "\n",
    "Cost function: $J(\\mathbf{w},b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})^2$\n",
    "\n",
    "- ${m}$ is the number of training examples in the data set\n",
    "\n",
    "Gradient descent:\n",
    "$$\\begin{align*}\n",
    "\\text{repeat}&\\text{ until convergence:} \\; \\lbrace \\newline\\;\n",
    "& w_j = w_j -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j} \\tag{5}  \\; & \\text{for j = 0..n-1}\\newline\n",
    "&b\\ \\ = b -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial b}  \\newline \\rbrace\n",
    "\\end{align*}$$\n",
    "\n",
    "To compute the gradient above:\n",
    "$$\\begin{align}\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j}  &= \\frac{1}{k} \\sum\\limits_{i = 0}^{k-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})x_{j}^{(i)} \\tag{6}  \\\\\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial b}  &= \\frac{1}{k} \\sum\\limits_{i = 0}^{k-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)}) \\tag{7}\n",
    "\\end{align}$$\n",
    "\n",
    "- ${k}$ is the defined batch size (instead of using all ${m}$ rows to compute the gradient)\n",
    "\n",
    "- $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)})$ is the model's prediction, while $y^{(i)}$ is the target value\n",
    "\n",
    "### Implementation\n",
    "If you've downloaded the dataset and running the notebook yourself, you can uncomment the two big commented out blocks in the gradient_descent method to watch gradient descent's progress in real time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model:\n",
    "    def __init__(self, training_examples, targets, alpha=0.01, epsilon=0.001):\n",
    "        # features and targets\n",
    "        self.m = training_examples.shape[0]\n",
    "        self.n = training_examples.shape[1]\n",
    "        self.training_examples = training_examples\n",
    "        self.targets = targets\n",
    "        \n",
    "        # initialize the parameters to random values\n",
    "        self.theta_0 = np.random.uniform(-1, 1)  # bias parameter (scalar)\n",
    "        self.theta_vector = np.random.randn(self.n)  # vector of parameters\n",
    "\n",
    "        # keeps track of the cost as iterations of gradient descent are applied\n",
    "        self.cost_history = []\n",
    "        \n",
    "        # learning rate and convergence threshold\n",
    "        self.alpha = alpha\n",
    "        self.epsilon = epsilon\n",
    "\n",
    "    def shuffle_dataset(self):\n",
    "        \"\"\" Shuffles the dataset to ensure randomness every mini-batch epoch. \"\"\"\n",
    "        \n",
    "        # create an array of indices from 0 to the size of the data\n",
    "        indices = np.arange(self.training_examples.shape[0])\n",
    "        \n",
    "        # shuffle this array of indices\n",
    "        np.random.shuffle(indices)\n",
    "        \n",
    "        # use the shuffled indices to reposition the training data and targets\n",
    "        self.training_examples = self.training_examples[indices]\n",
    "        self.targets = self.targets[indices]\n",
    "\n",
    "    def predict(self, training_example):\n",
    "        \"\"\" Makes a prediction based on the given feature inputs. \"\"\"\n",
    "        return self.theta_0 + np.dot(training_example, self.theta_vector)\n",
    "\n",
    "    \"\"\" UNVECTORIZED COST FUNCTION\n",
    "        \n",
    "        total = 0\n",
    "\n",
    "        # loop through the training examples and sum each one's squared error\n",
    "        for example, target in zip(self.training_examples, self.targets):\n",
    "            prediction = self.predict(example)\n",
    "                            # (h(x)-y)^2\n",
    "            total += (prediction - target)**2\n",
    "            \n",
    "        return total / (2*self.m) \"\"\"\n",
    "    \n",
    "    def cost(self):\n",
    "        \"\"\" Vectorized cost function, calculated on all the training examples. \"\"\"\n",
    "        predictions = self.predict(self.training_examples)\n",
    "        errors = predictions - self.targets\n",
    "        return np.sum(errors**2) / (2*self.m)\n",
    "\n",
    "    def compute_gradient(self, start: int, end: int):\n",
    "        \"\"\" Computes the gradient for the feature parameter vector and bias parameter. \"\"\"\n",
    "\n",
    "        # initialize gradient for parameter vector and bias parameter to zero\n",
    "        vector_gradient = np.zeros((self.n))\n",
    "        th0_gradient = 0\n",
    "        \n",
    "        # iterates through the given range of training rows\n",
    "        for i in range(start, end):\n",
    "            example, target = self.training_examples[i], self.targets[i]  # grabs feature row and target\n",
    "            cost = self.predict(example) - target  # makes prediction and computes cost\n",
    "\n",
    "            # add the cost to the respective gradient sums\n",
    "            vector_gradient += cost * example\n",
    "            th0_gradient += cost\n",
    "        \n",
    "        # average the gradient sums by the number of total training examples\n",
    "        vector_gradient /= self.m\n",
    "        th0_gradient /= self.m\n",
    "\n",
    "        return vector_gradient, th0_gradient\n",
    "\n",
    "    def gradient_descent(self, batch_size: int = None):\n",
    "        \"\"\" Gradient descent (batch, mini-batch, or stochastic depending the given batch size). \"\"\"\n",
    "\n",
    "        # vanilla batch gradient descent if no batch size is specified\n",
    "        if batch_size is None:\n",
    "            batch_size = self.m\n",
    "            \n",
    "        iteration = 0  # steps of gradient descent performed\n",
    "        index = 0  # position in the training set (for mini-batch)\n",
    "        \n",
    "        last_cost = float('inf')\n",
    "        current_cost = self.cost()\n",
    "        \n",
    "        # initialize cost plot (UNCOMMENT below to see real time gradient descent)\n",
    "        \"\"\" plt.figure(figsize=(10, 6))\n",
    "        plt.title('Cost Function vs. Iteration')\n",
    "        plt.xlabel('Iterations')\n",
    "        plt.ylabel('Cost') \"\"\"\n",
    "        \n",
    "        # while progress is greater than epsilon (convergence threshold), perform a step of gradient descent\n",
    "        while abs(last_cost - current_cost) > self.epsilon:\n",
    "            # computes the cost every 1000 iterations because it's an expensive operation\n",
    "            for _ in range(1000):\n",
    "                iteration += 1\n",
    "                \n",
    "                # if range is over, skip iteration, go back to start, and shuffle dataset (one epoch)\n",
