54 Introduction to Logistic Regresssion.ipynb

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    "# Introduction to Logistic Regression\n",
    "\n",
    "Section 4-4.1 of Introduction to Statistical Learning by Gareth James, et al.\n",
    "\n",
    "### Background\n",
    "- We want to learn about Logistic Regression as a method for __classification__.\n",
    "- Some examples of classification problems:\n",
    "    - Spam versus real emails (Fake / Real)\n",
    "    - Loan Default (Yes / No)\n",
    "    - Disease Diagnosis (Positive / Negative)\n",
    "- All of the above are examples of Binary Classification \n",
    "- So far, we've only seen regression problems where we try to predict a continuous value, such as the price of a house or the grades on a test\n",
    "- Althought the name may be confusing at first, logisitc regression allows us to solve classification problems where we are trying to predict discrete categories\n",
    "- The convention for binary classification is to have two classes 0 and 1.\n",
    "\n",
    "We can't use a normal linear regression model on a binary group. It won't lead to a good fit:"
   ]
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       "\n",
       "Call:\n",
       "lm(formula = Binary ~ Number, data = binary)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.7502 -0.4368  0.0000  0.4371  0.7497 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 2.488e-01  3.032e-02   8.205 7.08e-16 ***\n",
       "Number      5.020e-04  5.247e-05   9.567  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.479 on 998 degrees of freedom\n",
       "Multiple R-squared:  0.084,\tAdjusted R-squared:  0.08308 \n",
       "F-statistic: 91.52 on 1 and 998 DF,  p-value: < 2.2e-16\n"
      ]
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     "output_type": "display_data"
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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(dplyr)\n",
    "\n",
    "binary <- read.csv(\"binary.csv\")\n",
    "\n",
    "pl <- ggplot(data= binary, aes(x=Number, y = Binary))+geom_point()\n",
    "pl + geom_smooth(aes(group=1),method ='lm',formula = y~x,se=FALSE,color='red')\n",
    "model <- lm( Binary ~ Number, binary )\n",
    "summary(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sigmoid Function\n",
    "The Sigmoid (aka Logistic) Function takes in any value and outputs it to be between 0 and 1.\n",
    "\n",
    "$$ h_ \\theta (x) =  \\frac{\\mathrm{1} }{\\mathrm{1} + e^- \\theta^Tx }  $$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uX6o9OfIKRUTO0SSTi163CTqyc+jutI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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(-8,8,0.1)\n",
    "plot(x, 1/(1+exp(-x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- This means we can take our Linear Regression Solutions and place it into the Sigmoid Function\n",
    "- This results in a probability from 0 to 1 of belinging in the 1 class\n",
    "- We can set a cuttoff point at 0.5, anything below it results in class 0, anything above is class 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Review\n",
    "- We can use the logistic function to output a value ranging from 0 to 1. Based off of this probability, we can assign a class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model Evaluation\n",
    "- After you train a logistic regression model on some training data, you will evaluate your model's performance on some test data.\n",
    "- You can use a confustion matrix to evaluate classification mdoels.\n",
    "- For example, imagine testing for disease\n",
    "- Test for presence of disease\n",
    "    - NO = negative test = FALSE = 0\n",
    "    - YES = postive test = TRUE = 1\n",
    "\n",
    "##### Confusion Matrix\n",
    "| `           | Predicted:  NO | Predicted: YES |     |   |\n",
    "|-------------|:--------------:|:--------------:|-----|---|\n",
    "|  Actual: NO | TN = 50        | FP = 10        | 60  |   |\n",
    "| Actual: YES | FN = 5         | TP = 100       | 105 |   |\n",
    "|             | 55             | 110            |     |   |\n",
    "\n",
    "__Basic Terminology__\n",
    "- True Positive (TP)\n",
    "- True Negative (TN)\n",
    "- False Positive (FP)\n",
    "- False Negatives (FN)\n",
    "\n",
    "#### Accurary:\n",
    "Overall, how often is the model correct?\n",
    "\n",
    "<img src=\"https://latex.codecogs.com/gif.latex?\\frac{(TP&space;&plus;&space;TN&space;)}{Total}&space;=&space;150/165&space;=&space;0.91\" title=\"\\frac{(TP + TN )}{Total} = 150/160 = 0.91\" /></a>\n",
    "\n",
    "#### Misclassification Rate (Error Rate)\n",
    "Overall, how often is it wrong?\n",
    "\n",
    "<img src=\"https://latex.codecogs.com/gif.latex?\\frac{(FP&space;&plus;&space;FN&space;)}{Total}&space;=&space;15/165&space;=&space;0.09\" title=\"\\frac{(FP + FN )}{Total} = 15/165 = 0.09\" /></a>\n",
