{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing tweets and the Logistic Regression model\n",
    "\n",
    "**Objectives:** Visualize and interpret the logistic regression model\n",
    "\n",
    "**Steps:**\n",
    "* Plot tweets in a scatter plot using their positive and negative sums.\n",
    "* Plot the output of the logistic regression model in the same plot as a solid line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the required libraries\n",
    "\n",
    "We will be using [*NLTK*](http://www.nltk.org/howto/twitter.html), an opensource NLP library, for collecting, handling, and processing Twitter data. In this lab, we will use the example dataset that comes alongside with NLTK. This dataset has been manually annotated and serves to establish baselines for models quickly. \n",
    "\n",
    "So, to start, let's import the required libraries. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import nltk                         # NLP toolbox\n",
    "from os import getcwd\n",
    "import pandas as pd                 # Library for Dataframes \n",
    "from nltk.corpus import twitter_samples \n",
    "import matplotlib.pyplot as plt     # Library for visualization\n",
    "import numpy as np                  # Library for math functions\n",
    "\n",
    "from utils import process_tweet, build_freqs # Our functions for NLP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the NLTK sample dataset\n",
    "\n",
    "To complete this lab, you need the sample dataset of the previous lab. Here, we assume the files are already available, and we only need to load into Python lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of tweets:  8000\n"
     ]
    }
   ],
   "source": [
    "# select the set of positive and negative tweets\n",
    "all_positive_tweets = twitter_samples.strings('positive_tweets.json')\n",
    "all_negative_tweets = twitter_samples.strings('negative_tweets.json')\n",
    "\n",
    "tweets = all_positive_tweets + all_negative_tweets ## Concatenate the lists. \n",
    "labels = np.append(np.ones((len(all_positive_tweets),1)), np.zeros((len(all_negative_tweets),1)), axis = 0)\n",
    "\n",
    "# split the data into two pieces, one for training and one for testing (validation set) \n",
    "train_pos  = all_positive_tweets[:4000]\n",
    "train_neg  = all_negative_tweets[:4000]\n",
    "\n",
    "train_x = train_pos + train_neg \n",
    "\n",
    "print(\"Number of tweets: \", len(train_x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load the extracted features\n",
    "\n",
    "Part of this week's assignment is the creation of the numerical features needed for the Logistic regression model. In order not to interfere with it, we have previously calculated and stored these features in a CSV file for the entire training set.\n",
    "\n",
    "So, please load these features created for the tweets sample. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bias</th>\n",
       "      <th>positive</th>\n",
       "      <th>negative</th>\n",
       "      <th>sentiment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3020.0</td>\n",