    "                if index+batch_size > self.m:\n",
    "                    index = 0\n",
    "                    self.shuffle_dataset()\n",
    "                    continue\n",
    "                \n",
    "                # compute gradient and update parameters (take a step of gradient descent)\n",
    "                gradient, th0_grad = self.compute_gradient(index, index+batch_size)\n",
    "                self.theta_0 -= self.alpha * th0_grad\n",
    "                self.theta_vector -= self.alpha * gradient\n",
    "\n",
    "                # increment index by batch size\n",
    "                index = (index + batch_size) % self.m\n",
    "            \n",
    "            # set current cost to last cost and calculate new current cost\n",
    "            last_cost = current_cost\n",
    "            current_cost = self.cost()\n",
    "            \n",
    "            self.cost_history.append(current_cost)  # save cost\n",
    "            \n",
    "            # (UNCOMMENT below to see real time gradient descent)\n",
    "            \"\"\" print('iteration, index:', iteration, index)\n",
    "            \n",
    "            plt.plot(self.cost_history)\n",
    "            plt.show()\n",
    "\n",
    "            print('cost went', 'UP:' if current_cost >= last_cost else 'down:', current_cost)\n",
    "            print('difference:', abs(current_cost-last_cost)) \"\"\"\n",
    "        \n",
    "        return self.cost_history\n",
    "    \n",
    "    def batch_gradient_descent(self):\n",
    "        \"\"\" Performs default batch gradient descent (uses the whole training set per step). \"\"\"\n",
    "        return self.gradient_descent()\n",
    "\n",
    "    def mini_batch_gradient_descent(self, batch_size: int = 1500):\n",
    "        \"\"\" Performs mini-batch gradient descent given the batch size. \"\"\"\n",
    "        return self.gradient_descent(batch_size=batch_size)\n",
    "\n",
    "    def stochastic_gradient_descent(self):\n",
    "        \"\"\" Performs stochastic gradient descent (essentially batch size of 1). \"\"\"\n",
    "        return self.gradient_descent(batch_size=1)\n",
    "\n",
    "    def train(self, gradient_descent_alg):\n",
    "        return gradient_descent_alg()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Training\n",
    "Now that we've prepared our data and built our model, it's time for arguably the most crucial step: Model Training.\n",
    "\n",
    "We begin by setting our model's hyper parameters: the learning rate, denoted as alpha $\\alpha$, and the convergence threshold, epsilon $\\varepsilon$. The learning rate alpha regulates the step size our gradient descent algorithm takes when descending the cost function. Epsilon, in contrast, serves as our defined threshold that signals sufficient convergence of our model parameters. Training halts once the rate of descent dips below this specified threshold, indicating that further improvement would be minimal and perhaps unnecessary, unless we adjust our hyperparameters (mainly alpha).\n",
    "\n",
    "Given the substantial size of our dataset, using all rows for every step of gradient descent is very computationally expensive. Therefore, we resort to mini-batch gradient descent, which uses a subset of the data to calculate the gradient at each step. You might notice that when we defined gradient descent mathematically above, we used a batch size of ${k}$. This approach provides a balance - it will take a less direct path down the gradient, but it's significantly faster than using the full batch while still ensuring a reasonable estimation of the gradient, leading to steady learning progress.\n",
    "\n",
    "Once these parameters are set, we feed our training data into the model, and the learning journey commences. The model adjusts its parameters iteratively, seeking to minimize the cost function and, by extension, improve its predictive capability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize a model object and start training\n",
    "# X_train_np, y_train_np = X_train, y_train\n",
    "model = Model(X_train, y_train, alpha=1, epsilon=0.001)\n",
    "\n",
    "# for some reason scaling causes an index error for shuffling, so we need to do this\n",
    "model.training_examples = np.ascontiguousarray(model.training_examples)\n",
    "model.targets = np.ascontiguousarray(model.targets)\n",
    "    \n",
    "model.shuffle_dataset()\n",
    "_ = model.train(model.mini_batch_gradient_descent)  # using mini-batch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7m/7+/vZzu/vuu83Dhw/bx5xdhbCiFQR/q6Kav/rqK7Nr166mi4uLKanMz/fQoUPmxIkTzdDQUNPJyckMCAgwe/fubT733HPljv/hhx+WO15+fr758MMPm6Ghoaarq6vZrVs3c+nSpRX+3Cur47erIJ71z3/+0+zUqZPp7Oxs+vj4mDfffLO5e/fuMmPGjx9venh4lKuros8cAFjBME3TtCb6AQAAAEDDwj1gAAAAAFBDCGAAAAAAUEMIYAAAAABQQwhgAAAAAFBDCGAAAAAAUEMIYAAAAABQQ3gQ8yUqKSnRsWPH5OXlJcMwrC4HAAAAgEVM01RmZqZCQkLk4HD+OS4C2CU6duyYwsLCrC4DAAAAQC2RkJCgpk2bnncMAewSeXl5SSr9IXt7e1tcDQAAAACrZGRkKCwszJ4RzocAdonOXnbo7e1NAAMAAABwUbcmsQgHAAAAANQQAhgAAAAA1BACGAAAAADUEAIYAAAAANQQAhgAAAAA1BACGAAAAADUEAIYAAAAANQQAhgAAAAA1BACGAAAAADUEAIYAAAAANQQAhgAAAAA1BACGAAAAADUEAIYAAAAANQQAhgAAAAA1BACGAAAAADUEAIYAAAAANQQAlg9kJqVr4XfHdKp7AKrSwEAAABwHjarC8Dlu2vhZu1KTJeTo4N+3zPC6nIAAAAAVIIZsHrgps4hkqRPtidaXAkAAACA8yGA1QM3dQmRgyFtPXJK8Wk5VpcDAAAAoBIEsHog0NtVV7fwlyQtjWMWDAAAAKitCGD1xPAuoZJKL0M0TdPiagAAAABUhABWTwzuECRXJwcdSs3WjqPpVpcDAAAAoAK1JoDFxsbKMAxNmzatwv777rtPhmFozpw5593PggUL1KdPH/n6+srX11cDBgzQDz/8UGbMzJkzZRhGmS0oKKiazsQani42DW5feg6fbDtqcTUAAAAAKlIrAtjmzZs1f/58derUqcL+pUuXatOmTQoJCbngvtauXavRo0drzZo12rBhg8LDwzVo0CAlJpa9N6p9+/ZKSkqyb7t27aqWc7HS8K6llyF+vjNJhcUlFlcDAAAA4LcsD2BZWVkaM2aMFixYIF9f33L9iYmJmjx5st5//305OTldcH/vv/++HnzwQXXp0kVt2rTRggULVFJSoq+//rrMOJvNpqCgIPsWEBBQbedklT4t/OXv6ayT2QVav/+E1eUAAAAA+A3LA9ikSZM0dOhQDRgwoFxfSUmJxo4dq0ceeUTt27e/pP3n5OSosLBQjRs3LtO+f/9+hYSEKCoqSqNGjdLBgwfPu5/8/HxlZGSU2Wobm6ODhp15JtjH21gNEQAAAKhtLA1gixcv1rZt2xQbG1th/wsvvCCbzaYpU6Zc8jEef/xxhYaGlgl4PXr00DvvvKMVK1ZowYIFSk5OVu/evZWWllbpfmJjY+Xj42PfwsLCLrmmK2nEmcsQV+05rsy8QourAQAAAHAuywJYQkKCpk6dqvfee0+urq7l+rdu3aq5c+dq0aJFMgzjko7x4osv6oMPPtDHH39c5hg33HCDbr31VnXs2FEDBgzQF198IUl6++23K93XjBkzlJ6ebt8SEhIuqaYrrWOoj5oHeCi/qETLf0y2uhwAAAAA57AsgG3dulUpKSmKjo6WzWaTzWbTunXr9Morr8hms2nt2rVKSUlReHi4vf/IkSN66KGHFBkZecH9v/TSS3r++ee1cuXKShf3OMvDw0MdO3bU/v37Kx3j4uIib2/vMlttZBiGfRbsk+1chggAAADUJjarDty/f/9yKw/eddddatOmjR577DEFBwdr8ODBZfoHDx6ssWPH6q677jrvvv/2t7/pueee04oVKxQTE3PBWvLz87V371716dOn6idSC93cJVQvrfxZGw6mKSk9V8E+blaXBAAAAEAWBjAvLy916NChTJuHh4f8/Pzs7X5+fmX6nZycFBQUpNatW9vbxo0bp9DQUPt9ZC+++KKefvpp/fvf/1ZkZKSSk0svw/P09JSnp6ck6eGHH9awYcMUHh6ulJQUPffcc8rIyND48eOv2PnWpLDG7roqsrF+OHxSn8Yd0/39mltdEgAAAADVglUQL1d8fLySkpLsr+fNm6eCggLddtttCg4Otm8vvfSSfczRo0c1evRotW7dWrfccoucnZ21ceNGRUREWHEKV8TZZ4It5TJEAAAAoNYwTNM0rS6iLsrIyJCPj4/S09Nr5f1g6TmF6v7Xr