    "\n",
    "\n",
    "#### Type I vs Type II Errors\n",
    "\n",
    "<img src = \"https://www.statisticssolutions.com/wp-content/uploads/2017/12/rachnovblog-768x310.jpg\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Working with the Data\n",
    "We will use the Titanic Dataset from Kaggle. THis is a very famous dataset and is very often a student's first step in machine learning! We'll be trying to predict a classification: survival \n",
    "\n",
    "Let's begin our understanding of implementing Logistic Regression in R for classification.\n",
    "\n",
    "We'll use a \"semi-cleaned\" version of the titanic data set.\n",
    "\n",
    "# The Data\n",
    "\n",
    "We can begin by loading in the training data into a data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.train <- read.csv(\"titanic_train.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 12</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>PassengerId</th><th scope=col>Survived</th><th scope=col>Pclass</th><th scope=col>Name</th><th scope=col>Sex</th><th scope=col>Age</th><th scope=col>SibSp</th><th scope=col>Parch</th><th scope=col>Ticket</th><th scope=col>Fare</th><th scope=col>Cabin</th><th scope=col>Embarked</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td>0</td><td>3</td><td>Braund, Mr. Owen Harris                            </td><td>male  </td><td>22</td><td>1</td><td>0</td><td>A/5 21171       </td><td> 7.2500</td><td>    </td><td>S</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2</td><td>1</td><td>1</td><td>Cumings, Mrs. John Bradley (Florence Briggs Thayer)</td><td>female</td><td>38</td><td>1</td><td>0</td><td>PC 17599        </td><td>71.2833</td><td>C85 </td><td>C</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>3</td><td>1</td><td>3</td><td>Heikkinen, Miss. Laina                             </td><td>female</td><td>26</td><td>0</td><td>0</td><td>STON/O2. 3101282</td><td> 7.9250</td><td>    </td><td>S</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>4</td><td>1</td><td>1</td><td>Futrelle, Mrs. Jacques Heath (Lily May Peel)       </td><td>female</td><td>35</td><td>1</td><td>0</td><td>113803          </td><td>53.1000</td><td>C123</td><td>S</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>5</td><td>0</td><td>3</td><td>Allen, Mr. William Henry                           </td><td>male  </td><td>35</td><td>0</td><td>0</td><td>373450          </td><td> 8.0500</td><td>    </td><td>S</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>6</td><td>0</td><td>3</td><td>Moran, Mr. James                                   </td><td>male  </td><td>NA</td><td>0</td><td>0</td><td>330877          </td><td> 8.4583</td><td>    </td><td>Q</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 12\n",
       "\\begin{tabular}{r|llllllllllll}\n",
       "  & PassengerId & Survived & Pclass & Name & Sex & Age & SibSp & Parch & Ticket & Fare & Cabin & Embarked\\\\\n",
       "  & <int> & <int> & <int> & <fct> & <fct> & <dbl> & <int> & <int> & <fct> & <dbl> & <fct> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 1 & 0 & 3 & Braund, Mr. Owen Harris                             & male   & 22 & 1 & 0 & A/5 21171        &  7.2500 &      & S\\\\\n",
       "\t2 & 2 & 1 & 1 & Cumings, Mrs. John Bradley (Florence Briggs Thayer) & female & 38 & 1 & 0 & PC 17599         & 71.2833 & C85  & C\\\\\n",
       "\t3 & 3 & 1 & 3 & Heikkinen, Miss. Laina                              & female & 26 & 0 & 0 & STON/O2. 3101282 &  7.9250 &      & S\\\\\n",
       "\t4 & 4 & 1 & 1 & Futrelle, Mrs. Jacques Heath (Lily May Peel)        & female & 35 & 1 & 0 & 113803           & 53.1000 & C123 & S\\\\\n",
       "\t5 & 5 & 0 & 3 & Allen, Mr. William Henry                            & male   & 35 & 0 & 0 & 373450           &  8.0500 &      & S\\\\\n",
       "\t6 & 6 & 0 & 3 & Moran, Mr. James                                    & male   & NA & 0 & 0 & 330877           &  8.4583 &      & Q\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 12\n",
       "\n",
       "| <!--/--> | PassengerId &lt;int&gt; | Survived &lt;int&gt; | Pclass &lt;int&gt; | Name &lt;fct&gt; | Sex &lt;fct&gt; | Age &lt;dbl&gt; | SibSp &lt;int&gt; | Parch &lt;int&gt; | Ticket &lt;fct&gt; | Fare &lt;dbl&gt; | Cabin &lt;fct&gt; | Embarked &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1 | 0 | 3 | Braund, Mr. Owen Harris                             | male   | 22 | 1 | 0 | A/5 21171        |  7.2500 | <!----> | S |\n",
       "| 2 | 2 | 1 | 1 | Cumings, Mrs. John Bradley (Florence Briggs Thayer) | female | 38 | 1 | 0 | PC 17599         | 71.2833 | C85  | C |\n",
       "| 3 | 3 | 1 | 3 | Heikkinen, Miss. Laina                              | female | 26 | 0 | 0 | STON/O2. 3101282 |  7.9250 | <!----> | S |\n",
       "| 4 | 4 | 1 | 1 | Futrelle, Mrs. Jacques Heath (Lily May Peel)        | female | 35 | 1 | 0 | 113803           | 53.1000 | C123 | S |\n",