       "      <td>61.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3573.0</td>\n",
       "      <td>444.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3005.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2862.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3119.0</td>\n",
       "      <td>225.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2955.0</td>\n",
       "      <td>119.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3934.0</td>\n",
       "      <td>538.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3162.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>628.0</td>\n",
       "      <td>189.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.0</td>\n",
       "      <td>264.0</td>\n",
       "      <td>112.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bias  positive  negative  sentiment\n",
       "0   1.0    3020.0      61.0        1.0\n",
       "1   1.0    3573.0     444.0        1.0\n",
       "2   1.0    3005.0     115.0        1.0\n",
       "3   1.0    2862.0       4.0        1.0\n",
       "4   1.0    3119.0     225.0        1.0\n",
       "5   1.0    2955.0     119.0        1.0\n",
       "6   1.0    3934.0     538.0        1.0\n",
       "7   1.0    3162.0     276.0        1.0\n",
       "8   1.0     628.0     189.0        1.0\n",
       "9   1.0     264.0     112.0        1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('logistic_features.csv'); # Load a 3 columns csv file using pandas function\n",
    "data.head(10) # Print the first three data entries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us get rid of the data frame to keep only Numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8000, 3)\n",
      "[[1.000e+00 3.020e+03 6.100e+01]\n",
      " [1.000e+00 3.573e+03 4.440e+02]\n",
      " [1.000e+00 3.005e+03 1.150e+02]\n",
      " ...\n",
      " [1.000e+00 1.440e+02 7.830e+02]\n",
      " [1.000e+00 2.050e+02 3.890e+03]\n",
      " [1.000e+00 1.890e+02 3.974e+03]]\n"
     ]
    }
   ],
   "source": [
    "# Each feature is labeled as bias, positive and negative\n",
    "X = data[['bias', 'positive', 'negative']].values # Get only the numerical values of the dataframe\n",
    "Y = data['sentiment'].values; # Put in Y the corresponding labels or sentiments\n",
    "\n",
    "print(X.shape) # Print the shape of the X part\n",
    "print(X) # Print some rows of X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load a pretrained Logistic Regression model\n",
    "\n",
    "In the same way, as part of this week's assignment, a Logistic regression model must be trained. The next cell contains the resulting model from such training. Notice that a list of 3 numeric values represents the whole model, that we have called _theta_ $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = [7e-08, 0.0005239, -0.00055517]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the samples in a scatter plot\n",
    "\n",