1RQXKL/Te2jtsG1r0YAAACgPqhKNqjzM2ComI+7k65r00QSi3EAAAAAtQUBrB47exnip3GJKi5hohMAAACwGgGsHru2TYB83Jx0PCNfG36p/CHTAAAAAGoGAawec7E5aminYElchggAAADUBgSweu6WM5chLv8xSbkFxRZXAwAAADRsBLB6LjrCV0193ZRdUKyVe5KtLgcAAABo0Ahg9ZxhGBrBM8EAAACAWoEA1gCcXQ3xm/2pSs3Kt7gaAAAAoOEigDUAzQM81bmpj4pLTH2+45jV5QAAAAANFgGsgeAyRAAAAMB6BLAG4sbOIXJ0MLTjaLp+OZFldTkAAABAg0QAayD8PV3Ut6W/JGbBAAAAAKsQwBqQEd2aSip9KLNpmhZXAwAAADQ8BLAGZGDbQHk4O+roqVxtOXLK6nIAAACABocA1oC4OTvq+g7BkkpnwQAAAADULAJYA3NLt9LVEL/YmaT8omKLqwEAAAAaFgJYA9OzmZ8CvV2UnluoNftOWF0OAAAA0KAQwBoYRwdDw7vwTDAAAADACgSwBmj4mYcyr96XovScQourAQAAABoOAlgD1DbYW22CvFRQXKIvdiVZXQ4AAADQYBDAGqgRXbkMEQAAAKhpBLAG6qYuITIM6YfDJ5VwMsfqcgAAAIAGgQDWQAX7uKl3cz9J0qdxzIIBAAAANYEA1oCdXQ3x4+2JMk3T4moAAACA+o8A1oBd3yFILjYHHTyRrV2J6VaXAwAAANR7BLAGzMvVSYPaB0mSPmExDgAAAOCKI4A1cCO6hkiSPt9xTEXFJRZXAwAAANRvBLAGrk/LAPl5OCs1q0DrD6RaXQ4AAABQrxHAGjgnRwcN61w6C/bJNi5DBAAAAK4kAhg0/MxDmVfuSVZWfpHF1QAAAAD1FwEM6tzUR838PZRXWKIVPyZbXQ4AAABQbxHAIMMw7LNgrIYIAAAAXDkEMEj69aHM3/2SquMZeRZXAwAAANRPBDBIksL93BUT4SvTlD6NYxYMAAAAuBIIYLD79TLEYxZXAgAAANRPBDDY3dgpWE6OhvYmZWhfcobV5QAAAAD1DgEMdo3cnXVt6yaSWIwDAAAAuBIIYChjxJnLED/dfkwlJabF1QAAAAD1CwEMZVzbpom8XW1KzsjTxkNpVpcDAAAA1CsEMJTh6uSooZ2CJUmfbOMyRAAAAKA6EcBQztlngv3vx2TlFRZbXA0AAABQfxDAUE73yMYKbeSmrPwirdpz3OpyAAAAgHqDAIZyHBwMDe8aIklaymqIAAAAQLUhgKFCZ1dDXPfzCaVl5VtcDQAAAFA/1JoAFhsbK8MwNG3atAr777vvPhmGoTlz5px3PwsWLFCfPn3k6+srX19fDRgwQD/88EO5cfPmzVNUVJRcXV0VHR2t9evXV8NZ1B8tmnipY6iPikpMLduZZHU5AAAAQL1QKwLY5s2bNX/+fHXq1KnC/qVLl2rTpk0KCQm54L7Wrl2r0aNHa82aNdqwYYPCw8M1aNAgJSb+eindkiVLNG3aND355JPavn27+vTpoxtuuEHx8fHVdk71wfAzs2A8lBkAAACoHpYHsKysLI0ZM0YLFiyQr69vuf7ExERNnjxZ77//vpycnC64v/fff18PPvigunTpojZt2mjBggUqKSnR119/bR8ze/Zs3X333brnnnvUtm1bzZkzR2FhYXrjjTeq9dzqups6h8jRwVBcwmkdPJFldTkAAABAnWd5AJs0aZKGDh2qAQMGlOsrKSnR2LFj9cgjj6h9+/aXtP+cnBwVFhaqcePGkqSCggJt3bpVgwYNKjNu0KBB+v777yvdT35+vjIyMsps9V2Al4t+18JfkrQ07pjF1QAAAAB1n6UBbPHixdq2bZtiY2Mr7H/hhRdks9k0ZcqUSz7G448/rtDQUHvAS01NVXFxsQIDA8uMCwwMVHJycqX7iY2NlY+Pj30LCwu75Jrqklu6lV6GuHR7okzTtLgaAAAAoG6zLIAlJCRo6tSpeu+99+Tq6lquf+vWrZo7d64WLVokwzAu6RgvvviiPvjgA3388cfljvHbfZqmed7jzJgxQ+np6fYtISHhkmqqawa2C5S7s6PiT+ZoW/wpq8sBAAAA6jTLAtjWrVuVkpKi6Oho2Ww22Ww2rVu3Tq+88opsNpvWrl2rlJQUhYeH2/uPHDmihx56SJGRkRfc/0svvaTnn39eK1euLLO4h7+/vxwdHcvNdqWkpJSbFTuXi4uLvL29y2wNgbuzTde3D5LEYhwAAADA5bIsgPXv31+7du1SXFycfYuJidGYMWMUFxenCRMmaOfOnWX6Q0JC9Mgjj2jFihXn3fff/vY3/eUvf9Hy5csVExNTps/Z2VnR0dFatWpVmfZVq1apd+/e1X6e9cGIM5chLtuZpIKiEourAQAAAOoum1UH9vLyUocOHcq0eXh4yM/Pz97u5+dXpt/JyUlBQUFq3bq1vW3cuHEKDQ2130f24osv6umnn9a///1vRUZG2me6PD095enpKUmaPn26xo4dq5iYGPXq1Uvz589XfHy87r///it2vnVZ7+b+auLlopTMfK39KUWDzsyIAQAAAKgay1dBvFzx8fFKSvr1QcHz5s1TQUGBbrvtNgUHB9u3l156yT5m5MiRmjNnjmbNmqUuXbrom2++0ZdffqmIiAgrTqHWc3QwdHOX0mewLY3jMkQAAADgUhkmS9tdkoyMDPn4+Cg9Pb1B3A+2+1i6hr7yrZxtDtr85AD5uF34mWwAAABAQ1CVbFDnZ8BQM9oFe6tVoKcKikr0v11JF34DAAAAgHIIYLgohmFoRNemklgNEQAAALhUBDBctLP3gW06dFJHT+VYXA0AAABQ9xDAcNFCGrmpZ7PGkqRP445ZXA0AAABQ9xDAUCW3nHMZIuu3AAAAAFVDAEOVXN8xSC42Bx1IydLuYxlWlwMAAADUKQQwVIm3q5MGtAuUJC3ZnGBxNQAAAEDdQgBDld15Vbgk6T9bEpSSkWdxNQAAAEDdQQBDlfVu7qfoCF/lF5XoH98ctLocAAAAoM4ggKHKDMPQlP4tJUnvbzqiE5n5FlcEAAAA1A0EMFySvi391TmskfIKS/TP9cyCAQAAABeDAIZLYhiGpvZvIUl6Z8MRpWUxCwYAAABcCAEMl+za1k3UIdRbuYXF+te3h6wuBwAAAKj1CGC4ZIZhaMp1pfeCvf39YZ3OKbC4IgAAAKB2I4DhsgxsF6i2wd7KLijWW8yCAQAAAOdFAMNlKZ0FK70XbOF3h5WeW2hxRQAAAEDtRQDDZRvcPkitAj2VmV+kRd8dtrocAAAAoNYigOGyOTgY+uOZe8H+9e1BZeYxCwYAAABUhACGajGkY7BaNPFURl6R3tlwxOpyAAAAgFqJAIZq4ehg6I9n7gVbsP6gsvKLLK4IAAAAqH0IYKg2N3YKUTN/D53OKdS7zIIBAAAA5RDAUG0cHQxNuvbXWbCcAmbBAAAAgHMRwFCtbu4SovDG7jqZXaD3N8ZbXQ4AAABQqxDAUK1sjg6afGYW7B/fHFRuQbHFFQEAAAC1BwEM1W5Et1CFNnJTala+PviBWTAAAADgLAIYqp2To4P9XrA31/2ivEJmwQAAAACJAIYr5NboUIX4uColM1//2ZJgdTkAAABArUAAwxXhYnPUA9c0lyS9sfYX5RcxCwYAAAAQwHDF3NE9TEHerkpKz9N/tx61uhwAAADAcgQwXDEuNkfd36+ZJGneml9UUFRicUUAAACAtQhguKJGXRWuAC8XJZ7O1SfbmQUDAABAw0YAwxXl6uSo+/qWzoK9tuaACouZBQMAAEDDRQDDFTemR4T8PZ2VcDJXS7cnWl0OAAAAYBkCGK44N2dH3dundBbs9TUHVMQsGAAAABooAhhqxO97RsjX3UmH03L0+c5jVpcDAAAAWIIAhhrh4WLTPWdmwV5dfUDFJabFFQEAAAA1jwCGGjOuV4R83Jx08ES2vtiVZHU5AAAAQI0jgKHGeLk66e7fRUmSXv16v0qYBQMAAEADQwBDjZpwdaS8XG3an5Kl5buTrS4HAAAAqFEEMNQob1cnTby6dBbsFWbBAAAA0MAQwFDjJl4dJU8Xm/YlZ2rV3uNWlwMAAADUGAIYapyPu5Mm9I6UVDoLZprMggEAAKBhIIDBEnf/Lkruzo7afSxDq/elWF0OAAAAUCMIYLCEr4ezxvWKlMQsGAAAABqOWhPAYmNjZRiGpk2bVmH/fffdJ8MwNGfOnPPuZ/fu3br11lsVGRlZ6fiZM2fKMIwyW1BQ0OWfBKrknj5RcnNy1I6j6Vr78wmrywEAAACuuFoRwDZv3qz58+erU6dOFfYvXbpUmzZtUkhIyAX3lZOTo2bNmun//u//zhuq2rdvr6SkJPu2a9euS64fl8bf00W/7xkuSZr7FbNgAAAAqP8sD2BZWVkaM2aMFixYIF9f33L9iYmJmjx5st5//305OTldcH/du3fX3/72N40aNUouLi6VjrPZbAoKCrJvAQEBl3UeuDT39m0mF5uD4hJO69sDqVaXAwAAAFxRlgewSZMmaejQoRowYEC5vpKSEo0dO1aPPPKI2rdvX63H3b9/v0JCQhQVFaVRo0bp4MGD5x2fn5+vjIyMMhsuXxMvV93Zg1kwAAAANAyWBrDFixdr27Ztio2NrbD/hRdekM1m05QpU6r1uD169NA777yjFStWaMGCBUpOTlbv3r2VlpZW6XtiY2Pl4+Nj38LCwqq1pobs/n7N5Wxz0JYjp7ThYOV/BgAAAEBdZ1kAS0hI0NSpU/Xee+/J1dW1XP/WrVs1d+5cLVq0SIZhVOuxb7jhBt16663q2LGjBgwYoC+++EKS9Pbbb1f6nhkzZig9Pd2+JSQkVGtNDVmgt6tGdy8NtK98vd/iagAAAIArx7IAtnXrVqWkpCg6Olo2m002m03r1q3TK6+8IpvNprVr1yolJUXh4eH2/iNHjuihhx5SZGRktdbi4eGhjh07av/+yv/n38XFRd7e3mU2VJ/7r2kuZ0cHbTx4UpuYBQMAAEA9ZbPqwP379y+38uBdd92lNm3a6LHHHlNwcLAGDx5cpn/w4MEaO3as7rrrrmqtJT8/X3v37lWfPn2qdb+4eME+bro9pqne3xSvV1cfUI9mflaXBAAAAFQ7ywKYl5eXOnToUKbNw8NDfn5+9nY/v7L/E+7k5KSgoCC1bt3a3jZu3DiFhoba7yMrKCjQnj177L9PTExUXFycPD091aJFC0nSww8/rGHDhik8PFwpKSl67rnnlJGRofHjx1+x88WFPXBNcy3ZnKBvD6Rq65GTio5obHVJAAAAQLWyfBXEyxUfH6+kpCT762PHjqlr167q2rWrkpKS9NJLL6lr166655577GOOHj2q0aNHq3Xr1rrlllvk7OysjRs3KiIiwopTwBlNfd11W3RTSdIrXx+wuBoAAACg+hkm635fkoyMDPn4+Cg9PZ37wapRfFqOrv37WhWXmFo66Wp1CWtkdUkAAADAeVUlG9T5GTDUL+F+7hrRNVSS9CorIgIAAKCeIYCh1pl0bQs5GNLX+1K062i61eUAAAAA1YYAhlonyt9DN3cpnQV7ZTWzYAAAAKg/CGColSZd20KGIa3ac1y7jzELBgAAgPqBAIZaqUUTTw3rFCJJem01KyICAACgfiCAodaafF3pLNj/fkzWT8mZVpcDAAAAXDYCGGqtVoFeGtIhWJL0KveCAQAAoB4ggKFWm3xdC0nSF7uSdCCFWTAAAADUbQQw1Gptg701uH2gTFOa8xWzYAAAAKjbCGCo9ab0bynDkJbtTNLmwyetLgcAAAC4ZAQw1HrtQ3w0qnuYJOmZT3eruMS0uCIAAADg0hDAUCc8PKi1vF1t2pOUoX//EG91OQAAAMAlIYChTvDzdNFDg1pLkv6+8iedyi6wuCIAAACg6ghgqDPG9AhXmyAvnc4p1Esrf7K6HAAAAKDKCGCoM2yODpp5U3tJ0r9/iNePiekWVwQAAABUDQEMdUrPZn4a1jlEpinN/Gy3TJMFOQAAAFB3EMBQ5zwxpI3cnBy15cgpLY1LtLocAAAA4KIRwFDnBPu4afJ1LSRJsV/uU1Z+kcUVAQAAABeHAIY66Z4+UYr0c1dKZr5e/Xq/1eUAAAAAF4UAhjrJxeaoZ4aVLsjx1neH9MuJLIsrAgAAAC6MAIY669o2TdS/TRMVFpssyAEAAIA6gQCGOu3pG9vJ2dFB6/enauWe41aXAwAAAJwXAQx1WqS/h+7tGyVJ+suyPcorLLa4IgAAAKByBDDUeZOubaFgH1cdPZWrf6w7aHU5AAAAQKUIYKjz3J1temJIW0nSvLUHdPRUjsUVAQAAABUjgKFeuLFTsHo2a6z8ohL99Yu9VpcDAAAAVIgAhnrBMAzNvKm9HB0M/e/HZH13INXqkgAAAIByCGCoN9oEeWtszwhJ0jOf7VZhcYnFFQEAAABlEcBQr/xpQCs19nDWgZQsvf39YavLAQAAAMoggKFe8XF30qODW0uS5n61Xycy8y2uCAAAAPgVAQz1zh0xYerU1EeZ+UV6Yfk+q8sBAAAA7AhgqHccHAw9e1N7SdJ/tx7VtvhTFlcEAAAAlCKAoV7qGu6r26ObSpJmfrZbJSWmxRUBAAAABDDUY49e30ZeLjbtPJqu/2xJsLocAAAAgACG+ivAy0XTBraSJL244iel5xRaXBEAAAAaOgIY6rVxvSLUsomnTmYX6OWvfra6HAAAADRwBDDUa06ODvYFOd7ZcFh7kzIsrggAAAANGQEM9V7vFv4a0jFIJab0zGe7ZZosyAEAAABrEMDQIDw5tJ1cnRz0w6GT+nxnktXlAAAAoIEigKFBCG3kpgevaSFJev6LvcrOL7K4IgAAADREBDA0GH/o20xhjd2UnJGn19ccsLocAAAANEAEMDQYrk6OenpoO0nSP9cf0uHUbIsrAgAAQENDAEODMrBdoPq2ClBBcYlmLdtjdTkAAABoYAhgaFAMw9Azw9rJydHQ6n0pWr3vuNUlAQAAoAGpNQEsNjZWhmFo2rRpFfbfd999MgxDc+bMOe9+du/erVtvvVWRkZHnHT9v3jxFRUXJ1dVV0dHRWr9+/eWdAOqM5gGemnh1lCRp1ud7lF9UbHFFAAAAaChqRQDbvHmz5s+fr06dOlXYv3TpUm3atEkhISEX3FdOTo6aNWum//u//1NQUFCFY5YsWaJp06bpySef1Pbt29WnTx/dcMMNio+Pv6zzQN3xx/4t1cTLRYfTcvTP9YesLgcAAAANhOUBLCsrS2PGjNGCBQvk6+tbrj8xMVGTJ0/W+++/Lycnpwvur3v37vrb3/6mUaNGycXFpcIxs2fP1t1336177rlHbdu21Zw5cxQWFqY33nij0v3m5+crIyOjzIa6y9PFpieGtJUkvbb6gJLScy2uCAAAAA2B5QFs0qRJGjp0qAYMGFCur6SkRGPHjtUjjzyi9u3bV8vxCgoKtHXrVg0aNKhM+6BBg/T9999X+r7Y2Fj5+PjYt7CwsGqpB9a5uUuIukf6KrewWM9/uc/qcgAAANAAWBrAFi9erG3btik2NrbC/hdeeEE2m01TpkyptmOmpqaquLhYgYGBZdoDAwOVnJxc6ftmzJih9PR0+5aQkFBtNcEahmFo5k3t5WBIn+84po0H06wuCQAAAPWcZQEsISFBU6dO1XvvvSdXV9dy/Vu3btXcuXO1aNEiGYZR7cf/7T5N0zzvcVxcXOTt7V1mQ93XPsRHd/YIlyTN/Gy3iopLLK4IAAAA9ZllAWzr1q1KSUlRdHS0bDabbDab1q1bp1deeUU2m01r165VSkqKwsPD7f1HjhzRQw89pMjIyEs+rr+/vxwdHcvNdqWkpJSbFUPD8NDA1mrk7qR9yZl6fxMLsQAAAODKsSyA9e/fX7t27VJcXJx9i4mJ0ZgxYxQXF6cJEyZo586dZfpDQkL0yCOPaMWKFZd8XGdnZ0VHR2vVqlVl2letWqXevXtf7mmhDvL1cNbDg1pLkv6+8ielZeVbXBEAAADqK5tVB/by8lKHDh3KtHl4eMjPz8/e7ufnV6bfyclJQUFBat26tb1t3LhxCg0Ntd9HVlBQoD179th/n5iYqLi4OHl6eqpFixaSpOnTp2vs2LGKiYlRr169NH/+fMXHx+v++++/YueL2m30VeH64Id47T6Wob+t+En/d2vFj0QAAAAALoflqyBervj4eCUlJdlfHzt2TF27dlXXrl2VlJSkl156SV27dtU999xjHzNy5EjNmTNHs2bNUpcuXfTNN9/oyy+/VEREhBWngFrA0cHQszeVrrS5ZEuCdh49bW1BAAAAqJcM0zRNq4uoizIyMuTj46P09HQW5KhH/rQkTp9sT1SXsEb6+IHecnCo/gVgAAAAUL9UJRvU+RkwoDrNuKGNPJwdFZdwWh9tO2p1OQAAAKhnCGDAOZp4u2pK/5aSpP/73z6lsiAHAAAAqhEBDPiNu66OUpsgL6VlF+jxj3aKq3QBAABQXQhgwG842xw0Z1QXOTs66Ku9KfrghwSrSwIAAEA9QQADKtAmyFuPXl/6uIO/LNujgyeyLK4IAAAA9QEBDKjExKujdHULP+UWFutPS+JUWFxidUkAAACo4whgQCUcHAy9dHtnebvatONoul5dfcDqkgAAAFDHEcCA8wj2cdPzt3SUJL22er+2HjllcUUAAACoywhgwAXc2ClEt3QNVYlZ+qDmrPwiq0sCAABAHUUAAy7CzJvbK7SRm+JP5mjW57utLgcAAAB1FAEMuAjerk6afUdnGYb0ny1HtfzHZKtLAgAAQB1EAAMuUo9mfrq/X3NJ0oyPdyolI8/iigAAAFDXEMCAKvjTgFZqH+KtUzmFevi/O2WaptUlAQAAoA4hgAFV4Gxz0NxRXeRic9A3P5/QOxuOWF0SAAAA6hACGFBFLZp46YkhbSVJz3+5V/uPZ1pcEQAAAOoKAhhwCcb1ilC/VgHKLyrRtCVxKigqsbokAAAA1AGXFMBmzZqlnJyccu25ubmaNWvWZRcF1HaGYehvt3WSr7uTdh/L0Mtf/Wx1SQAAAKgDDPMSVhFwdHRUUlKSmjRpUqY9LS1NTZo0UXFxcbUVWFtlZGTIx8dH6enp8vb2trocWGT5j0m6/71tMgxp8b091aOZn9UlAQAAoIZVJRtc0gyYaZoyDKNc+44dO9S4ceNL2SVQJ13fIVh3xDSVaUrT/7NDGXmFVpcEAACAWsxWlcG+vr4yDEOGYahVq1ZlQlhxcbGysrJ0//33V3uRQG3252HttfHgScWfzNHMT3dr9sguVpcEAACAWqpKAWzOnDkyTVMTJ07Us88+Kx8fH3ufs7OzIiMj1atXr2ovEqjNPF1senlkF93+5vf6eHuirm3TRMM6h1hdFgAAAGqhS7oHbN26dbr66qtls1Upv9Ur3AOG35q98ie9svqAvF1tWvGnvgr2cbO6JAAAANSAK34PmJeXl/bu3Wt//emnn2r48OF64oknVFBQcCm7BOq8P/Zvqc5NfZSRV6SH/rNDJSVV/rcNAAAA1HOXFMDuu+8+/fxz6bLbBw8e1MiRI+Xu7q4PP/xQjz76aLUWCNQVTo4OenlkF7k5Oer7X9L01neHrC4JAAAAtcwlBbCff/5ZXbp0kSR9+OGH6tevn/79739r0aJF+uijj6qzPqBOaRbgqadubCtJenH5T9qXnGFxRQAAAKhNLnkZ+pKSEknSV199pSFDhkiSwsLClJqaWn3VAXXQnVeFq3+bJiooLtG0xXHKK6z/z8UDAADAxbmkABYTE6PnnntO7777rtatW6ehQ4dKkg4dOqTAwMBqLRCoawzD0Au3dZK/p7P2JWfqpRU/WV0SAAAAaolLCmBz5szRtm3bNHnyZD355JNq0aKFJOm///2vevfuXa0FAnWRv6eLXri1kyTpn98e0ncHmBkGAADAJS5DX5m8vDw5OjrKycmpunZZa7EMPS7GE5/s0r83xSvI21XLp/VRI3dnq0sCAABANatKNrisB3lt3bpVe/fulWEYatu2rbp163Y5uwPqnaeGttWGX9J0KDVbTy79Ua+N7irDMKwuCwAAABa5pEsQU1JSdO2116p79+6aMmWKJk+erJiYGPXv318nTpyo7hqBOsvd2aY5I7vI0cHQFzuTtDQu0eqSAAAAYKFLCmB//OMflZmZqd27d+vkyZM6deqUfvzxR2VkZGjKlCnVXSNQp3UOa6Rp/VtKkv68dLcSTuZYXBEAAACsckn3gPn4+Oirr75S9+7dy7T/8MMPGjRokE6fPl1d9dVa3AOGqigqLtEd/9igbfGndVVkY33wh55ydOBSRAAAgPqgKtngkmbASkpKKlxow8nJyf58MAC/sjk66OWRXeTh7KgfDp/U/G8OWl0SAAAALHBJAey6667T1KlTdezYMXtbYmKi/vSnP6l///7VVhxQn0T4eeiZm9pLkmav+kk/JqZbXBEAAABq2iUFsNdee02ZmZmKjIxU8+bN1aJFC0VFRSkzM1OvvvpqddcI1Bu3RzfV9e2DVFhsauri7cotKLa6JAAAANSgy3oO2KpVq7Rv3z6Zpql27dppwIAB1VlbrcY9YLhUJ7MLNHjONzqRma/xvSL07M0drC4JAAAAl+GK3QO2evVqtWvXThkZGZKkgQMH6o9//KOmTJmi7t27q3379lq/fv2lVw40AI09nPXS7Z0lSW9vOKK1P6VYXBEAAABqSpUC2Jw5c3TvvfdWmOp8fHx03333afbs2dVWHFBf9WsVoAm9IyVJj/x3p05mF1hbEAAAAGpElQLYjh07dP3111faP2jQIG3duvWyiwIagsdvaKMWTTx1IjNfj3+0U5dxNTAAAADqiCoFsOPHj1e4/PxZNptNJ06cuOyigIbA1clRc0Z2kZOjoZV7juvDLUetLgkAAABXWJUCWGhoqHbt2lVp/86dOxUcHHzZRQENRYdQH00f2FqSNPPz3dqblGFxRQAAALiSqhTAhgwZoj//+c/Ky8sr15ebm6tnnnlGN954Y7UVBzQEf+jbTL2b+ymnoFgTF23W8Yzy/30BAACgfqhSAHvqqad08uRJtWrVSi+++KI+/fRTffbZZ3rhhRfUunVrnTx5Uk8++eQlFRIbGyvDMDRt2rQK+++77z4ZhqE5c+ZccF8fffSR2rVrJxcXF7Vr106ffPJJmf6ZM2fKMIwyW1BQ0CXVDVwuRwdDb4yJVvMADyWl5+muhZuVlV9kdVkAAAC4AqoUwAIDA/X999+rQ4cOmjFjhkaMGKHhw4friSeeUIcOHfTdd98pMDCwykVs3rxZ8+fPV6dOnSrsX7p0qTZt2qSQkJAL7mvDhg0aOXKkxo4dqx07dmjs2LG64447tGnTpjLj2rdvr6SkJPt2vksrgSvNx91Ji+66Sv6eztqTlKE//nubiopLrC4LAAAA1axKAUySIiIi9OWXXyo1NVWbNm3Sxo0blZqaqi+//FKRkZFVLiArK0tjxozRggUL5OvrW64/MTFRkydP1vvvv3/eBUDOmjNnjgYOHKgZM2aoTZs2mjFjhvr3719u5sxmsykoKMi+BQQEVLl2oDqFNXbXP8d3l6uTg9b8dEIzP9/NyogAAAD1TJUD2Fm+vr7q3r27rrrqqgqD08WaNGmShg4dqgEDBpTrKykp0dixY/XII4+offv2F7W/DRs2aNCgQWXaBg8erO+//75M2/79+xUSEqKoqCiNGjVKBw8ePO9+8/PzlZGRUWYDqluXsEaaM7KrDEN6b2O8/rn+kNUlAQAAoBpdcgCrDosXL9a2bdsUGxtbYf8LL7wgm82mKVOmXPQ+k5OTy10GGRgYqOTkZPvrHj166J133tGKFSu0YMECJScnq3fv3kpLS6t0v7GxsfLx8bFvYWFhF10TUBXXdwjSk0PaSpKe/99e/W9XksUVAQAAoLpYFsASEhI0depUvffee3J1dS3Xv3XrVs2dO1eLFi2SYRhV2vdvx5umWabthhtu0K233qqOHTtqwIAB+uKLLyRJb7/9dqX7nDFjhtLT0+1bQkJClWoCquLu30VpXK8ImaY0bUmctsWfsrokAAAAVAPLAtjWrVuVkpKi6Oho2Ww22Ww2rVu3Tq+88opsNpvWrl2rlJQUhYeH2/uPHDmihx566Lz3mgUFBZWZ7ZKklJSU8y4O4uHhoY4dO2r//v2VjnFxcZG3t3eZDbhSDMPQn29sp/5tmii/qET3vr1F8Wk5VpcFAACAy2RZAOvfv7927dqluLg4+xYTE6MxY8YoLi5OEyZM0M6dO8v0h4SE6JFHHtGKFSsq3W+vXr20atWqMm0rV65U7969K31Pfn6+9u7dy0OkUavYHB30yuiuah/irbTsAk1Y9INO5xRYXRYAAAAug82qA3t5ealDhw5l2jw8POTn52dv9/PzK9Pv5OSkoKAgtW7d2t42btw4hYaG2u8jmzp1qvr27asXXnhBN998sz799FN99dVX+vbbb+3vefjhhzVs2DCFh4crJSVFzz33nDIyMjR+/PgrdbrAJfFwsemtCd014vXvdPBEtv7w7la9e/dVcrE5Wl0aAAAALoGli3BUh/j4eCUl/bpIQe/evbV48WItXLhQnTp10qJFi7RkyRL16NHDPubo0aMaPXq0WrdurVtuuUXOzs7auHGjIiIirDgF4LwCvV311l3d5eVi0w+HTuqx/+5keXoAAIA6yjD5P7lLkpGRIR8fH6Wnp3M/GGrE+v0ndNfCzSoqMTXluhaaPqj1hd8EAACAK64q2aDOz4ABDUWflgH664jSy3NfWX1AH25hJU4AAIC6hgAG1CEju4dr0rXNJUkzPt6l7w6kWlwRAAAAqoIABtQxDw1srZs6h6ioxNT9723Vz8czrS4JAAAAF4kABtQxDg6G/nZ7J3WP9FVmXpHuWrhZKZl5VpcFAACAi0AAA+ogF5uj5o+NUZS/hxJP5+ruRVuUU1BkdVkAAAC4AAIYUEf5ejhr4YTuauzhrF2J6ZryQZyKS1jUFAAAoDYjgAF1WKS/hxaMi5azzUFf7T2uvyzbY3VJAAAAOA8CGFDHRUc01st3dJEkLfr+sN769pC1BQEAAKBSBDCgHhjaKViP39BGkvSXL/Zo5e5kiysCAABARQhgQD1xX99murNHuExTmrJ4u3YknLa6JAAAAPwGAQyoJwzD0Kyb2qtfqwDlFZbo7re3KOFkjtVlAQAA4BwEMKAesTk66PUx3dQ22FupWfmauGiz0nMLrS4LAAAAZxDAgHrG08WmtybEKMjbVftTsvTAe1tVUFRidVkAAAAQAQyol4J93PTWhO7ycHbU97+kacbHu2SaPCMMAADAagQwoJ5qF+Kt18Z0k6ODoY+2HdWrqw9YXRIAAECDRwAD6rFrWzfRrJvbS5Jmr/pZn2w/anFFAAAADRsBDKjnxvSI0H39mkmSHv3vTm08mGZxRQAAAA0XAQxoAB4b3EZDOwarsNjUH97ZogMpWVaXBAAA0CARwIAGwMHB0N/v6Kxu4Y2UkVekuxb9oNSsfKvLAgAAaHAIYEAD4erkqAXjYhTh566Ek7m65+0tyikosrosAACABoUABjQgfp4uWjihuxq5Oyku4bQmLNys7HxCGAAAQE0hgAENTLMAT701obu8XGz64dBJjX/rB2XmFVpdFgAAQINAAAMaoG7hvnrvnh7ydrVpy5FTGvfWD0rPJYQBAABcaQQwoIHqHNZI/763pxq5O2l7/GmN/dcmnc4psLosAACAeo0ABjRgHUJ99O97eqqxh7N2Hk3XnQs26VQ2IQwAAOBKIYABDVy7EG99cG9P+Xs6a09ShkYv2Kg0lqgHAAC4IghgANQ6yEuL/9BTAV4u2pecqVHzNyolM8/qsgAAAOodAhgASVKLJl5a8oeeCvJ21f6ULI2av1HHMwhhAAAA1YkABsCuWYCnltzXUyE+rjp4Iluj5m9UUnqu1WUBAADUGwQwAGVE+HloyX291NTXTYdSszXyHxt19FSO1WUBAADUCwQwAOWENXbXkvt6KcLPXfEnczTyHxuVcJIQBgAAcLkIYAAqFNrITUv+0EtR/h5KPJ2rO/6xQYdTs60uCwAAoE4jgAGoVJCPq5b8oaeaB3goKT1PI+dv0C8nsqwuCwAAoM4igAE4ryberlr8h15qFeip4xn5GjV/o/Yfz7S6LAAAgDqJAAbgggK8XPTBvT3VJshLJzJLQ9i+5AyrywIAAKhzCGAALoqfZ2kIax/irbTsAo2ev1G7j6VbXRYAAECdQgADcNF8PZz173t6qnNTH53KKdSdCzZp11FCGAAAwMUigAGoEh93J717Tw91C2+k9NxC3fnPjYpLOG11WQAAAHUCAQxAlXm7Oumdu3uoe6SvMvOK9Pt/btLWIyetLgsAAKDWI4ABuCSeLjYtuusq9WzWWFn5RRr3rx/0wyFCGAAAwPkQwABcMg8XmxZOuEpXt/BTdkGxxr/1g77/JdXqsgAAAGotAhiAy+Lm7Kh/je+uvq0ClFtYrImLNmv9/hNWlwUAAFArEcAAXDZXJ0fNHxut69o0UV5hie5+e4vW/JRidVkAAAC1DgEMQLVwdXLUm7+P1sB2gSooKtF972zVV3uOW10WAABArVJrAlhsbKwMw9C0adMq7L/vvvtkGIbmzJlzwX199NFHateunVxcXNSuXTt98skn5cbMmzdPUVFRcnV1VXR0tNavX3+ZZwDA2eageWO66YYOQSooLtED72/V8h+TrS4LAACg1qgVAWzz5s2aP3++OnXqVGH/0qVLtWnTJoWEhFxwXxs2bNDIkSM1duxY7dixQ2PHjtUdd9yhTZs22ccsWbJE06ZN05NPPqnt27erT58+uuGGGxQfH19t5wQ0VE6ODnpldFfd2ClYhcWmJv97m77YmWR1WQAAALWC5QEsKytLY8aM0YIFC+Tr61uuPzExUZMnT9b7778vJyenC+5vzpw5GjhwoGbMmKE2bdpoxowZ6t+/f5mZs9mzZ+vuu+/WPffco7Zt22rOnDkKCwvTG2+8UZ2nBjRYTo4OmjOyi0Z0DVVRiakpi7fr07hEq8sCAACwnOUBbNKkSRo6dKgGDBhQrq+kpERjx47VI488ovbt21/U/jZs2KBBgwaVaRs8eLC+//57SVJBQYG2bt1absygQYPsYyqSn5+vjIyMMhuAytkcHfTS7Z11W3RTFZeY+tOSOL278YjVZQEAAFjK0gC2ePFibdu2TbGxsRX2v/DCC7LZbJoyZcpF7zM5OVmBgYFl2gIDA5WcXHofSmpqqoqLi887piKxsbHy8fGxb2FhYRddE9BQOToYevHWThp9VbhKTOnppT/qqaW7VFhcYnVpAAAAlrAsgCUkJGjq1Kl677335OrqWq5/69atmjt3rhYtWiTDMKq079+ON02zXNvFjDnXjBkzlJ6ebt8SEhKqVBPQUDk4GHp+RAc9en1rGYb03sZ4jf3XJp3MLrC6NAAAgBpnWQDbunWrUlJSFB0dLZvNJpvNpnXr1umVV16RzWbT2rVrlZKSovDwcHv/kSNH9NBDDykyMrLS/QYFBZWbyUpJSbHPePn7+8vR0fG8Yyri4uIib2/vMhuAi2MYhh68poUWjI2Rh7OjNh48qZtf/1Y/JWdaXRoAAECNsiyA9e/fX7t27VJcXJx9i4mJ0ZgxYxQXF6cJEyZo586dZfpDQkL0yCOPaMWKFZXut1evXlq1alWZtpUrV6p3796SJGdnZ0VHR5cbs2rVKvsYAFfGgHaB+mTS1Qpv7K6Ek7m6Zd53WrmbZeoBAEDDYbPqwF5eXurQoUOZNg8PD/n5+dnb/fz8yvQ7OTkpKChIrVu3treNGzdOoaGh9vvIpk6dqr59++qFF17QzTffrE8//VRfffWVvv32W/t7pk+frrFjxyomJka9evXS/PnzFR8fr/vvv/9KnS6AM1oFeunTSVfrwfe3acPBNN333lY9PKi1HrymeZUvNwYAAKhrLAtg1SU+Pl4ODr9O5PXu3VuLFy/WU089paefflrNmzfXkiVL1KNHD/uYkSNHKi0tTbNmzVJSUpI6dOigL7/8UhEREVacAtDg+Ho46527r9Jflu3ROxuO6G8rftK+5Ey9eGsnuTk7Wl0eAADAFWOYpmlaXURdlJGRIR8fH6Wnp3M/GHAZ3t90RM98ultFJaY6hvpo/rhoBfu4WV0WAADARatKNrD8OWAAGrYxPSL03j095OvupF2J6brpte+0Lf6U1WUBAABcEQQwAJbr2cxPn03+ndoEeelEZr5G/WOjPtp61OqyAAAAqh0BDECtENbYXf99oLcGtQtUQXGJHvpwh57/cq+KS7hKGgAA1B8EMAC1hqeLTW/+Plp/vK6FJGn+Nwc1cdFmZeQVWlwZAABA9SCAAahVHBwMPTSotV4d3VWuTg5a9/MJDX/9Ox1Kzba6NAAAgMtGAANQKw3rHKL/3t9bwT6uOngiWze/9q3W7z9hdVkAAACXhQAGoNbqEOqjTydfrW7hjZSRV6Txb/2gt749JJ6eAQAA6ioCGIBarYmXqz74Q0/dFt1UJaY0a9kePf7RLuUXFVtdGgAAQJURwADUei42R/3ttk56amhbORjSki0JGrNgk05k5ltdGgAAQJUQwADUCYZh6J4+zfTWhO7ycrVpy5FTuvm1b7X7WLrVpQEAAFw0AhiAOuWa1k20dNLVaubvoWPpebrtjQ36cleS1WUBAABcFAIYgDqneYCnPnnwavVtFaDcwmI9+P42zV71s0p4aDMAAKjlCGAA6iQfdye9NT5G9/wuSpL0ytf79eD725SdX2RxZQAAAJUjgAGos2yODnrqxnZ68bZOcnZ00PLdybr1je919FSO1aUBAABUiAAGoM67IyZMH/yhh/w9XbQvOVM3v/adfjh00uqyAAAAyiGAAagXoiMa67PJV6t9iLfSsgs05p8btfC7Q9wXBgAAahUCGIB6I6SRm/57f28N7RSswmJTz36+R7//1yYuSQQAALUGAQxAveLm7KjXRnfVrJvby9XJQd//kqbr56zXf7YkyDSZDQMAANYigAGodwzD0Lhekfrf1L7qFt5IWflFevS/O3XvO1uUkplndXkAAKABI4ABqLei/D304f299dj1beTs6KCv9qZo0MvfaNnOY1aXBgAAGigCGIB6zdHB0APXNNdnf7xa7YK9dTqnUJP/vV1//GC7TucUWF0eAABoYAhgABqENkHeWjrpak25roUcHQx9vuOYBr78jdbsS7G6NAAA0IAQwAA0GM42B00f1FofPdBbzQM8dCIzX3ct2qzHP9qpzLxCq8sDAAANAAEMQIPTJayRvpjSR3f/LkqGIS3enKDr56zXhl/SrC4NAADUcwQwAA2Sq5Ojnr6xnT64t6ea+rop8XSuRi/YqGc/3628wmKrywMAAPUUAQxAg9azmZ+WT+ur0VeFS5IWfndYQ15Zr+3xpyyuDAAA1EcEMAANnqeLTbG3dNTCu7qriZeLDp7I1q1vfK+XVvykgqISq8sDAAD1CAEMAM64tnUTrfxTX93cJUQlpvTamgO6+fXvtDcpw+rSAABAPUEAA4BzNHJ31txRXTVvTDf5ujtpb1KGbnrtW81be0BFxcyGAQCAy0MAA4AKDOkYrJV/6qcBbQNVWGzqxeU/6fZ/bNDBE1lWlwYAAOowAhgAVCLAy0ULxkXrpds7y8vFpu3xpzXklfVa9N0hlZSYVpcHAADqIAIYAJyHYRi6Lbqplv+pr65u4ae8whLN/HyPfv+vTTp6Ksfq8gAAQB1DAAOAixDayE3vTuyhWTe3l6uTg77/JU3Xz1mv/2xJkGkyGwYAAC4OAQwALpKDg6FxvSL1v6l91S28kbLyi/Tof3fqnre3KCUzz+ryAABAHUAAA4AqivL30If399Zj17eRs6ODvt6XokEvf6Ol2xOZDQMAAOdFAAOAS+DoYOiBa5rrsz9erXbB3jqdU6hpS+J06xvfKy7htNXlAQCAWooABgCXoU2Qt5ZOuloPD2olNydHbYs/reGvf6fpS+KUnM5liQAAoCzD5HqZS5KRkSEfHx+lp6fL29vb6nIA1ALHM/L04vKf9NG2o5IkNydHPXBNc93bp5ncnB0trg4AAFwpVckGBLBLRAADUJkdCac1a9kebT1ySpIU4uOqx25oo5s6h8gwDIurAwAA1Y0AVgMIYADOxzRNLduZpP/73z4lns6VJHULb6Q/D2uvLmGNrC0OAABUKwJYDSCAAbgYeYXFWvDNQc1b+4tyC4slSbd0DdWj17dRkI+rxdUBAIDqQACrAQQwAFVR0f1h9/drrj/05f4wAADqOgJYDSCAAbgU3B8GAED9QwCrAQQwAJeK+8MAAKhfqpINas1zwGJjY2UYhqZNm2Zvmzlzptq0aSMPDw/5+vpqwIAB2rRp03n3U1hYqFmzZql58+ZydXVV586dtXz58jJjZs6cKcMwymxBQUFX4rQAoBzDMDSsc4i+fqifHhrI88MAAGhIakUA27x5s+bPn69OnTqVaW/VqpVee+017dq1S99++60iIyM1aNAgnThxotJ9PfXUU/rHP/6hV199VXv27NH999+vESNGaPv27WXGtW/fXklJSfZt165dV+TcAKAyrk6O+mP/llr7yDW6tVtTSdLH2xN17UtrNfer/cotKLa4QgAAUN0svwQxKytL3bp107x58/Tcc8+pS5cumjNnToVjz07tffXVV+rfv3+FY0JCQvTkk09q0qRJ9rbhw4fL09NT7733nqTSGbClS5cqLi7ukuvmEkQA1Y37wwAAqJvq1CWIkyZN0tChQzVgwIDzjisoKND8+fPl4+Ojzp07VzouPz9frq5ll3Z2c3PTt99+W6Zt//79CgkJUVRUlEaNGqWDBw+e9/j5+fnKyMgoswFAdeoc1kj/vb+XXh3dVaGN3HQsPU9TF8fp1je+V1zCaavLAwAA1cDSALZ48WJt27ZNsbGxlY5ZtmyZPD095erqqpdfflmrVq2Sv79/peMHDx6s2bNna//+/SopKdGqVav06aefKikpyT6mR48eeuedd7RixQotWLBAycnJ6t27t9LS0irdb2xsrHx8fOxbWFjYpZ00AJwH94cBAFC/WXYJYkJCgmJiYrRy5Ur7jNY111xT7hLE7OxsJSUlKTU1VQsWLNDq1au1adMmNWnSpML9njhxQvfee68+//xzGYah5s2ba8CAAVq4cKFycnIqfE92draaN2+uRx99VNOnT69wTH5+vvLz8+2vMzIyFBYWxiWIAK4onh8GAEDtVyeWoV+6dKlGjBghR8df/weiuLhYhmHIwcFB+fn5ZfrOatmypSZOnKgZM2acd/95eXlKS0tTSEiIHn/8cS1btky7d++udPzAgQPVokULvfHGGxdVP/eAAahJFd0f9sj1rTWsU4hsjpZfTQ4AQINWJ+4B69+/v3bt2qW4uDj7FhMTozFjxiguLq7C8CWVPj/n3Jmoyri6uio0NFRFRUX66KOPdPPNN1c6Nj8/X3v37lVwcPAlnw8AXEkV3R/2pyU7NGD2Oi3ZHK+CohKrSwQAABfBZtWBvby81KFDhzJtHh4e8vPzU4cOHZSdna2//vWvuummmxQcHKy0tDTNmzdPR48e1e23325/z7hx4xQaGmq/j2zTpk1KTExUly5dlJiYqJkzZ6qkpESPPvqo/T0PP/ywhg0bpvDwcKWkpOi5555TRkaGxo8fXzMnDwCX4Oz9YQPbBepf3x7SP9cf1OG0HD320S7N/Wq/7uvXXCO7h8nViUsTAQCorSwLYBfi6Oioffv26e2331Zqaqr8/PzUvXt3rV+/Xu3bt7ePi4+Pl4PDrxN5eXl5euqpp3Tw4EF5enpqyJAhevfdd9WoUSP7mKNHj2r06NFKTU1VQECAevbsqY0bNyoiIqImTxEALomrk6MmXdtCE3pH6t+b4jV//UEdS8/TM5/t1qurD+jePlEa0zNCni619iseAIAGy/LngNVV3AMGoLbIKyzWh1sS9Oa6g0o8nStJ8nFz0sSrozShd6R83J0srhAAgPqtTizCUdcRwADUNoXFJVq6PVHz1v6iQ6nZkiRPF5t+3zNC9/SJkr+ni8UVAgBQPxHAagABDEBtVVxi6stdSXp9zQHtS86UJLk6OWhU93Dd16+Zgn3cLK4QAID6hQBWAwhgAGq7khJTX+9L0WtrDmhHwmlJkpOjoduim+r+fs0V4edhbYEAANQTBLAaQAADUFeYpqlvD6TqtdUHtOnQSUmSgyHd3CVUD17TXC0DvSyuEACAuo0AVgMIYADqos2HT+q11Qe07ucTkiTDkK5vH6RJ17ZQh1Afi6sDAKBuIoDVAAIYgLps19F0vb7mgJbvTra3XdM6QH+8roWiIxpbWBkAAHUPAawGEMAA1Ac/H8/UvDUH9NmOYyo587dBz2aN9cfrWqp3cz8ZhmFtgQAA1AEEsBpAAANQnxxOzdab637RR9uOqrC49K+FLmGNNPnaFurftglBDACA8yCA1QACGID66NjpXM3/5qA++CFe+UUlkqQ2QV6afF0L3dAhWI4OBDEAAH6LAFYDCGAA6rMTmfn617eH9O6Gw8ouKJYkRfl7aPRVYbqlW1Me6gwAwDkIYDWAAAagITidU6BF3x/Wwu8OKz23UFLps8QGtgvUyO7h+l0Lf2bFAAANHgGsBhDAADQkWflF+nzHMS3enGB/qLMkhTZy0+0xTXVHTJhCGrlZVyAAABYigNUAAhiAhmpvUoaWbE7Qx9uOKiOvSFLp88T6tQrQqO5h6t82UE6ODhZXCQBAzSGA1QACGICGLq+wWCt2J2vxDwnacDDN3u7v6axbuzXVyO5hahbgaWGFAADUDAJYDSCAAcCvDqdma8mWBP1361GdyMy3t18V1Vijuofphg7BcnN2tLBCAACuHAJYDSCAAUB5hcUlWrMvRUs2J2jNTyn2hzt7udo0vEuoRl0VpvYhPtYWCQBANSOA1QACGACcX3J6nv67NUFLtiQo4WSuvb1jqI9Gdg/TTV1C5O3qZGGFAABUDwJYDSCAAcDFKSkx9f0vaVq8OV4rdx9XQXHpA55dnRw0tGOIRl8VpugIXxkGy9kDAOomAlgNIIABQNWdzC7QJ9sTtfiHeO1PybK3Nw/w0Kju4bqlW6j8eMgzAKCOIYDVAAIYAFw60zS1Lf60lmyO1+c7kpRbWCzp14c8jzrzkGcHHvIMAKgDCGA1gAAGANUjM69Qy3YmafEP8dpxNN3eHtrITTd2DtawTiFqH+LNJYoAgFqLAFYDCGAAUP32HMvQf7aUfcizJEX6uWtop2Dd2ClEbYK8CGMAgFqFAFYDCGAAcOXkFRZr9b4ULdt5TKv3pSivsMTe1zzAQ0M7hWhYp2C1DPSysEoAAEoRwGoAAQwAakZ2fpG+3peiZTuOae3PJ1RQ9GsYaxXoqRs7hejGTsFqFuBpYZUAgIaMAFYDCGAAUPMy8wr11d7jWrYjSd/sP6HC4l//Cmsb7K0bOwXrxk7BivDzsLBKAEBDQwCrAQQwALBWem6hVu5O1he7kvTt/lQVlfz611nHUB/d2ClYQzoGK6yxu4VVAgAaAgJYDSCAAUDtcSq7QCvOhLHvf0lT8TlhrEtYI3sYC2nkZmGVAID6igBWAwhgAFA7pWXla/nuZC3bkaRNh9J0ThZTTISvhnYK1tCOwWri7WpdkQCAeoUAVgMIYABQ+6Vk5mn5j6VhbPORkzr7N55hSFdFNtaNnYJ1fYdgBXi5WFsoAKBOI4DVAAIYANQtyel5+nJXkpbtPKZt8aft7Q6G1Ku5n4Z2DNGAtk2YGQMAVBkBrAYQwACg7ko8nasvdyZp2a4k7Ug4XaavTZCX+rUOUL9WAYqJaCxnm4M1RQIA6gwCWA0ggAFA/ZBwMkfLdiZp+e5k7Tx6Wuf+rejh7Khezf1LA1nLAIX7saIiAKA8AlgNIIABQP1zMrtA6/ef0LqfT+ibn1OVmpVfpj/K30P9WpXOjvVo1ljuzjaLKgUA1CYEsBpAAAOA+q2kxNTe5Ayt+/mE1v10QluPnCrzrDFnRwddFdW4NJC1DlDLJp4yDMPCigEAViGA1QACGAA0LJl5hfr+lzR98/MJrf3phBJP55bpD/ZxVb9WAerbKkBXt/CXj5uTRZUCAGoaAawGEMAAoOEyTVMHU7O17qfSyxU3HkxTflGJvd/RwVDXsEb22bEOIT5ycGB2DADqKwJYDSCAAQDOyiss1g+HTpZervjzCR1IySrT39jDWX1a+qtfqwD1aRnAc8cAoJ4hgNUAAhgAoDKJp3P1zZl7x747kKrM/KIy/e1DvNWvVYB6N/dX1/BG8nBhMQ8AqMsIYDWAAAYAuBiFxSXaHn9a635O0Tc/p2pXYnqZfkcHQ22DvRQT0VjdIxsrJtJXgTwMGgDqFAJYDSCAAQAuxYnMfH17oHSZ+82HT+roqdxyY8Iau6l7RGNFR/qqe2RjtQjw5B4yAKjFCGA1gAAGAKgOSem52nL4lLYeOaXNh09qb1KGSn7zN7OPm5OiI3wVcyaQdQz1kauTozUFAwDKIYDVAAIYAOBKyMwrVFzCaW0+fEpbDp/U9vjTyi0sLjPG2dFBHZv6KCbSVzERjRUT4StfD2eLKgYAEMBqAAEMAFATCotLtDcpQ5sPn9LWIye1+fApncjMLzeuRRNPxUT4KiaysbpH+iq8sTsPhgaAGkIAqwEEMACAFUzTVPzJHG05fEpbzgSy3y57L0n+ni7qHlkayGIifNUuxFtOjg4WVAwA9V9VskGt+SaOjY2VYRiaNm2avW3mzJlq06aNPDw85OvrqwEDBmjTpk3n3U9hYaFmzZql5s2by9XVVZ07d9by5cvLjZs3b56ioqLk6uqq6OhorV+/vrpPCQCAamcYhiL8PHRrdFPF3tJJX03vp+1PD9Q/x8Xovn7NFBPhK2dHB6Vm5et/PybrL8v26ObXv1OnmSt1xz82aNbne/TxtqP6+XimiopLLnxAAEC1qhUPHtm8ebPmz5+vTp06lWlv1aqVXnvtNTVr1ky5ubl6+eWXNWjQIB04cEABAQEV7uupp57Se++9pwULFqhNmzZasWKFRowYoe+//15du3aVJC1ZskTTpk3TvHnzdPXVV+sf//iHbrjhBu3Zs0fh4eFX/HwBAKhOvh7OGtAuUAPaBUoqfTD0rsT00lmywye15cgppecW6odDJ/XDoZP297k6OahNkLc6hHqrQ4iPOoT6qGWgp1xsLPABAFeK5ZcgZmVlqVu3bpo3b56ee+45denSRXPmzKlw7Nmpva+++kr9+/evcExISIiefPJJTZo0yd42fPhweXp66r333pMk9ejRQ926ddMbb7xhH9O2bVsNHz5csbGxF1U3lyACAOqKkhJTv5zI0s6j6frxWLp2J2Zo97F0ZRcUlxvr5GioVaCX2od4q0Ooj9qH+KhtsJfcnWvFv9kCQK1UlWxg+bfppEmTNHToUA0YMEDPPfdcpeMKCgo0f/58+fj4qHPnzpWOy8/Pl6tr2QdYurm56dtvv7XvZ+vWrXr88cfLjBk0aJC+//778+43P//Xm54zMjLOe14AANQWDg6GWgZ6qWWgl26NbiqpNJQdTsvWj8dKw9juxAz9eCxdp3MKtftYhnYfy9B/thwtfb8hNQ/wPBPIvNU+xEftQ73l7epk5WkBQJ1kaQBbvHixtm3bps2bN1c6ZtmyZRo1apRycnIUHBysVatWyd/fv9LxgwcP1uzZs9W3b181b95cX3/9tT799FMVF5f+K19qaqqKi4sVGBhY5n2BgYFKTk6udL+xsbF69tlnq3iGAADUTg4OhpoFeKpZgKdu6hwiqXSBj8TTufrxzAzZj4np2n0sQymZ+dqfkqX9KVn6ZHuifR8Rfu7qcCaMdQgpDWd+ni5WnRIA1AmWBbCEhARNnTpVK1euLDdjda5rr71WcXFxSk1N1YIFC3THHXdo06ZNatKkSYXj586dq3vvvVdt2rSRYRhq3ry57rrrLi1cuLDMuN8uzWua5nmX650xY4amT59uf52RkaGwsLCLOVUAAOoEwzDU1NddTX3ddX2HIHt7Skaedh/L0I+JpZcw/piYocTTuTqSlqMjaTn6YleSfWywj6vah/ioQ6i32gV7q2Wgl8Ibu8vRgSXxAUCy8B6wpUuXasSIEXJ0/PVG3+LiYhmGIQcHB+Xn55fpO6tly5aaOHGiZsyYcd795+XlKS0tTSEhIXr88ce1bNky7d69WwUFBXJ3d9eHH36oESNG2MdPnTpVcXFxWrdu3UXVzz1gAICG7FR2wZlLFdNLL2NMTNfB1OwKxzrbHNTM30OtAr3UsomnWgZ6qkUTL0X4ubM0PoB6oU7cA9a/f3/t2rWrTNtdd92lNm3a6LHHHqswfEmlM1Xn3otVGVdXV4WGhqqwsFAfffSR7rjjDkmSs7OzoqOjtWrVqjIBbNWqVbr55psv44wAAGg4fD2c9buW/vpdy19vC8jMK9TepEz7TNlPyZk6kJKl/KIS7UvO1L7kzDL7cHI0FOXvoZZNvNTiTDBrFeilSD8POdsIZgDqJ8sCmJeXlzp06FCmzcPDQ35+furQoYOys7P117/+VTfddJOCg4OVlpamefPm6ejRo7r99tvt7xk3bpxCQ0Ptqxdu2rRJiYmJ6tKlixITEzVz5kyVlJTo0Ucftb9n+vTpGjt2rGJiYtSrVy/Nnz9f8fHxuv/++2vm5AEAqIe8XJ10VVRjXRXV2N5WXGIq8VSu9qdkan9Kln4+XhrKDqRkKaegWD8fz9LPx8s+SNrRwVCkn7taNvE6M1vmqZZNvNQswEOuTiyRD6Bus3wVxMo4Ojpq3759evvtt5Wamio/Pz91795d69evV/v27e3j4uPj5eDw67+S5eXl6amnntLBgwfl6empIUOG6N1331WjRo3sY0aOHKm0tDTNmjVLSUlJ6tChg7788ktFRETU5CkCAFDvOToYCvdzV7ifu/q3/XUBrJISU8fSc7U/JUsHjmfZA9qB41nKzC/SLyey9cuJbC3f/eu+HAwpvLG7WpwJZq0CS4NZ8wBPuTkTzADUDZY/B6yu4h4wAACqn2maOp6Rr5+PnwlkKZnaf7x05iwjr6jC9xiG1NTXTS0CPBXh56Gwxu4KP7OFNXbjGWYArrg6cQ8YAADAbxmGoSAfVwX5uKpvqwB7u2maOpGVf2a2rHTG7OfjWdp/PFOncgqVcDJXCSdzJZ0ot09/TxeFN3Y7J5S5K8LPQ+GN3dXEy0UOrNAIoAYxA3aJmAEDAKB2SMsqfU7ZLyeyzgSxHMWf2dJzC8/7Xmebg8J8y4az8Mall0yG+brLw4V/qwZwYcyAAQCABsPP00V+ni7q2cyvXF96TqESTv0ayI6k5dgDWuLpXBUUldjvN6tIRbNnZwNaoJcrs2cAqowABgAA6i0fdyf5uPuoQ6hPub6i4hIlpefZw9nZ7WxAO51TqNSsfKVm5Wtb/Oly73d2dCi9XNK79JLJYJ9zf3VTsI+r/D1deAg1gDIIYAAAoEGyOToo7Mys1tUV9KfnFirhnEB27pZ4KlcFxSX215VxdDDUxMvl12Dm7faboOaqJl6uPPcMaEAIYAAAABXwcXOST2jls2fJGXlKTs9TUnqejmeU/lr6OlfJ6Xk6npmv4hJTSWfGbD/Psfw9XcoFs7OB7ewsG0vtA/UDAQwAAKCKbI4Oaurrrqa+7pWOKS4xlZqVfyaYlYaypHNCW/KZraC4xH6p467E9Er318jdyX65Y5C3qwK9S0NaoD2sucrHzUmGwSWPQG1GAAMAALgCHB0MBZ4JSgprVOEY0zR1Mrugglm0PCVn5Npf5xQU63ROoU7nFGpfcmalx3R1crCHs7PL+QedDWpn2gI8XWRz5JJHwCoEMAAAAIsYhmFfxbGiSx2l0pCWkVdUOmOWkafj9oB2ZmYtI1/HM/J0MrtAeYUlOpyWo8Npld+X5mBIAV4uZWfTfH4NacE+blzyCFxBBDAAAIBazDCM0vvR3JzUOsir0nF5hcVKycgvvQct49cZteMZv17umJKZr6ISU8cz8nU8I187jlZ+yaO3q01NvF3l5+Esfy8X+Xs4y/9MWPTzLP29/5lf3Z0dufQRuEgEMAAAgHrA1clR4X6lzyirTHGJqbSsfPsCIsnnhLPkjF9f5xQUKyOvSBl5WTpwUcd2kJ+Hy2+CmrP8zglpZ9t83Z1Zmh8NGgEMAACggXB0MNTE21VNvF3VqWnFY0zTVGZ+kY6n5+lEZr5SswuUmpmvtOx8pWYWlP6aVWBfOCSvsER5hSVKPJ2rxNO5F6zBwZAaezifCWxnfj0b2Dyc1cjdST5upb82cndSIzdnuTo5MMOGeoMABgAAADvDMOTt6iRvVye1DKz8ksezsvOLlJZVoNTs/DNBrcD+64msfKVl5Zf2Z+XrVE6hSkydCXAF+un4xdXkbHNQI7dfA5mPu5N83Z3UyN1ZPue0l4a3M6/dneXBpZGohQhgAAAAuGQeLjZ5uNjOe+njWUXFJTqZXRq+SmfSSsPZiazS2bXTOQU6nVuo0zkFSs8tXfWxqMRUQVGJUjLzlZKZX6XabA7GOaHM+UyIOzO75uYkH3cnebrY5OV69tfS7WwbD8jGlUAAAwAAQI2wOTrYL4G8GKZpKruguDSY5RTaQ9np3HNfF+hUTqHSz2k/nVOoguISFZWY9tk2KbvK9TrbHOR9TiA7G9I8XW3yOtt2Tmjz/s1rL5fS19zzhnMRwAAAAFArGYYhT5fSMNPU9+LfZ5qm8gpLygSy9LO/zy37Oiu/SJl5RWd+LVRWXpGyC4olSQVFJecEuEvn7uxoD2Xuzja5OzuWbi42uTs5ysPFJjdnR7k7nWk72+9sk4ezY2nfOe/zcLHJxcZ9cXUVAQwAAAD1imEYcnN2lJuzm4J93Kr8/uIS89dAdjag5RUp4zevM/MKlXnO63Pfk5FXpIKiEklSTkGxcgqKdVxVu4TyfBwMyd35THD7TUBzd3aUR6V9pb93OxPk3M4EwLNt7k6OPKj7CiOAAQAAAOdwdPj12WuXI7+o+JxgVrrlFhYpO79YuQXFyikonW3LLShWdkHRmV+LlVtQpJxzfp+dX6zcwmJl5xcp/0yoKzGlrPzSfVc3Z5tDBSHO0R74PH4T6tzOmalzc3KUq31zsL92cXIobbM5ysnRaNCzdwQwAAAA4ApwsTnKxdNRfp4u1bbP4hJTuYXFysk/G9IuHNxyCoqUk186C5dzznvPhrqzAbDELD1GQVGJCopKdDqnsNrqPpejgyFXm4M9qLmcE9RcnRzkaisb4s5td3N2lIuTY5n3D2jbpE4FOgIYAAAAUEc4Ovx6X1x1Mk1T+UUlZWbjcn7z+5wzAe/c3+f+JvDlFRWfeTZc8TlbifKKimWeCXjFJaWLq5y91+5yODka2v/XIZe9n5pEAAMAAAAaOMMw7DNKvh7O1b7/swEv/0wYOxvMcn8T1PKLSkNdXmGx8opKg1xuYXHp+wrLv8+hDs18nUUAAwAAAHBFnRvwfHR599bVdSxxAgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANcRmdQF1lWmakqSMjAyLKwEAAABgpbOZ4GxGOB8C2CXKzMyUJIWFhVlcCQAAAIDaIDMzUz4+PucdY5gXE9NQTklJiY4dOyYvLy8ZhmFpLRkZGQoLC1NCQoK8vb0trQV1A58ZVBWfGVQVnxlUFZ8ZVFVt+syYpqnMzEyFhITIweH8d3kxA3aJHBwc1LRpU6vLKMPb29vyDx/qFj4zqCo+M6gqPjOoKj4zqKra8pm50MzXWSzCAQAAAAA1hAAGAAAAADWEAFYPuLi46JlnnpGLi4vVpaCO4DODquIzg6riM4Oq4jODqqqrnxkW4QAAAACAGsIMGAAAAADUEAIYAAAAANQQAhgAAAAA1BACGAAAAADUEAJYPTBv3jxFRUXJ1dVV0dHRWr9+vdUloZaaOXOmDMMoswUFBVldFmqRb775RsOGDVNISIgMw9DSpUvL9JumqZkzZyokJERubm665pprtHv3bmuKRa1woc/MhAkTyn3v9OzZ05piYbnY2Fh1795dXl5eatKkiYYPH66ffvqpzBi+Z3Cui/nM1LXvGQJYHbdkyRJNmzZNTz75pLZv364+ffrohhtuUHx8vNWloZZq3769kpKS7NuuXbusLgm1SHZ2tjp37qzXXnutwv4XX3xRs2fP1muvvabNmzcrKChIAwcOVGZmZg1XitriQp8ZSbr++uvLfO98+eWXNVghapN169Zp0qRJ2rhxo1atWqWioiINGjRI2dnZ9jF8z+BcF/OZkerW9wzL0NdxPXr0ULdu3fTGG2/Y29q2bavhw4crNjbWwspQG82cOVNLly5VXFyc1aWgDjAMQ5988omGDx8uqfRfpUNCQjRt2jQ99thjkqT8/HwFBgbqhRde0H333WdhtagNfvuZkUr/Zfr06dPlZsYASTpx4oSaNGmidevWqW/fvnzP4IJ++5mR6t73DDNgdVhBQYG2bt2qQYMGlWkfNGiQvv/+e4uqQm23f/9+hYSEKCoqSqNGjdLBgwetLgl1xKFDh5ScnFzmO8fFxUX9+vXjOwfntXbtWjVp0kStWrXSvffeq5SUFKtLQi2Rnp4uSWrcuLEkvmdwYb/9zJxVl75nCGB1WGpqqoqLixUYGFimPTAwUMnJyRZVhdqsR48eeuedd7RixQotWLBAycnJ6t27t9LS0qwuDXXA2e8VvnNQFTfccIPef/99rV69Wn//+9+1efNmXXfddcrPz7e6NFjMNE1Nnz5dv/vd79ShQwdJfM/g/Cr6zEh173vGZnUBuHyGYZR5bZpmuTZAKv2COqtjx47q1auXmjdvrrffflvTp0+3sDLUJXznoCpGjhxp/32HDh0UExOjiIgIffHFF7rlllssrAxWmzx5snbu3Klvv/22XB/fM6hIZZ+ZuvY9wwxYHebv7y9HR8dy/yKUkpJS7l+OgIp4eHioY8eO2r9/v9WloA44u2Im3zm4HMHBwYqIiOB7p4H74x//qM8++0xr1qxR06ZN7e18z6AylX1mKlLbv2cIYHWYs7OzoqOjtWrVqjLtq1atUu/evS2qCnVJfn6+9u7dq+DgYKtLQR0QFRWloKCgMt85BQUFWrduHd85uGhpaWlKSEjge6eBMk1TkydP1scff6zVq1crKiqqTD/fM/itC31mKlLbv2e4BLGOmz59usaOHauYmBj16tVL8+fPV3x8vO6//36rS0Mt9PDDD2vYsGEKDw9XSkqKnnvuOWVkZGj8+PFWl4ZaIisrSwcOHLC/PnTokOLi4tS4cWOFh4dr2rRpev7559WyZUu1bNlSzz//vNzd3XXnnXdaWDWsdL7PTOPGjTVz5kzdeuutCg4O1uHDh/XEE0/I399fI0aMsLBqWGXSpEn697//rU8//VReXl72mS4fHx+5ubnJMAy+Z1DGhT4zWVlZde97xkSd9/rrr5sRERGms7Oz2a1bN3PdunVWl4RaauTIkWZwcLDp5ORkhoSEmLfccou5e/duq8tCLbJmzRpTUrlt/PjxpmmaZklJifnMM8+YQUFBpouLi9m3b19z165d1hYNS53vM5OTk2MOGjTIDAgIMJ2cnMzw8HBz/PjxZnx8vNVlwyIVfVYkmQsXLrSP4XsG57rQZ6Yufs/wHDAAAAAAqCHcAwYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAKizIiMjNWfOHKvL0NNPP60//OEP9tfXXHONpk2bZl1BFnv44Yc1ZcoUq8sAgFqJAAYAuKAJEyZo+PDh9tc1HTAWLVqkRo0alWvfvHlzmeBjhePHj2vu3Ll64oknrvixpk6dqujoaLm4uKhLly4Vjtm1a5f69esnNzc3hYaGatasWTJNs8yYdevWKTo6Wq6urmrWrJnefPPNcvv56KOP1K5dO7m4uKhdu3b65JNPLrrORx99VAsXLtShQ4eqdH4A0BAQwAAAlikoKLis9wcEBMjd3b2aqrk0//rXv9SrVy9FRkZe8WOZpqmJEydq5MiRFfZnZGRo4MCBCgkJ0ebNm/Xqq6/qpZde0uzZs+1jDh06pCFDhqhPnz7avn27nnjiCU2ZMkUfffSRfcyGDRs0cuRIjR07Vjt27NDYsWN1xx13aNOmTRdVZ5MmTTRo0KAKgx0ANHQEMABAlUyYMEHr1q3T3LlzZRiGDMPQ4cOHJUl79uzRkCFD5OnpqcDAQI0dO1apqan2915zzTWaPHmypk+fLn9/fw0cOFCSNHv2bHXs2FEeHh4KCwvTgw8+qKysLEnS2rVrdddddyk9Pd1+vJkzZ0oqfwlifHy8br75Znl6esrb21t33HGHjh8/bu+fOXOmunTponfffVeRkZHy8fHRqFGjlJmZaR/z3//+Vx07dpSbm5v8/Pw0YMAAZWdnV/rzWLx4sW666aZy7UVFRZo8ebIaNWokPz8/PfXUU/aZqFmzZqljx47l3hMdHa0///nPlR7rlVde0aRJk9SsWbMK+99//33l5eVp0aJF6tChg2655RY98cQTmj17tv3Yb775psLDwzVnzhy1bdtW99xzjyZOnKiXXnrJvp85c+Zo4MCBmjFjhtq0aaMZM2aof//+ZX7WF/o53XTTTfrggw8qPRcAaKgIYACAKpk7d6569eqle++9V0lJSUpKSlJYWJiSkpLUr18/denSRVu2bNHy5ct1/Phx3XHHHWXe//bbb8tms+m7777TP/7xD0mSg4ODXnnlFf344496++23tXr1aj366KOSpN69e2vOnDny9va2H+/hhx8uV5dpmho+fLhOnjypdevWadWqVfrll1/KzRb98ssvWrp0qZYtW6Zly5Zp3bp1+r//+z9JUlJSkkaPHq2JEydq7969Wrt2rW655ZZyl/CdderUKf3444+KiYkp13f2PDdt2qRXXnlFL7/8sv75z39KkiZOnKg9e/Zo8+bN9vE7d+7U9u3bNWHChIv8kyhvw4YN6tevn1xcXOxtgwcP1rFjx+whecOGDRo0aFCZ9w0ePFhbtmxRYWHhecd8//33ki7u53TVVVcpISFBR44cueTzAYD6yGZ1AQCAusXHx0fOzs5yd3dXUFCQvf2NN95Qt27d9Pzzz9vb3nrrLYWFhennn39Wq1atJEktWrTQiy++WGaf595PFhUVpb/85S964IEHNG/ePDk7O8vHx0eGYZQ53m999dVX2rlzpw4dOqSwsDBJ0rvvvqv27dtr8+bN6t69uySppKREixYtkpeXlyRp7Nix+vrrr/XXv/5VSUlJKioq0i233KKIiAhJqnCm6qwjR47INE2FhISU6wsLC9PLL78swzDUunVr7dq1Sy+//LLuvfdeNW3aVIMHD9bChQvtdS1cuFD9+vWrdHbrYiQnJ5e7FDIwMNDeFxUVpeTkZHvbuWOKioqUmpqq4ODgSsckJydL0kX9nEJDQyVJhw8fto8BADADBgCoJlu3btWaNWvk6elp39q0aSOpdNbprIpmi9asWaOBAwcqNDRUXl5eGjdunNLS0s576d9v7d27V2FhYfbwJUnt2rVTo0aNtHfvXntbZGSkPXxJUnBwsFJSUiRJnTt3Vv/+/dWxY0fdfvvtWrBggU6dOlXpMXNzcyVJrq6u5fp69uwpwzDsr3v16qX9+/eruLhYknTvvffqgw8+UF5engoLC/X+++9r4sSJF32+lTn3mJLss1Lntl/qmLNtF/NzcnNzkyTl5ORczukAQL1DAAMAVIuSkhINGzZMcXFxZbb9+/erb9++9nEeHh5l3nfkyBENGTJEHTp00EcffaStW7fq9ddflyT7JXEX49yAcL52JyenMv2GYaikpESS5OjoqFWrVul///uf2rVrp1dffVWtW7eudDU/f39/STpvSKvMsGHD5OLiok8++USff/658vPzdeutt1Z5P+cKCgqyz1KddTZcnp3RqmyMzWaTn5/fecec3cfF/JxOnjwpqXShFADArwhgAIAqc3Z2ts/knNWtWzft3r1bkZGRatGiRZntt6HrXFu2bFFRUZH+/ve/q2fPnmrVqpWOHTt2weP9Vrt27RQfH6+EhAR72549e5Senq62bdte9LkZhqGrr75azz77rLZv3y5nZ+dKl2Bv3ry5vL29tWfPnnJ9GzduLPe6ZcuWcnR0lCTZbDaNHz9eCxcu1MKFCzVq1KjLXtGxV69e+uabb8qsLrly5UqFhITYL03s1auXVq1aVeZ9K1euVExMjD2cVjamd+/e9tcX+jn9+OOPcnJyUvv27S/rnACgviGAAQCqLDIyUps2bdLhw4eVmpqqkpISTZo0SSdPntTo0aP1ww8/6ODBg1q5cqUmTpx43vDUvHlzFRUV6dVXX9XBgwf17rvvllu+PDIyUllZWfr666+Vmppa4WVtAwYMUKdOnTRmzBht27ZNP/zwg8aNG6d+/fpVeNljRTZt2qTnn39eW7ZsUXx8vD7++GOdOHGi0gDn4OCgAQMG6Ntvvy3Xl5CQoOnTp+unn37SBx98oFdffVVTp04tM+aee+7R6tWr9b///e+iLj88cOCA4uLilJycrNzcXPss49nAdeedd8rFxUUTJkzQjz/+qE8++UTPP/+8pk+fbp8FvP/++3XkyBFNnz5de/fu1VtvvaV//etfZRY2mTp1qlauXKkXXnhB+/bt0wsvvKCvvvrKfq/exfyc1q9frz59+tgvRQQAnGECAHAB48ePN2+++Wb7659++sns2bOn6ebmZkoyDx06ZJqmaf7888/miBEjzEaNGplubm5mmzZtzGnTppklJSWmaZpmv379zKlTp5bb/+zZs83g4GDTzc3NHDx4sPnOO++YksxTp07Zx9x///2mn5+fKcl85plnTNM0zYiICPPll1+2jzly5Ih50003mR4eHqaXl5d5++23m8nJyfb+Z555xuzcuXOZY7/88stmRESEaZqmuWfPHnPw4MFmQECA6eLiYrZq1cp89dVXz/uzWb58uRkaGmoWFxfb2/r162c++OCD5v333296e3ubvr6+5uOPP27/OZyrT58+Zrt27c57jHP3K6ncdvbnb5qmuXPnTrNPnz6mi4uLGRQUZM6cObPccdeuXWt27drVdHZ2NiMjI8033nij3LE+/PBDs3Xr1qaTk5PZpk0b86OPPrL3XczPqVWrVuYHH3xwUecFAA2JYZqVrK0LAAAuyDRN9ezZU9OmTdPo0aOr/N42bdrovvvu0/Tp069QhTXviy++0COPPKKdO3fKZmPBZQA4F5cgAgBwGQzD0Pz581VUVFSl96WkpGj27NlKTEzUXXfddYWqs0Z2drYWLlxI+AKACjADBgCABQzDkL+/v+bOnas777zT6nIAADWEf5oCAMAC/PsnADRMXIIIAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANYQABgAAAAA1hAAGAAAAADWEAAYAAAAANeT/AWssDnY0hcNcAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current cost: 43.875251419688105\n"
     ]
    }
   ],
   "source": [
    "# plot cost history after first round of training (before adjusting alpha)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(model.cost_history)\n",
    "plt.title('Cost Function vs. Iteration')\n",
    "plt.xlabel('Iterations (by 1000s)')\n",
    "plt.ylabel('Cost')\n",
    "plt.show()\n",
    "\n",