       "| 5 | 5 | 0 | 3 | Allen, Mr. William Henry                            | male   | 35 | 0 | 0 | 373450           |  8.0500 | <!----> | S |\n",
       "| 6 | 6 | 0 | 3 | Moran, Mr. James                                    | male   | NA | 0 | 0 | 330877           |  8.4583 | <!----> | Q |\n",
       "\n"
      ],
      "text/plain": [
       "  PassengerId Survived Pclass\n",
       "1 1           0        3     \n",
       "2 2           1        1     \n",
       "3 3           1        3     \n",
       "4 4           1        1     \n",
       "5 5           0        3     \n",
       "6 6           0        3     \n",
       "  Name                                                Sex    Age SibSp Parch\n",
       "1 Braund, Mr. Owen Harris                             male   22  1     0    \n",
       "2 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female 38  1     0    \n",
       "3 Heikkinen, Miss. Laina                              female 26  0     0    \n",
       "4 Futrelle, Mrs. Jacques Heath (Lily May Peel)        female 35  1     0    \n",
       "5 Allen, Mr. William Henry                            male   35  0     0    \n",
       "6 Moran, Mr. James                                    male   NA  0     0    \n",
       "  Ticket           Fare    Cabin Embarked\n",
       "1 A/5 21171         7.2500       S       \n",
       "2 PC 17599         71.2833 C85   C       \n",
       "3 STON/O2. 3101282  7.9250       S       \n",
       "4 113803           53.1000 C123  S       \n",
       "5 373450            8.0500       S       \n",
       "6 330877            8.4583       Q       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t891 obs. of  12 variables:\n",
      " $ PassengerId: int  1 2 3 4 5 6 7 8 9 10 ...\n",
      " $ Survived   : int  0 1 1 1 0 0 0 0 1 1 ...\n",
      " $ Pclass     : int  3 1 3 1 3 3 1 3 3 2 ...\n",
      " $ Name       : Factor w/ 891 levels \"Abbing, Mr. Anthony\",..: 109 191 358 277 16 559 520 629 417 581 ...\n",
      " $ Sex        : Factor w/ 2 levels \"female\",\"male\": 2 1 1 1 2 2 2 2 1 1 ...\n",
      " $ Age        : num  22 38 26 35 35 NA 54 2 27 14 ...\n",
      " $ SibSp      : int  1 1 0 1 0 0 0 3 0 1 ...\n",
      " $ Parch      : int  0 0 0 0 0 0 0 1 2 0 ...\n",
      " $ Ticket     : Factor w/ 681 levels \"110152\",\"110413\",..: 524 597 670 50 473 276 86 396 345 133 ...\n",
      " $ Fare       : num  7.25 71.28 7.92 53.1 8.05 ...\n",
      " $ Cabin      : Factor w/ 148 levels \"\",\"A10\",\"A14\",..: 1 83 1 57 1 1 131 1 1 1 ...\n",
      " $ Embarked   : Factor w/ 4 levels \"\",\"C\",\"Q\",\"S\": 4 2 4 4 4 3 4 4 4 2 ...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "  PassengerId       Survived          Pclass     \n",
       " Min.   :  1.0   Min.   :0.0000   Min.   :1.000  \n",
       " 1st Qu.:223.5   1st Qu.:0.0000   1st Qu.:2.000  \n",
       " Median :446.0   Median :0.0000   Median :3.000  \n",
       " Mean   :446.0   Mean   :0.3838   Mean   :2.309  \n",
       " 3rd Qu.:668.5   3rd Qu.:1.0000   3rd Qu.:3.000  \n",
       " Max.   :891.0   Max.   :1.0000   Max.   :3.000  \n",
       "                                                 \n",
       "                                    Name         Sex           Age       \n",
       " Abbing, Mr. Anthony                  :  1   female:314   Min.   : 0.42  \n",
       " Abbott, Mr. Rossmore Edward          :  1   male  :577   1st Qu.:20.12  \n",
       " Abbott, Mrs. Stanton (Rosa Hunt)     :  1                Median :28.00  \n",
       " Abelson, Mr. Samuel                  :  1                Mean   :29.70  \n",
       " Abelson, Mrs. Samuel (Hannah Wizosky):  1                3rd Qu.:38.00  \n",
       " Adahl, Mr. Mauritz Nils Martin       :  1                Max.   :80.00  \n",
       " (Other)                              :885                NA's   :177    \n",
       "     SibSp           Parch             Ticket         Fare       \n",
       " Min.   :0.000   Min.   :0.0000   1601    :  7   Min.   :  0.00  \n",
       " 1st Qu.:0.000   1st Qu.:0.0000   347082  :  7   1st Qu.:  7.91  \n",
       " Median :0.000   Median :0.0000   CA. 2343:  7   Median : 14.45  \n",
       " Mean   :0.523   Mean   :0.3816   3101295 :  6   Mean   : 32.20  \n",
       " 3rd Qu.:1.000   3rd Qu.:0.0000   347088  :  6   3rd Qu.: 31.00  \n",
       " Max.   :8.000   Max.   :6.0000   CA 2144 :  6   Max.   :512.33  \n",
       "                                  (Other) :852                   \n",
       "         Cabin     Embarked\n",
       "            :687    :  2   \n",
       " B96 B98    :  4   C:168   \n",
       " C23 C25 C27:  4   Q: 77   \n",
       " G6         :  4   S:644   \n",
       " C22 C26    :  3           \n",
       " D          :  3           \n",
       " (Other)    :186           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df.train)\n",
    "str(df.train)\n",
    "summary(df.train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploratory Data Analysis\n",