    "The vector theta represents a plane that split our feature space into two parts. Samples located over that plane are considered positive, and samples located under that plane are considered negative. Remember that we have a 3D feature space, i.e., each tweet is represented as a vector comprised of three values: `[bias, positive_sum, negative_sum]`, always having `bias = 1`. \n",
    "\n",
    "If we ignore the bias term, we can plot each tweet in a cartesian plane, using `positive_sum` and `negative_sum`. In the cell below, we do precisely this. Additionally, we color each tweet, depending on its class. Positive tweets will be green and negative tweets will be red."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Negative')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4DPh+3n57Sqmc7J4KZcBhEfEG0D6l9Gxez83AacDofJ3L8m3dDVwTEZFS8kZNkiTVwbZ6ClbV8IDsW/r36/B5PVJK8wDyn93z9j5A9YGMc/K2Dacr3tu+yToppQpgGdClpg+NiHMjojQiShcuXFiHsiVJ2vVttacgpXT1hucR0Q74FnA22XTHV29pvTqImj5+K+1bW2fzxpSuB64HGDZsmD0JkiTVYJtjCvLBgZcDr5KFiCEppe+nlBbU4fPejohe+XZ7ARu2MYds6uQN9gDm5u171NC+yToRUQJ0ABbXoSZJksQ2QkFEXAWMA1YA70spXZZSWlKPz7sPGJk/HwmMqtY+Ir+iYG+yAYUv5KcYVkTE4flVB198zzobtnU68KjjCSRJqrttzVPwHaAcuBT4YX41IGRd9yml1H5LK0bE38kGFXaNiDnAj4ErgDsj4hxgNvAZsg1Niog7yaZRrgDOTyltmBzp62RXMrQiG2A4Om+/AbglH5S4mOzqBUmSVEexu325HjZsWCotLS10GZIkNYmIGJ9SGlabZWs9zbEkSdq1GQokSRJgKJAkSTlDgSRJAgwFkiQpZyiQJEmAoUCSJOUMBZIkCTAUSJKknKFAkiQBhgJJkpQzFEiSJMBQIEmScoYCSZIEGAokSVLOUCBJkgBDgSRJyhkKJEkSYCiQJEk5Q4EkSQIMBZIkKWcokCRJgKFAkiTlDAWSJAkwFDSNOXPg8sth3bpCVyJJ0hYZCppCu3bQty+UlBS6EkmStshQ0NhuugnefhtGjoSi9xzuqiooLy9MXZIkvYdfXRtbVRWkVPN7N90Ec+fCPvvAvvvCoYc2bW2SJFVjKGhsZ5+95fc+/WlYsQLGjYNmzZquJkmSamAoaArz50OPHhCxaXv79tmjT5/C1CVJUjWGgsYweTJMnZqNFxg+HL71LfjYx2DVKvja1wpdnSRJNTIUNIaxY2HRIujdOwsI++wDy5fDfvsVujJJkrbIUNDQqqrgr3+Fnj2hQwdYsADOPDMLCF27Fro6SZK2yFDQ0IYOzcYQfOQjcNhhMGwY7LknTJwIs2Zl70uStANynoKG8vbb8NRT8NZb8NWvwhVXwMqVcMstMG0aTJqUPSRJ2kHZU1Bf69fDGWfAE09ARQV06wavvprNTfD5z0NlJVx4IXzqU1nvQW3svz9873twzjmNW7skSdVE2tLEOruoYcOGpdLS0obb4Ac+ANOnQ9u22dUF69dnYwdef/3daY3XroWWLWu/zQ2XLu5m/24kSQ0vIsanlIbVZllPH9RXRQWcdBKcdRb06wfNm8NRR8GVV8Kzz2bLbE8ggGw65GOOafBSJUnaGkNBfd1xByxbBtdcA927w5Ah2YREhx5a90sQKyvhsccatExJkrbFUFAfq1bBscfCww9nXf7vvJP1ECxdCscdB126FLpCSZJqzYGG9dGqVdbV37x5NnPhxz8OBx8MN9zgbZIlSTsd/3LVx7/+BXPmwJe+BP/3f9C6ddZuIJAk7YT861Ufp56a3f74858vdCWSJNWbYwrqo6TEQCBJ2mUYCiRJEmAokCRJOUOBJEkCDAWSJClnKJAkSYChQJIk5QwFkiQJMBRIkqScoUCSJAGGAkmSlDMUSJIkwFAgSZJyhgJJkgQYCiRJUs5QIEmSAEOBJEnKGQokSRJgKJAkSTlDgSRJAgwFkiQpZyiQJEmAoUCSJOUMBZIkCTAUSJKknKFAkiQBhgJJkpQzFEiSJMBQIEmScoYCSZIEGAokSVLOUCBJkgBDgSRJyhkKJEkSYCjY8b38Mpx/PqxeDRUVha5GkrQLMxTs6AYOhDPPhN/9Dm68sdDVSJJ2YSWFLkDb0Lw5HHkkDBgArVoVuhpJ0i6sID0FEfFGREyIiJcjojRv6xwRD0fEtPxnp2rLXxIRZRExJSJOrNY+NN9OWUT8LiKiEPvTJHr0gPbtC12FJGkXVsjTB8emlAanlIblry8GHkkpDQAeyV8TEQOBEcAg4CTg2ogozte5DjgXGJA/TmrC+utv1Cj429/efT17Nrzxxruv167NlkmpyUuTJO1+dqQxBcOBm/LnNwGnVWu/PaVUnlKaCZQBh0VEL6B9SunZlFICbq62zo4tJbj/fujbF958Ex59FJYtgzFjYPTod5ebMweeegrWrStcrZKk3UahQkECHoqI8RFxbt7WI6U0DyD/2T1v7wO8WW3dOXlbn/z5e9s3ExHnRkRpRJQuXLiwAXdjO02bll1NsGIFPPwwdO8OQ4fC9OnwjW/AIYfA6adngQFg333hqqugRYvC1SxJ2m0UKhR8KKU0BDgZOD8ijt7KsjWNE0hbad+8MaXrU0rDUkrDunXrtv3VNpRXXoEXXsjGBvz2tzB/Ptx9Nzz5JHz3uzBsWHYKYeLEwtUoSdptFSQUpJTm5j8XAPcChwFv56cEyH8uyBefA/SttvoewNy8fY8a2ndMq1ZlYeCrX3237Y9/hBkz4OSTs/cisqsNDj64cHVKknZbTR4KIqJNRLTb8Bw4AZgI3AeMzBcbCYzKn98HjIiIFhGxN9mAwhfyUwwrIuLw/KqDL1ZbZ8dSWZkFgPPOgy9/GT77WbjlFpg1CwYNgptugnHjsmVXrIAFC7a+PUmSGkEh5inoAdybXz1YAtyWUhoTEeOAOyPiHGA28BmAlNKkiLgTeA2oAM5PKVXm2/o6cCPQChidP3Y8c+bA5Mlw881QUgLXXQe/+EU2Q+FTT2VXGfTuDZ/5DBxxRPaQJKmJNXkoSCnNADbrH08pLQI+soV1fg78vIb2UuCghq6xQY0aBe9/P4wdm50qePrpbM6Bt9+Gjh2huBg6dICiouyqhF14qgVJ0o7NGQ0by/33ZwMHzzsP9toLFi2CefOyywuXLcuuPCgvh169sl6Cb3/bQCBJKqgdaZ6CXUdVFTz7bDY24NRToV076NkzO12QUtY7sM8+sGZNdqOj738/u8fBloweDUuXNl39kqTdkqGgIVVVZT+LirIegV//OpuY6NFH3+0lAOjaNbsKISLrRRg6NGt/6il45pmsvXqvwbhx2RwHkiQ1Ik8fNKSf/AQGD4ZPfjKbnGjGjGwQYUrZKYMN3ngjux1y+/bwpS/BkiXZH/3Fi7NA8V7/8z9NtQeSpN2YoaAhnXEGdOoEZ52V3e74xz+G9evffb+kJOtN2Hff7I6HrVtnVxyceWY2adFtt2VzFHivA0lSARgKGtLq1XDJJfDgg3DffdlAwuoqKqBly2x8QN++0K1b1ltQXAwHHJCdVpAkqUAMBQ1l+fLslEBZWfZNf9Wqmpfr0iULA6+8AiedlJ1e+OY34cADoU+Nt26QJKlJONCwoaxcmV1auHLllu9qWFwMH/94dorgpJOy0wiLFmXjD+68M+tpeOONbHzBmDFNWr4kSfYUNJRXXoH//GfLgaBNm2xOgrvuysYVlJdn4w+KiqBZMzjnHHjggewuih/7GDz3XDbw8KyzmnY/JEm7LUNBQ3jwQRg+fNNBhe+1fn0WGI46Cj7xCSgtzQYeXnBBFhggu23yJz6R3Sq5bVt48cWmqV+SJDx90DB+8IOtBwLIegQisjkJfvazbNzBJz6R3RNhg4gsEAC8730wcmTN25IkqREYCurrmWe2/Y2+pCTrJWjePLv0sH//7FLEZctgypQtr1dZueX3JElqYJ4+qK8PfWjbywwdmgWAtWth/Hj4v//b9p0Q//nPbCbDn292HyhJkhqFoaCxNWuWzVr4yivw1lvZqYODN7tJ5OaOPx7237/Ry5MkaQNDQWM7+GA49tgsEBx1VO3/0Ldtm81dIElSE3FMQX1ceunW3//oR7P5B973vuwKhbPOymY0lCRpB2RPQX3cfXfN7SeckM1o+NBD2TiCk0+G73ynaWuTJGk7GQrqoWLKFIrz5wHQs2c2O+FBB727UMuWMGpUAaqTJGn7GArqoQSoAhJQvHChNzSSJO3UDAX1kZKDMiRJuwz/pkmSJMBQIEmScoYCSZIEGAokSVLOUCBJkgBDgSRJyhkKJEkSYCiQJEk5Q4EkSQIMBZIkKWcokCRJgKFAkiTlDAWSJAkwFEiSpJyhQJIkAYYCSZKUMxRIkiTAUCBJknKGAkmSBBgKJElSzlAgSZIAQ4EkScoZCiRJEmAokCRJOUOBJEkCDAWSJClnKJAkSYChQJIk5QwF2iHMWDKDOcvnFLoMSdqtGQq0Q3hg6gM8NP2hQpchSbu1kkIXIAF88wPfLHQJkrTbs6dAO4wnZz3J1c9cXegyJGm3ZU+Bdhj9O/envLK80GVI0m7LUKAdRu92vendrnehy5Ck3ZanD5ra88/DnXcWugpJkjZjKGgojz4Kf/3rtpdr1gxatKj5vZtvhueea9i6JEmqJU8fNJTu3SECbr0V+vSBD3+45uWGDMkeNencGdq2bbQSJUnaGkNBQznooOzniBEwdy5ccAEsXw6HHJI9auNjH6vVYusq1/G3V//GiING0LpZ6zoWLEnSpgwFDe3222HSJOjRAx5/HFq1avCPWFe5jrkr5rJm/RpDgSSpwTimoDEMGgRdu8KnPw0HHLD5+1Onwssvw8yZW9/O5ZfDww9v1ty2eVsuPfpSurTu0kAF192a9Wu4cMyFTF88fZP20rml/OSxnxSoKklSXRgKGtqkSXDDDTW/N306zJ8PzzwD118Pf/rT1rd13HEwbFjD19iAWpa05IT+J9C3Q99N2vftvC+H9jm0QFU1jllLZ/HU7KcKXYYkNRpPHzSkxx+HiROhY8dN21PKBiHedx+UlsJnPwu//z2sW7f5Nh58EI48Etq0gSOOaJq66yEiOGXAKZu1d2zZscb2ndnURVN57Z3XOHLPIwtdiiQ1CkNBQ2rRAvr3h5NOerftf/4nG3D4v/8LF14IL76YjTeI2PzSxJTgscegW7ctX6GwE6tKVUxdNJUDutZwSmUn8NH+H+Wj/T9a6DIkqdEYChrS4Ydv3tahA+y3X/Y8AoYO3fL6EfDLXzZObU3ktYWvATCw28Aa3/vFk7/gxtNupHlx86YuTZK0DY4paEhr1kBlZfZ8xozs53e+k/UAjBoFd98Nd921xdUXrFrArKWzNmuftGASP3v8Z6SUGqPqOhk9bTSvvv3qZu2lc0spnVu6SdvairUcct0hPDLjEf4y/C8GAknaQdlT0JCuvDI7fQDZlQM33JBdifC3v0FRETRvDkcdtcXVb3z5RlatX8WQXkP4UN8P0bV1VyC7J8DenfZuij2otYWrF9KhZQcAfvf87+jXoR+Dew3mC+//AhEBwLRF05i0cBLD9x9O34596dq6Ky1LWhay7N3GM28+Q8eWHWvssZGkLbGnoL5ee+3d6Y3PPRcWL4Yf/SjrMTj3XNh7b3j9dTjhhGxsQY8em23irtfu4sdjf8zK8pWURAlXPX0Vt7xyy8b3ZyyZwZiyMTz/1vNNtVc1mrpoKotWLwKgqqqKHm168GDZgxzY9UBmLp