    "print('current cost:', model.cost_history[-1])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decreasing Alpha (learning rate) and More Training\n",
    "As our model learns, it's important to adjust the alpha value (learning rate). The learning rate is a controlling factor in our model's learning process, determining the size of the steps it takes towards the minimum of the cost function. An overly large alpha might cause the model to overshoot this minimum (by taking too large of a step past it), while a small alpha could result in an excessively long convergence time (tip toeing forever towards it).\n",
    "\n",
    "In mini-batch gradient descent we can't reach an absolute minimum, because due to the fact that it's computing using a subset of the rows, each step will be a bit random. Due to this, our cost will oscillate the minimum. To combat this, we decrease the learning rate so that it takes smaller steps and as result will oscillate a smaller radius; closer to the absolute minimum.\n",
    "\n",
    "![Gradient Descents vs Learning Rate Contour Plot Drawing](gradient_descent_contour_plot.JPG)\n",
    "\n",
    "Now that we've sufficiently trained and converged (according to epsilon) at a higher alpha value, we'll pursue further training at a lower alpha in hopes that it might edge us even closer to the absolute minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lower alpha to reduce the oscillation range and close in on the minimum, then continue training\n",
    "\n",
    "# prev alpha: 1, prev epsilon: 0.001\n",
    "model.alpha = 0.3\n",
    "model.epsilon = 0.0001\n",
    "\n",
    "# model.shuffle_dataset()\n",
    "_ = model.train(model.mini_batch_gradient_descent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final cost: 43.872354730112605\n"
     ]
    }
   ],
   "source": [
    "# plot the final cost history\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(model.cost_history)\n",
    "plt.title('Cost Function vs. Iteration')\n",
    "plt.xlabel('Iterations (by 1000s)')\n",
    "plt.ylabel('Cost')\n",
    "plt.show()\n",
    "\n",
    "print('final cost:', model.cost_history[-1])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Evaluation\n",
    "We've finally trained our model! We now move to the evaluation stage, where we assess how well our model performs. We will use the test data (kept separate from the training data to prevent information leakage) to evaluate the model's predictive performance.\n",
    "\n",
    "The metric we'll use is the **Root Mean Squared Error (RMSE)**, which calculates the average squared difference between the model's predictions and the actual values. It's a popular metric for regression models because it penalizes larger errors more due to squaring each difference. Our aim is to have the lowest RMSE possible, which would indicate that our model's predictions closely match the actual values.\n",
    "\n",
    "However, it's important to remember that no model is perfect; this is especially true when it's an engineer's first-ever model, and doubly so when built entirely from scratch! It's this exciting journey of constant growth and improvement that truly embodies the spirit of machine learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bias parameter (theta 0): 4.732267739870727\n",
      "weights parameters (theta vector): [ 4.61203248  2.25985513  2.96979475  0.53490732  0.79826477  0.17124345\n",
      " -0.48131699  0.58302452]\n",
      "Root Mean Squared Error: 9.439272446209852\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "count    300250.000000\n",
       "mean         11.367405\n",
       "std           9.442485\n",
       "min           3.300000\n",
       "25%           6.000000\n",
       "50%           8.500000\n",
       "75%          12.500000\n",
       "max         100.000000\n",
       "Name: fare_amount, dtype: float64"
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test_np = y_test.to_numpy()\n",
    "\n",
    "# generate predictions for every training example in the testing set\n",
    "y_predicted = np.array([model.predict(x_row) for x_row in X_test])\n",
    "y_actual = y_test.to_numpy()\n",
    "\n",
    "# root mean squared error of the model\n",
    "rmse = mean_squared_error(y_actual, y_predicted, squared=False)\n",
    "\n",
    "# printing the parameters' final values and the error they produce\n",
    "print(f'bias parameter (theta 0): {model.theta_0}\\nweights parameters (theta vector): {model.theta_vector}')\n",
    "print('Root Mean Squared Error:', rmse)\n",
    "\n",
    "y_test.describe()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results and Conclusion\n",
    "We have journeyed from data wrangling, exploratory data analysis, feature engineering, to the nitty-gritty of building and training of our model. At each stage, we’ve learned something new and faced exciting challenges.\n",
    "\n",
    "Now, let's look at the model's performance. When I ran the notebook, my model yielded these parameters:\n",
    "- bias parameter (theta 0): 0.6638866705693053  \n",
    "- weights parameters (theta vector): [-0.1950215  -0.21778255 -0.04735735  0.01070294  0.19123685  0.11586946 0.03743055  0.02385733]\n",
    "\n",
    "Our model registered a **Root Mean Squared Error (RMSE)** score of 9.44 on the test data (rounded to two decimal places). RMSE is a standard way to measure the error of a model in predicting quantitative data. It indicates the standard deviation of the residuals or prediction errors. To put this into context, given that our target variable is 'fare_amount', an RMSE of 9.44 means that our model's predicted taxi fares tend to deviate from the actual fares by approximately $9.44 dollars.\n",
    "\n",
    "Reflecting on this, it's clear that while our model has room for improvement, it represents a promising start. What's particularly impressive is that it's the first model I've ever built and was created entirely from scratch! As we move forward, we could experiment with different algorithms, additional feature engineering, and hyperparameter tuning to enhance our model's performance.\n",
    "\n",
    "Ultimately, this project served as an invaluable hands-on experience in the field of machine learning. It has shown that model-building in machine learning is a delicate balance of managing complexity, understanding data, and cultivating an intuitive sense. This sense, which matures over time, is key for making strategic decisions on methodologies and for navigating model development effectively.\n",
    "\n",
    "As we conclude this project, we are reminded that in the world of machine learning, every end is simply a new beginning, setting the stage for further learning and exploration. Here's to many more fascinating projects ahead!"
   ]
  }
 ],
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