    "It's always important to explore the data before jumping in head first. Let's see if we have any issues with NA values in our data. The 'Amelia' package can be used to help us visualize the missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# install.packages('Amelia')\n",
    "library(Amelia)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Shp5upvoJaWZrfeCKyREIySZtZIQC0t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\nAxQJMECRAAMUCTDwfxd7+EsZ6TLWAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Titanic Traning Set: N/A Map\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "missmap(df.train,main= 'Titanic Traning Set: N/A Map',\n",
    "        col = c('yellow','black'), legend = FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Roughly 20 percent of the \"Age\" data is missing. The proportion of Age \"missings\" is likely small enough for reasonable replacement with some form of __imputation.__ We will touch on that later\n",
    "\n",
    "Let's continue on by visualizing some of the data.\n",
    "\n",
    "## Data Visualization with ggplot2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Fx7w9CgIg3g7BQpNtfeMDSoSAM4O0WKzbU3DA0q0gDOTpFic+0NQ4OKNICzU6TY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\nKJLICVAkkROgSCInQJFEToAiiZyA/w+Lmu4OZqV/ggAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the survivor ratio along with the sex of the passangers\n",
    "\n",
    "ggplot(data = df.train, aes(Survived, fill = Sex)) + \n",
    "geom_bar( alpha = 0.8 ) + \n",
    "theme_bw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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n/r+vB+ICfIHuHO71y/74sgUr8L/GEi\nHc4PSF8+Hg7H6/s7bj6ebjw8Tt1c3X0Kd3N6u6/HO2+uj7dPzpzf4vz25188xfxzPLz79MON\n8/3JR/Hyn0sJIvW7wB8p0ufzp2p3U/9++lTv44NI518dv9+/3fvD1e33w6MzD6/j7U+/eIq5\nPt349OzG3a3v+Ufxyj+klwte0A53eoE/TKSzFe8O/729/Xp/8/pOly/3N073nz57e384PULd\nK/TP4XO8y+33q7s3/fHtn2IOh5u7u4/PbtxZ9k/+Qbzqj2ik4AXtcKcX+CNFuvsM7fM/788u\nfH92/7s7DW5v7p/Vuxfi9vbj4fxp3gM3P7/9Y8zx8PA03eONu5iP+QdR/pG8DCL1u8CfKdL7\nw8MXS4/PGZxunH/1dH+8PH3Cd3r6+8e3f4z5fPcZ37t76R5vlE9HINLyfERKqA7oRZGuDu8+\nfb4ZF+mnd48bTzF3n+G9O5yf8X68gUid8hEpoTqgF0U6vfhef2r3eOcPRvzw9k8x93z66QYi\ndcpHpITqgAZE+nL7/f35yYbreLrg9scnG+7fOL5Genr3H97+KeZ4d+vr/XMMjzf4GqlXPiIl\nVAf0okjXh/ji5ub0dPbpIej449Pf92/8/Fm7M8/e/nnM+dY/z27wrF2vfERKqA7o5Scbrg6H\n96dnsW+/vj9/C/bT+WHk6Ruy92/24/eRTsTbP3ytFTHXx8PxJM7TDb6P1CkfkRKqA5r309/X\nb5/8gZ9s6JSPSAnVAU38axTHT298R37Wrlc+IiVUBzRRpC+VDxX89HevfERKqA5o5l/s+3z1\npnfj7yM1y0ekhOqA+Buy80Gk4XzP4BFJgEjL8xEpoTogRJoPIg3newaPSAJEWp6PSAnVASHS\nfBBpON8zeEQSINLyfERKqA4IkeaDSMP5nsF3E+l/ORNP9QUQaXk+IiVUB4RI80Gk4XzP4BFJ\ngEjL8xEpoTogRJoPIg3newaPSAJEWp6PSAnVASHSfBBpON8zeEQSINLyfERKqA5obyLF32U/\njv7lJ0TqdwFE2lik4+EZg++PSP0ugEgbi/TpmUejf68dkfpdAJESkX7365iK5FO7YRCp3wUQ\nSYv06nG/Bp5sWJ6PSAnVAU0Q6bDyEen+H8Pja6SdXwCRtv/U7ponGy6pgGfwiCT4Kfs4/CzD\nA4jU7wKItL1IPNlwUQU8g0ckwU/ZH4t/JlyCSP0ugEjbi3RzfH/zqvdHpH4XQKTtReInGy6q\ngGfwiCRApOX5iJRQHdDeRHo1iNTvAoiUiOTkt0X6Bn35sCuqJnsTiU/tLqqA55GDRyQBIi3P\nR6SE6oD2JtKZm/f5f735JxCp3wUQqYtIt9+L/w76jyBSvwsgUhuRxn9UCJH6XeBPE6kFWpj/\nHvg3G/Z7AUTagOzJhuvB90ekfhf400T6T87EU30BLdJx1CNEangBRNpepFeDSP0ugEiINAIi\nDed7Bo9Igp9F+n797nB4dz38t5IQqd8FEGl7kW4e/u2T4+jfSkKkfhdApO1Fujrc/8W+m/eH\nq8H3R6R+F0Ck7UWKb8TyDdkdXwCREGkERBrO9wwekQR8arc8H5ESqgPam0g82XBRBTyD36lI\nr/jLQW+Ap7+X5yNSQnVAvy/S4fGFBb4huzwfkRKqA0Kk+SDScL5n8PsU6cQ6kT6exX3H10j7\nvQAibS/S9fnrsQPP2u34AoiUibTuyYbj4cv9q698H2nHF0Ck7UXiG7IXVcAz+N2KtPS/RnH1\n/f458MP7wfdHpH4XQCQtktOj9BuyXwffH5H6XQCRpEhWj7JvyA7/t10Qqd8FEEmJ9Kp/9/T1\n8H2k5fmIlFAd0N5+1u7VIFK/CyASIo2ASMP5nsEjkgCRlucjUkJ1QIg0H0QazvcMHpEEiLQ8\nH5ESqgNCpPkg0nC+Z/DdRGoBIi3PR6SE6oAQaT6INJzvGXw3kUYi7SDS8nxESqgOCJHmg0jD\n+Z7BI5IAkZbnI1JCdUCINB9EGs73DB6RBIi0PB+REqoDQqT5INJwvmfwiCRApOX5iJRQHRAi\nzQeRhvM9g0ckASItz0ekhOqAJoi09t/+fi2I1O8CiPRrJP9k8a8g0nC+Z/CIJECk5fmIlFAd\n0KSvkfYp0v88/OuJFQVMIJKmOiBEmg8iDed7Br9XkXb7ZINn8Ig0nu8Z/F5FuuUR6QcQaTjf\nM3hEEiBSIAqYQCRNdUB/9LN2nsEj0ni+Z/CIJECkQBQwgUia6oD+6J9s8AwekcbzPYPfqUhe\nECkQBUwgkqY6IESaDyIN53sGj0gCRApEAROIpKkOCJHmg0jD+Z7BI5IAkQJRwAQiaaoDQqT5\nINJwvmfwiCRApEAUMIFImuqA/uh/+9szeEQaz/cMHpEEiBSIAiYQSVMdECLNB5GG8z2DRyQB\nIgWigAlE0lQHdAEiHe9Qr88g0utBJE11QPsX6fjw4ufXDyDS60EkTXVAiDQfRBrO9wwekQRj\nXyMh0kwQSVMd0CWL9PeJbzn/7oqiyG75sCuqJpch0vGWR6SJ8IikqQ4IkeaDSMP5nsEjkmBE\npOPzF4j02yCSpjqgSxDp+PQSkWaASJrqgC5ApOOzV4g0A0TSVAe0f5GOx4cfZeAnG2aBSJrq\ngPYv0gsg0utBJE11QIg0H0QazvcMHpEEiBSIAiYQSVMdECLNB5GG8z2DRyQBIgWigAlE0lQH\nhEjzQaThfM/gEUmASIEoYAKRNNUBIdJ8EGk43zN4RBIgUiAKmEAkTXVAiDQfRBrO9wwekQSI\nFIgCJhBJUx0QIs0HkYbzPYNHJAEiBaKACUTSVAeESPNBpOF8z+ARSYBIgShgApE01QEh0nwQ\naTjfM3hEEiBSIAr8x8NfnlhRwDN4RBIgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIg\nCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2Yg\nUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGz\nZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJA\nsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJ\nokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