3Jfz3wX0xYMAGAmUtm8sNHf8iL815k9rLZnNj/RI7pd8xm21y9fnWT7kNtzV42m3kr5hW6jDp7/Z3Xmb1sdqHLkLSTsaegvoqLYdo0OPts2HNPGD8eli7N3luxgvXNSohURckzz0C/ftm9D+bOhd7v3g2wS4su3PbqbezVcS/GfH4MFx95McvWLqMqVREEfxj/Bz476LMc1uewjeusr1zPsvJlG3sTauvOSXdyzF7H0KPt5uFkW06/43Tat2jPY2c/xjXjrqFscRltW7Slb/u+TH5nMkN7DWVQt0H89PGf0rFFR9o2b8u3PvAtXpr/Ev+Z+R/277o/e7TfY+P2Jrw9gV8+9UtuPO1GmhU1Y9X6VbRtvmNM8/zP1/9Jy5KWnDv03EKXUidfPuTLhS5B0k7InoL62n//bMzAHXdkj1dfhWXLskdVFWvbNGNV57bZIMKTT4Z58+D+++G66zZuYuSokbyz5h2O6XcMlamSa8ddy+A/Duanj/+UiGBg14H0aNODonj3X9c/Jv+DXz/76+0ud9ayWbyz+p3tWueFt17giqeu4KtDv8qkhZP4f0//P6oqq7j5lZtpXdKav0/4O5MXTCalRFEUsX+X/enUshPTF0/nhpduYOGqhdx7xr0cv8/xm2x3UPdBXPaLSnAaAAAVOklEQVThy2he3Jz7ptzHjx/78XbvT31cO+5abp94e43vfeOwb/DVIV9t0noa0yvzX+FXz/yq0GVI2sHZU9AQxo7NBhlOmbJp+8CBtLvhhuz0wb33ZvMTAJSVwYIFGxcbNWJU1g3f7UBalLRgeflymhc1Z+zMsVRUVjBz6UyaFTXjA3t8YOM6nz7w05zQ/4SNr0dPG82URVM4tPehfGjPD22x1O8e8d3t3r3/zPgPo8tG8+TZTzJr6SyqqqpYsX4Fc1bM4bfP/ZZmxc0IgqmLpxIRnHHQGVz+xOW0ataKNeVrmL4om+3wotEXcfpBp7O6YjXH7X0cRVHEfl3247bHbqN0RSn/ffR/b3dt9XH0XkfTplmbGt+rHsB2Bd3bdKd/p/6FLkPSDi52pBHtTWHYsGGptLR02wvW1ne/C9dem4WC6seypCQbRzBoEAwaxNp+fZk5sBf3TL6HkYNHbuxGf23ha7QobsGFYy5k/or5PHb2Y7Rp3obpi6dzzqhzOKbfMbw872USifvOuo/7p9zPQT0Ool/HfpuUcfMrNzN/xXyO2usoPtj3g0A22Gzmkpl87v2fq9cuPlj2IGPKxrBk7RKmvjOV8XPHUxRFdGndhfkr5wPQvmV7RgwaQfe23Tlmr2O46umraNWsFfe+fi8lUUK7Zu1YvG4xJ+19Eucddh6nHXDaxu3HT7KBienHu9fvoiQ1hYgYn1Kq1fS4u9bXoUL41a9g9epNAwFkAw2ffpqqRx6Ba67huXde4v5//JIDX1+08bx5ZVUlv3n2N9z92t2sWreKF+e/yOWPX86YsjF0bNmRLw/5MsfvczxL1y7lgK4H8NgbjzGmbMzGP8TVffHgL/K9I7+3MRAAtGnWhs6tOtdr9/5Q+gfWV61n9rLZ3PbqbTz71rOsS+tYW7WWtRVradmsJS2KW9CueTtemvcSXVt3ZdSUUVRUVbC+aj3H7HUMQ3sPZfRnRtOiuAX3fe4+urTqwowlMzZ+RjHF9apxdzembMzGAaCSVB+ePqivNm1g1apN29q3h+bNWbe+nPGtFnPYH//F4H324JbvHES35gPo2LIjN750I8+8+Qzj3hrH6Gmj+cqQrzB76Wzat2jPefefx6cP+DT9O/fn7xP+Tt8Ofendvjc/evRHrK1Yy1eH1u5c98E9D+bgngfXabeqUhXzVsyjoqqCsTPH8uSsJ1mf1m98v3/7/vRs35Nla5exfN1yOrfszKtvv8qyF5Zx7tBz+dQBn2J5+XJef+d1RpeN5kfP/ojfn/J7qlIVr779KuWV5ezTaR8AKn5cUacalXlx3ot0bNlxh7hBlqSdm6Ggvlq33jwUDBkCxx9PycQJvP/l8Tx03Xd56xMf5qYe85ncZ08GvvUCryx4hadmP0Wvdr2YuXQm15Vex5I1S3hk5iM88oVHuOGlG5i5ZCZLy5fSrnk73lz2JiMHj+TwPQ7noO4HbbWk8opyVq1fVedeghtevIHRZaOZtmgaby59kxXrVlDBpn+4py+fziF9DqFscRlrKtewcNVC1lauZc7yOSwtX8oFoy+gWVEzerTrwYNfeJCpi6by9sq3+faD3+bqE6+mRXGLLXx6w5u0YBL3T72f7x/5fV6e/zJ/fvHP/O7k39Vp3MA/X/8nPdr02KRHptB+cNQPCl2CpF2EoaA+ZsyAhQs3aaosLqby8ceoLF/DnK+fRcviVXS+fwzjDmzP6ktX8/Mnfs7Nr9zMynUrmbJoCmWLy1if1rNq3SoqqeSJWU/wzX9/k7067cVB3Q5ixPtG0LlVZ5578zlGTRnFR/f5KEvXLuWGF2/g64d+nbLFZUxfMp1PHvBJ5q+cz+VPXM6gboOYv3I+Pzm2brcu/ve0fzNhwQRmLZnFulTDTZty/5j8D4KgiqqNbbd9+jbum3IfM5bOoFVxK7535PcoKSphYLeB7Nt5X3q07cGPHv0RR+55JMMPGF6n+rZXtzbd6N85G2T3UNlDDOo2iKIoIqVERLB6/WomLZjEoX0OZd6KebQoabHFQFUURQTRJHVLUlMzFNTHB9/zbfHoo1n30jgWt4SKJbN54OHfM+vTx7L+Y2fRvVd/Fq9ZzAUfuID/HvPfPDD1Aaqooiplf1ArqaQkSmhW3IxJCyexZO0SDu9zOPOWz+Pp2U9zx8Q7mLZ4GhVVFRRHMS1KWlAURVmvQHnWU1FEEePnjueCD1xA9zbd67RLY8rGcMqAU3j8jce3GggAUv5PdSPvHUmb5m3Yo90eHLf3cUxcMJHPDPoMAM2LmzOw20C+Nuxr9Gnfp0711UX3Nt05feDpLC9fzoPTs8mWLnroInq27clFR1zEc3Oe45rnr+H6T1zPrRNuZcXaFZQUl/CjY360yXbWVWbHo/pVIJK0KzEU1Ee1ywq55x7m3nwt7fr0psdb85nWswtHNetL/z/9h/