2YgUiAKeAaP\nSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4\nBo9ICaJAsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIg\nCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2Yg\nUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGz\nZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJA\nsbNmIFIgCngGj0gJokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJ\nokCxs2YgUiAKeAaPSAmiQLGzZiBSIAp4Bo9ICaJAsbNmIFIgCngGj0gJokCxs2b8tkjfcv7d\nFaLAX7tCFPiwK4opfbt8kX65h0ekl+ARSSMKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQg\nChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CI\nlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn\n8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWi\ngGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYi\nBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtr\nBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoU\nO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQg\nChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CI\nlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn\n8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWi\ngGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYi\nBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtr\nBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoU\nO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQg\nChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CI\nlCAKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrBiIFooBn\n8IiUIAoUO2sGIgWigGfwiJQgChQ7awYiBaKAZ/CIlCAKFDtrxohIx/PLO56/PoNIrweRNKJA\nsbNmDIj04M/Di6dfnECk14NIGlGg2FkzXhbpeItIc0EkjShQ7KwZw5/aIdI0EEkjChQ7a8Zv\niPT3iW85/+4KUeCvXSEKfNgVxZS+XbJIJ3hEej08ImlEgWJnzUCkQBTwDB6REkSBYmfNQKRA\nFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfN4CcbAlHAM3hEShAFip01\ng5+1C0QBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEU\nKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEp\nQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/g\nESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQB\nz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQK\nRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYM\nRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh2\n1gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEU\nKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEp\nQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/g\nESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQB\nz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQK\nRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYM\nRApEAc/gESlBFCh21gxECkQBz+ARKWjF6jsAAAhCSURBVEEUKHbWDEQKRAHP4BEpQRQodtYM\nRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh2\n1gxECkQBz+ARKUEUKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEU\nKHbWDEQKRAHP4BEpQRQodtYMRApEAc/gESlBFCh21gxECkQBz+ARKUEUKHbWDEQKRAHP4BEp\nQRQodtaM3xbpW86/u0IU+GtXiAIfdkUxpW+XL9Iv9/CI9BI8ImlEgWJnzUCkQBTwDB6REkSB\nYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpES\nRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8Awe\nkRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTw\nDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRA\nFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81A\npEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJn\nzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSB\nYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpES\nRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8Awe\nkRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTw\nDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRA\nFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81A\npEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJn\nzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSB\nYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpES\nRIFiZ81ApEAU8AwekRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8Awe\nkRJEgWJnzUCkQBTwDB6REkSBYmfNQKRAFPAMHpESRIFiZ81ApEAU8AwekRJEgWJnzXi9SMc7\nnn6FSK8HkTSiQLGzZrxapOPjixOI9HoQSSMKFDtrBiIFooBn8IiUIAoUO2sGIgWigGfwiJQg\nChQ7a8ZviPT3iW8Afi5ZpBPVI5IJ9wUosPUF/rBHpBOI1O8Cl1gAkebDDjfORyQBIi3Pp8Ab\n8hFpPuxw43xEEjh/ssEEO9w4H5EEzp+1M8EON85HJAEiLc+nwBvyEWk+7HDjfEQSINLyfAq8\nIR+R5sMON85HJAEiLc+nwBvyEWk+7HDjfEQSINLyfAq8IR+R5sMON85HJAEiLc+nwBvyEWk+\n7HDjfEQSINLyfAq8IR+R5sMON85HJAEiLc+nwBvyEWk+7HDjfEQSINLyfAq8IR+R5sMON85H\nJAEiLc+nwBvyEWk+7HDjfEQSINLyfAq8IR+R5sMON85HJAEiLc+nwBvyEWk+7HDjfEQSINLy\nfAq8IR+R5sMON85HJAEiLc+nwBvyEWk+7HDjfEQSINLyfAq8If/yRQJYwZS1G/ldkTag/Zm+\nBAUuEERaDwUuEERaDwUukB2KBNAPRAKYACIBTACRACaASAATQCSACexQpOPWH8Dvcbxj64/h\nt9h9AQv7E2nnf4rHxxc7ZfcFPOxOpOPO/xB3v8PdF/CwO5Eu4g9x9xV2X2A6iLQFu6+w+wLT\nQaQN2HkDnmwQINIG0ODyQKT17L7ARVSYDCItZ+cfP8/aSRBpNTv/8BFJg0iLOR73/pMBe//4\nPexQJIB+IBLABBAJYAKIBDABRAKYACIBTACRACaASAATQCSACSCSi8OZq68/3rnVhwNe+IN1\ncQi+/nDnZh8PWOEP1sWDM9eH97/eCRcHf7AuwpnT65uPh+N1/OLLx8P5V7f/HA/vPv1wA3YK\nIrl4LtL34/3neB/Pv/h8/ozv+v7R6p5Pz27AXkEkF2eRvl8dru5Fubr9cn/H/f/eHf57e/v1\n/Kubu7uPz27AXkEkF49PNtzcu/M97rx/efP5n/f3t46Hq8+nux9vwF5BJBdni46np78fn2M4\n3Xh//q27T/LuPuN7d+fZ0w3YK4jk4vkTdD+IdHV49+nzzfmur+8Oxy8/3IB9gkgunov0w6d2\np9/4Hr/96ZcbsEf4w3Px3Ivrw3U8vXD/vy+33x++Rvpyd/fx2Q3YK4jk4rlIN6env9+d77w+\nxNdI51v/PLsBewWRXPzwmdrXu0egq5uHO68Oh/enJ8Nvr4+H40mfxxuwUxAJYAKIBDABRAKY\nACIBTACRACaASAATQCSACSASwAQQCWACiAQwAUQCmAAiAUzg/wFXcEvcU0gNHwAAAABJRU5E\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the number of passangers by class\n",
    "\n",
    "ggplot(df.train, aes(Pclass)) + \n",
    "geom_bar(aes(fill = factor(Pclass)) , alpha = 0.8) + \n",
    "theme_bw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pLkWwBJaqYBUgUkybcAktRMA6QKSJJvASSpmQZIFZAk3wJIUjMNkCogSb4FkKRm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\nAhLRBgGJaIOARLRB/w/cfQdL+1svpwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the Survivors based on their embark location\n",
    "\n",
    "ggplot(df.train, aes(Survived)) + \n",
    "geom_bar(aes(fill = factor(Embarked)), alpha = 0.8) + theme_bw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"Removed 177 rows containing non-finite values (stat_bin).\""
     ]
    },
    {
     "data": {
      "image/png": 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81vAdIu7UCqjWlcBhKQ9mgHUt/tY0ceSP1vAkhvCtLYb1UAUv+bANKbgpS1t49Y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\nCNkhQCJkhwCJkB3y/0+1BgehRHZbAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of the age of the passangers\n",
    "\n",
    "ggplot(df.train, aes(Age)) + \n",
    "geom_histogram(bins = 30, alpha = 0.5, color = 'blue', fill = 'cyan' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HVCIrP1I5Kbdb6I/dFRjFJ9RAI1lrTQKEQCNZe00ChEAjWXtNAoRAI1l7TQqIJI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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bar graph of the number of family\n",
    "ggplot(df.train, aes(factor(SibSp)))+geom_bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z4cPl+f/d9K2hLskACCEQnh1SHdPPxv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\nSJ4XOIfkeYFzSJ4XOIfkeYFzSJ4XuP8HBGxGusuwMKMAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the average ticket price per passanger\n",
    "\n",
    "ggplot(df.train,aes(Fare))+ geom_histogram(bins = 40, fill = 'green', color = 'black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Cleaning\n",
    "We want to fill in the missing age data instead of just dropping the missing age data rows. One way to do that is by filling in the mean age of all the passangers (imputation)\n",
    "\n",
    "However, we can be smarted about this and check the average age by passanger class. For example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"Removed 177 rows containing non-finite values (stat_boxplot).\""
     ]
    },
    {
     "data": {
      "image/png": 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3N3+PCiy4/dwXD/8Opt0w0VaqfQt+7x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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(df.train, aes(Pclass, Age)) +\n",
    "geom_boxplot(aes(group = Pclass, fill = factor(Pclass)), alpha = 0.4) +\n",
    "scale_y_continuous(breaks = seq(min(0),max(80),by= 2))+ theme_bw()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the wealthier passangers in the higher classse tend to be older, which makes sense. We can use these average age values to impute based n Pclass for Age."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Imputation of Age based on Class\n",
    "\n",
    "impute_age <- function(age,class){\n",
    "    out <- age\n",
    "    for (i in 1:length(age)){\n",
    "        \n",
    "        if (is.na(age[i])){\n",
    "\n",
    "            if (class[i] == 1){\n",
    "                out[i] <- 37\n",
    "\n",
    "            }else if (class[i] == 2){\n",
    "                out[i] <- 29\n",
    "\n",
    "            }else{\n",
    "                out[i] <- 24\n",
    "            }\n",
    "        }else{\n",
    "            out[i]<-age[i]\n",
    "        }\n",
    "    }\n",
    "    return(out)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "fixed.ages <- impute_age(df.train$Age,df.train$Pclass)\n",
    "\n",
    "df.train$Age <- fixed.ages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check to see if it worked"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CgjF8OgVbjlIidEkeCWi5wQRYJbLnJC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\nLIAiAQugSMACKBKwgP8HUQr4r5IUJgcAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Imputation Check\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "missmap(df.train,main = 'Imputation Check', col = c('yellow', 'black'),legend = T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It worked! Let's continue with building our model!\n",
    "\n",
    "## Building a Logistic Regression Model\n",