2+cjH/araUR2Y8wm0TbuOhsoc2644HCIJvf/DbjJ0xlrbN2/LNf3+TRKK4qJhubbrRvLg5byx9g/6d+/ONw74BwKF9DuXQPocC0L1td+767F2bTBC0vVaWr+SnY3/KorWL+PoLMKMTPDig9uuvWr+KZeXL6NSqE+WV5ZtdJQFs/NbeFFJK/Gvqv2hV3IrLnriMMwaewbi3xtG7fW8+sf8nuHXCrQzpOYS2Ldpy9TNX8/H9Ps6ALgN4avZTm21r7oq5PD7rcY7f53haN2vdZPtQXUVVBSVF/mcrqXH4f5f6SAnmzIHjjqPiR5ey6q3X6LkUlraAQ46ezDHd2nBwqxL6so4169dwwegLWLx28cbV93sHWlbAqz2heVFzOrfqzKgpo5iwYAK92/RmZcVKiilmn077cGifQ1m4euHGwXlbUp9A8OTsJ7n3/85naacF0BJe6gULar6Mv0Yn7nMiB3Q5gMVrFzOk1xDOev9Z2z3jYkNbvX41j896nH0778sJ+5xAh5YdmL18Nof3PZz9uuzHM28+Q2Wq5FMHfoqJCyaytHwp3dp045MHfnKzbfXr2I+rT7i6AHsBD09/mM6tOvOb537jTaV2AA9Pf5hFqxcx4n0jCl2K1KC8JLG+uneHVq0oensBXdfAjPbwpdOgvKiSLz6xnON7H8lbB+3Fza/cvEkgADh4Pgydmz1vUdSCVJUoW1RG5xadOXbvYxnacyidWnZiYNeBzFkxh/Yt2jfajZEqqioYec9IBry+gEF5B8hzfWHGNsYqVj+//vLbL3N0v6OZtWwWayrW0L1N94JPAtSmeRuu+MgVPDnrSd5a/hZXPXUVK8pXcPrA0wH40uAvcVD3gzjtgNO49OhLOWXAKQWttyZVqYoHpz/IynUr+e4R3zUQ7AC6tO5Sp6nCpW1ZvX41byx9o2Cfbyior5tuonL6dN6pWsWqVsW0rIL/9Idb/gELDurHB790KSfueyKL1yzebNW7DoK/Dsmen9T/JBavWcyayjWsWr+KsW+MpUPLDhy3z3H079Kfg3sczEUfvIiqVFWvWyjPXzmf/33uf6mo2vT0RUlRCT3b9OQnx8Kze9Z+e73a9qJLiy70btubi464iEdmPsJVJ1zFxUdeXOcaG8KkBZM4575zuOjBi3h71ducPfhs+nfuz95d9qZ7m+78Z8Z/Clrf9iiKIjq27MjlT17OgC4DeOGtFza5PXV5RTlli8sKWOHuZ0ivIRy797GFLqPe3lr+FmPKxhS6DFVz/9T7+fOLfy7Y5+/0pw8i4iTgt0Ax8OeU0hVNWsADDxCrVtFpNZz5SXhuT6gMGBq9uTLNZ+QT36Z76+6b9RJUV0QRd025a+PrDYPwBvcczAFdD+CBqQ9w6n6n0rZFW377/G9p37w95ww5p07lFkcxzYubbzaCvryinGfnPrvd21u0ahEHdj+QWz51CwO7DWThqoU7xDeovTruxaryVby+8HUOeeMQHpn5CN854jtcePiFFEXRTndefv8u+3PUnkfRullr3lz2JkVRxLDe2QRlD01/iMdnPc6vTvDeBto+by5/k8kLJ3PSvicVupQG8dgbj7G2Yu1OvT+fGfgZhu/fNFdm1WSnnuY4IoqBqcBHgTnAOODMlNJrW1qnQac5fu01qgYNIoCVRfCPQfCDj8LSjq1YeelKVq9bzW0TbuO8B86rcfW2xW05oPsBlM57t54SSjjzfWfSrU03vjbsawzoko3yu27cdayrXMfwA4bTsqQlPdv23Gx7S9Ys4YqnruCiIy6iW5tu27UrfS7vw9zKuVt8/6IPXsSvnn33j06bojbs3WlvmjdrziVHXbKxO35HcOvLt3LVs1fRqVUn5iybw37d9uOBsx4odFl1MnbmWF6c9yLNS5qzf5f9N7nfxQYpJdZVrqNFSdPN/SDtiMbOHEt5ZflOHQoaw/ZMc7xzfV3a3GFAWUppBkBE3A4MB7YYChrS788byn8BFcAd74fJ3eD8Dsez+LD3UxRFtG3RdouBAODA7gfywrkvsGj1In445oc8PfdpKM56Cn55/C83WbZjy478cfwfaVnSklbNWvHFg7+42fbat2jPoX0OpWPLjjw560kmvzO51rf+3VIgKKGE357yW77w/i8wuOdgVpSvoIoqDux6IIf0OoRX336Vo/c6ulaf0RTmr5jP50d9niDo064PRRSxsnxlocuqk18/82t++OgP+cGRP+DwPQ6nd7veNS4XEQaCJvLQ9IcYN3ccPzzqh4UuRTXYFU7pFNrOHgr6AG9Wez0H2Owi8og4FzgXYM89t+OE+Tb8Y3BLTpi4ljM/BeP3hJ8d9TMuOfYHWz3nf+o+p3LNx67h7FFnM/ZLY4Fs0NKvP/5rgmDUlFF8oM/m18EPP2A4HVt2pGPLjkxYMKHGbRcXFW/8xt6tTTfKK8rrvG9XfvhKzhx8Js2KmtGzXdYr0bd9X9q1aMchvQ7ZuNyOFAgAurbuysCuA/nFR37B8AOGb5zXYWc0tNdQhh8wnEuPuZQIJ0zaEQztNXSLd9aUdgU7++mDzwAnppS+kr/+AnBYSumbW1qnwe+SKEnSDmx3ukviHKBvtdd7AFs+MS5JkrZoZw8F44ABEbF3RDQHRgD3FbgmSZJ2Sjv1mIKUUkVEfAN4kOySxL+klCYVuCxJknZKO3UoAEgp/Rv4d6HrkCRpZ7eznz6QJEkNxFAgSZIAQ4EkScoZCiRJEmAokCRJOUOBJEkCDAWSJClnKJAkSYChQJIk5QwFkiQJMBRIkqScoUCSJAGGAkmSlDMUSJIkACKlVOgamlRELARmNeAmuwLvNOD2tDmPcePzGDc+j3Hj8xjXbK+UUrfaLLjbhYKGFhGlKaVhha5jV+Yxbnwe48bnMW58HuP68/SBJEkCDAWSJClnKKi/6wtdwG7AY9z4PMaNz2Pc+DzG9eSYAkmSBNhTIEmScoYCSZIEGArqJSJOiogpEVEWERcXup6dSUS8ERETIuLliCjN2zpHxMMRMS3/2ana8pfkx3lKRJxYrX1ovp2yiPhdREQh9mdHEBF/iYgFETGxWluDHdOIaBERd+Ttz0dEv6bcvx3BFo7xZRHxVv67/HJEnFLtPY/xdoiIvhExNiImR8SkiPhW3u7vcVNJKfmowwMoBqYD+wDNgVeAgYWua2d5AG8AXd/T9v+Ai/PnFwNX5s8H5se3BbB3ftyL8/deAD4IBDAaOLnQ+1bAY3o0MASY2BjHFPgv4A/58xHAHYXe5x3kGF8GXFTDsh7j7T++vYAh+fN2wNT8OPp73EQPewrq7jCgLKU0I6W0DrgdGF7gmnZ2w4Gb8uc3AadVa789pVSeUpoJlAGHRUQvoH1K6dmU/Rd+c7V1djsppSeAxe9pbshjWn1bdwMf2d16ZrZwjLfEY7ydUkrzUkov5s9XAJOBPvh73GQMBXXXB3iz2us5eZtqJwEPRcT4iDg3b+uRUpoH2f8cgO55+5aOdZ/8+Xvb9a6GPKYb10kpVQDLgC6NVvnO5RsR8Wp+emFD17bHuB7ybv1DgOfx97jJGArqrqZk6fWdtfehlNIQ4GTg/Ig4eivLbulY+++g7upyTD3eNbsO6A8MBuYBV+ftHuM6ioi2wD+AC1NKy7e2aA1tHuN6MBTU3Rygb7XXewBzC1TLTielNDf/uQC4l+x0zNt5tx/5zwX54ls61nPy5+9t17sa8phuXCciSoAO1L4rfZeVUno7pVSZUqoC/kT2uwwe4zqJiGZkgeDWlNI9ebO/x03EUFB344ABEbF3RDQnG7ByX4Fr2ilERJuIaLfhOXACMJHs+I3MFxsJjMqf3weMyEcN7w0MAF7IuxFXRMTh+TnBL1ZbR5mGPKbVt3U68Gh+vna3tuGPVe6TZL/L4DHebvnxuAGYnFL6dbW3/D1uKoUe6bgzP4BTyEbHTgd+WOh6dpYH2RUbr+SPSRuOHdl5vUeAafnPztXW+WF+nKdQ7QoDYBjZ/4SnA9eQz9K5Oz6Av5N1X68n+zZ0TkMeU6AlcBfZYK4XgH0Kvc87yDG+BZgAvEr2B6eXx7jOx/dIsq78V4GX88cp/h433cNpjiVJEuDpA0mSlDMUSJIkwFAgSZJyhgJJkgQYCiRJUs5QIGmrIqIyv/vfxIi4KyJa12Ebf46IgfnzH7znvWcaqlZJ9eMliZK2KiJWppTa5s9vBcanTSeWqfP2JO1Y7CmQtD2eBPYFiIhv570HEyPiwrytTUQ8EBGv5O1n5O2PRcSwiLgCaJX3PNyav7cy/3lHRJyy4YMi4saI+HREFEfEVRExLr/p0HlNvdPS7qKk0AVI2jnk88SfDIyJiKHA2cAHyG4w83xEPE42W+XclNKp+Todqm8jpXRxRHwjpTS4ho+4HTgD+Hc+dfhHgK+TzRq4LKV0aES0AJ6OiIdSdqtcSQ3IngJJ29IqIl4GSoHZZHPTHwncm1JalVJaCdwDHEU23e/xEXFlRByVUlq2HZ8zGjgu/8N/MvBESmkN2b0xvpjX8DzZlLcDGmrnJL3LngJJ27Lmvd/s85vMbCalNDXvRTgF+GX+jf6ntfmQlNLaiHgMOJGsx+DvGz4O+GZK6cG67oCk2rGnQFJdPAGcFhGt8ztdfhJ4MiJ6A6tTSn8DfgUMqWHd9fntcWtyO9lpiaOADSHgQeDrG9aJiP3yz5TUwOwpkLTdUkovRsSNZHeZA/hzSumliDgRuCoiqsjuJPj1Gla/Hng1Il5MKX3uPe89BNwM3JdSWrdh20A/4MW8h2IhcFqD7pAkwEsSJUlSztMHkiQJMBRIkqScoUCSJAGGAkmSlDMUSJIkwFAgSZJyhgJJkgTA/wd5XX4JWfOWWgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the samples using columns 1 and 2 of the matrix\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "\n",
    "colors = ['red', 'green']\n",
    "\n",
    "# Color based on the sentiment Y\n",
    "ax.scatter(X[:,1], X[:,2], c=[colors[int(k)] for k in Y], s = 0.1)  # Plot a dot for each pair of words\n",
    "plt.xlabel(\"Positive\")\n",
    "plt.ylabel(\"Negative\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot, it is evident that the features that we have chosen to represent tweets as numerical vectors allow an almost perfect separation between positive and negative tweets. So you can expect a very high accuracy for this model! \n",
    "\n",
    "## Plot the model alongside the data\n",
    "\n",
    "We will draw a gray line to show the cutoff between the positive and negative regions. In other words, the gray line marks the line where $$ z = \\theta * x = 0.$$\n",
    "To draw this line, we have to solve the above equation in terms of one of the independent variables.\n",
    "\n",
    "$$ z = \\theta * x = 0$$\n",
    "$$ x = [1, pos, neg] $$\n",
    "$$ z(\\theta, x) = \\theta_0+ \\theta_1 * pos + \\theta_2 * neg = 0 $$\n",
    "$$ neg = (-\\theta_0 - \\theta_1 * pos) / \\theta_2 $$\n",
    "\n",
    "The red and green lines that point in the direction of the corresponding sentiment are calculated using a perpendicular line to the separation line calculated in the previous equations(neg function). It must point in the same direction as the derivative of the Logit function, but the magnitude may differ. It is only for a visual representation of the model. \n",
    "\n",
    "$$direction = pos * \\theta_2 / \\theta_1$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Equation for the separation plane\n",
    "# It give a value in the negative axe as a function of a positive value\n",
    "# f(pos, neg, W) = w0 + w1 * pos + w2 * neg = 0\n",
    "# s(pos, W) = (w0 - w1 * pos) / w2\n",
    "def neg(theta, pos):\n",
    "    return (-theta[0] - pos * theta[1]) / theta[2]\n",
    "\n",
    "# Equation for the direction of the sentiments change\n",
    "# We don't care about the magnitude of the change. We are only interested \n",
    "# in the direction. So this direction is just a perpendicular function to the \n",
    "# separation plane\n",
    "# df(pos, W) = pos * w2 / w1\n",
    "def direction(theta, pos):\n",
    "    return    pos * theta[2] / theta[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The green line in the chart points in the direction where z > 0 and the red line points in the direction where z < 0. The direction of these lines are given by the weights $\\theta_1$ and $\\theta_2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the samples using columns 1 and 2 of the matrix\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "\n",
    "colors = ['red', 'green']\n",
    "\n",
    "# Color base on the sentiment Y\n",
    "ax.scatter(X[:,1], X[:,2], c=[colors[int(k)] for k in Y], s = 0.1)  # Plot a dot for each pair of words\n",
    "plt.xlabel(\"Positive\")\n",
    "plt.ylabel(\"Negative\")\n",
    "\n",
    "# Now lets represent the logistic regression model in this chart. \n",
    "maxpos = np.max(X[:,1])\n",
    "\n",
    "offset = 5000 # The pos value for the direction vectors origin\n",
    "\n",
    "# Plot a gray line that divides the 2 areas.\n",
    "ax.plot([0,  maxpos], [neg(theta, 0),   neg(theta, maxpos)], color = 'gray') \n",
    "\n",
    "# Plot a green line pointing to the positive direction\n",
    "ax.arrow(offset, neg(theta, offset), offset, direction(theta, offset), head_width=500, head_length=500, fc='g', ec='g')\n",
    "# Plot a red line pointing to the negative direction\n",
    "ax.arrow(offset, neg(theta, offset), -offset, -direction(theta, offset), head_width=500, head_length=500, fc='r', ec='r')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that more critical than the Logistic regression itself, are the features extracted from tweets that allow getting the right results in this exercise.**\n",
    "\n",
    "That is all, folks. Hopefully, now you understand better what the Logistic regression model represents, and why it works that well for this specific problem. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
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 },
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}