    "Now it's time to build our model! Let's begin by doing a final \"clean-up \" of our data by removing the features that won't be useful to us and make sure the features we will be using are the correct data types."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t891 obs. of  12 variables:\n",
      " $ PassengerId: int  1 2 3 4 5 6 7 8 9 10 ...\n",
      " $ Survived   : int  0 1 1 1 0 0 0 0 1 1 ...\n",
      " $ Pclass     : int  3 1 3 1 3 3 1 3 3 2 ...\n",
      " $ Name       : Factor w/ 891 levels \"Abbing, Mr. Anthony\",..: 109 191 358 277 16 559 520 629 417 581 ...\n",
      " $ Sex        : Factor w/ 2 levels \"female\",\"male\": 2 1 1 1 2 2 2 2 1 1 ...\n",
      " $ Age        : num  22 38 26 35 35 24 54 2 27 14 ...\n",
      " $ SibSp      : int  1 1 0 1 0 0 0 3 0 1 ...\n",
      " $ Parch      : int  0 0 0 0 0 0 0 1 2 0 ...\n",
      " $ Ticket     : Factor w/ 681 levels \"110152\",\"110413\",..: 524 597 670 50 473 276 86 396 345 133 ...\n",
      " $ Fare       : num  7.25 71.28 7.92 53.1 8.05 ...\n",
      " $ Cabin      : Factor w/ 148 levels \"\",\"A10\",\"A14\",..: 1 83 1 57 1 1 131 1 1 1 ...\n",
      " $ Embarked   : Factor w/ 4 levels \"\",\"C\",\"Q\",\"S\": 4 2 4 4 4 3 4 4 4 2 ...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 1 × 12</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>PassengerId</th><th scope=col>Survived</th><th scope=col>Pclass</th><th scope=col>Name</th><th scope=col>Sex</th><th scope=col>Age</th><th scope=col>SibSp</th><th scope=col>Parch</th><th scope=col>Ticket</th><th scope=col>Fare</th><th scope=col>Cabin</th><th scope=col>Embarked</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td>0</td><td>3</td><td>Braund, Mr. Owen Harris</td><td>male</td><td>22</td><td>1</td><td>0</td><td>A/5 21171</td><td>7.25</td><td></td><td>S</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 12\n",
       "\\begin{tabular}{r|llllllllllll}\n",
       "  & PassengerId & Survived & Pclass & Name & Sex & Age & SibSp & Parch & Ticket & Fare & Cabin & Embarked\\\\\n",
       "  & <int> & <int> & <int> & <fct> & <fct> & <dbl> & <int> & <int> & <fct> & <dbl> & <fct> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 1 & 0 & 3 & Braund, Mr. Owen Harris & male & 22 & 1 & 0 & A/5 21171 & 7.25 &  & S\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 12\n",
       "\n",
       "| <!--/--> | PassengerId &lt;int&gt; | Survived &lt;int&gt; | Pclass &lt;int&gt; | Name &lt;fct&gt; | Sex &lt;fct&gt; | Age &lt;dbl&gt; | SibSp &lt;int&gt; | Parch &lt;int&gt; | Ticket &lt;fct&gt; | Fare &lt;dbl&gt; | Cabin &lt;fct&gt; | Embarked &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1 | 0 | 3 | Braund, Mr. Owen Harris | male | 22 | 1 | 0 | A/5 21171 | 7.25 | <!----> | S |\n",
       "\n"
      ],
      "text/plain": [
       "  PassengerId Survived Pclass Name                    Sex  Age SibSp Parch\n",
       "1 1           0        3      Braund, Mr. Owen Harris male 22  1     0    \n",
       "  Ticket    Fare Cabin Embarked\n",
       "1 A/5 21171 7.25       S       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "str(df.train)\n",
    "head(df.train,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can deselect the columns we don't want using dplyrs \"select\" feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.train <- select(df.train, -PassengerId, -Name, -Ticket, -Cabin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t891 obs. of  8 variables:\n",
      " $ Survived: int  0 1 1 1 0 0 0 0 1 1 ...\n",
      " $ Pclass  : int  3 1 3 1 3 3 1 3 3 2 ...\n",
      " $ Sex     : Factor w/ 2 levels \"female\",\"male\": 2 1 1 1 2 2 2 2 1 1 ...\n",
      " $ Age     : num  22 38 26 35 35 24 54 2 27 14 ...\n",
      " $ SibSp   : int  1 1 0 1 0 0 0 3 0 1 ...\n",
      " $ Parch   : int  0 0 0 0 0 0 0 1 2 0 ...\n",
      " $ Fare    : num  7.25 71.28 7.92 53.1 8.05 ...\n",
      " $ Embarked: Factor w/ 4 levels \"\",\"C\",\"Q\",\"S\": 4 2 4 4 4 3 4 4 4 2 ...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 1 × 8</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Survived</th><th scope=col>Pclass</th><th scope=col>Sex</th><th scope=col>Age</th><th scope=col>SibSp</th><th scope=col>Parch</th><th scope=col>Fare</th><th scope=col>Embarked</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0</td><td>3</td><td>male</td><td>22</td><td>1</td><td>0</td><td>7.25</td><td>S</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 8\n",
       "\\begin{tabular}{r|llllllll}\n",
       "  & Survived & Pclass & Sex & Age & SibSp & Parch & Fare & Embarked\\\\\n",
       "  & <int> & <int> & <fct> & <dbl> & <int> & <int> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 0 & 3 & male & 22 & 1 & 0 & 7.25 & S\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 8\n",
       "\n",
       "| <!--/--> | Survived &lt;int&gt; | Pclass &lt;int&gt; | Sex &lt;fct&gt; | Age &lt;dbl&gt; | SibSp &lt;int&gt; | Parch &lt;int&gt; | Fare &lt;dbl&gt; | Embarked &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 0 | 3 | male | 22 | 1 | 0 | 7.25 | S |\n",
       "\n"
      ],
      "text/plain": [
       "  Survived Pclass Sex  Age SibSp Parch Fare Embarked\n",
       "1 0        3      male 22  1     0     7.25 S       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "str(df.train)\n",
    "head(df.train,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will need to factorize all the remaining columns that are non-continuous. This leaves only Age and Fare a number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.train$Survived <- factor(df.train$Survived)\n",
    "df.train$Pclass <- factor(df.train$Pclass)\n",
    "df.train$Parch <- factor(df.train$Parch)\n",
    "df.train$SibSp <- factor(df.train$SibSp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t891 obs. of  8 variables:\n",
      " $ Survived: Factor w/ 2 levels \"0\",\"1\": 1 2 2 2 1 1 1 1 2 2 ...\n",
      " $ Pclass  : Factor w/ 3 levels \"1\",\"2\",\"3\": 3 1 3 1 3 3 1 3 3 2 ...\n",
      " $ Sex     : Factor w/ 2 levels \"female\",\"male\": 2 1 1 1 2 2 2 2 1 1 ...\n",
      " $ Age     : num  22 38 26 35 35 24 54 2 27 14 ...\n",
      " $ SibSp   : Factor w/ 7 levels \"0\",\"1\",\"2\",\"3\",..: 2 2 1 2 1 1 1 4 1 2 ...\n",
      " $ Parch   : Factor w/ 7 levels \"0\",\"1\",\"2\",\"3\",..: 1 1 1 1 1 1 1 2 3 1 ...\n",
      " $ Fare    : num  7.25 71.28 7.92 53.1 8.05 ...\n",
      " $ Embarked: Factor w/ 4 levels \"\",\"C\",\"Q\",\"S\": 4 2 4 4 4 3 4 4 4 2 ...\n"
     ]
    }
   ],
   "source": [
    "str(df.train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "log.model <- glm(Survived ~. , family = binomial(link = 'logit'), data = df.train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "glm(formula = Survived ~ ., family = binomial(link = \"logit\"), \n",
       "    data = df.train)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-2.8158  -0.6134  -0.4138   0.5808   2.4896  \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)  1.845e+01  1.660e+03   0.011 0.991134    \n",
       "Pclass2     -1.079e+00  3.092e-01  -3.490 0.000484 ***\n",
       "Pclass3     -2.191e+00  3.161e-01  -6.930 4.20e-12 ***\n",
       "Sexmale     -2.677e+00  2.040e-01 -13.123  < 2e-16 ***\n",
       "Age         -3.971e-02  8.758e-03  -4.534 5.79e-06 ***\n",
       "SibSp1       8.135e-02  2.245e-01   0.362 0.717133    \n",
       "SibSp2      -2.897e-01  5.368e-01  -0.540 0.589361    \n",
       "SibSp3      -2.241e+00  7.202e-01  -3.111 0.001862 ** \n",
       "SibSp4      -1.675e+00  7.620e-01  -2.198 0.027954 *  \n",
       "SibSp5      -1.595e+01  9.588e+02  -0.017 0.986731    \n",
       "SibSp8      -1.607e+01  7.578e+02  -0.021 0.983077    \n",
       "Parch1       3.741e-01  2.895e-01   1.292 0.196213    \n",
       "Parch2       3.862e-02  3.824e-01   0.101 0.919560    \n",
       "Parch3       3.655e-01  1.056e+00   0.346 0.729318    \n",
       "Parch4      -1.586e+01  1.055e+03  -0.015 0.988007    \n",
       "Parch5      -1.152e+00  1.172e+00  -0.983 0.325771    \n",
       "Parch6      -1.643e+01  2.400e+03  -0.007 0.994536    \n",
       "Fare         2.109e-03  2.490e-03   0.847 0.397036    \n",
       "EmbarkedC   -1.458e+01  1.660e+03  -0.009 0.992995    \n",
       "EmbarkedQ   -1.456e+01  1.660e+03  -0.009 0.993001    \n",
       "EmbarkedS   -1.486e+01  1.660e+03  -0.009 0.992857    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 1186.66  on 890  degrees of freedom\n",
       "Residual deviance:  763.41  on 870  degrees of freedom\n",
       "AIC: 805.41\n",
       "\n",
       "Number of Fisher Scoring iterations: 15\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"not plotting observations with leverage one:\n",
      "  679\""
     ]
    },
    {
     "data": {
      "image/png": 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KTmz+ZG/3/501/UdA+ub7dnKf9ESIOF\nzGzGQkp0NOBtcZlcflYf/p5/ilBiru3ta3HFlHmjePrm02JmukbqvEybWbtV1zXVbhZ+nNIV\n1hSyYCSaiW2Hpx1cGMzL1/dvDD78izGUtxeEZMzYnddBmf/+y/Px/0z99d+/4f/6jzEvt6eG\n++m/sfG9jtvFf8px/XM0zUH/p9m0u2QzTv5WrJHKr69rm+c10vhqYGSN5GQloiebop/7m/0G\nt2ukxn3G60iPfaTzrbzlaR9pI4XMppn07f79LXO6j9R9c8aAst7GW3pfPIoIj9p9Ikhpw/+Q\nWOblqN1xelOtdjmUryMluz9eRxL5teMWQXH4OlK3RvhbPqB5o8C0VSnQkYoopPQom6LXUeCT\n72sgIxmHL8j+1iiC8mVKrI90CCkM3xx9pCOhFSGZZ56nKnrLs6AjIUIKx7K1EusjqbWbdruk\nuHzQJZG+r4+QvrQkJTqSWhnSoT7t56p9Zx8hjfm06p+dEh1prT78/XpDgpCGzTo3Y1ZLdCS2\nMqSkXSPNObPhq1GgM/P0jM8p0ZHa6k27pDjb55xwZoMD3bmG61LiOIPe2oMNzYmo0mvoE9Iw\n0/434zDpaEtbPuH9d61+QfZUnIe6k175m5BGmG7jzny9WiIjKzizYUvqt1ZV7xKZt1b69/oN\naxMXN0Lakuf3isx6HbxLZ9NvYvx5q85seDq7wfNURaJZG9UVzZrxm38r8BYQ0sa0ayKTz10p\nwQE27Tan+Yer9w+Z70kCIW2R6VqipB+xNqRjmue31KTSD+wjpE9eOiIl71aGVH6sS1I8kXz0\npVu9kuYdcoBVK0PKzCm/mjQ/8dGXrplXvicoboKzv8u3UHDUzj12lH6IIKSdOROSJ6yUfsXq\nTbvruXgHBZt2fhDSr1h/sKG8NqQx0tNWWSLmoqQfsfrwd3U5/PQkmp6BUWASKf0EXpDdPEr6\nBYS0fZT0A1aHdN6VR+5uoukZGgU+oSTvJG81f3wvkZbEsrAQJfm2MqSjye7FE3ec8Yl9X44C\nc1CSZ6svx3Wfd7G170eBWSjJL8GZDYT0EyjJq5UhpfUaqThxVYjl4AuU5JNmH+mcGOlH9rEY\nfIOSPFp71G5XP23SU+0I6TuU5I/kdSSz054hREhfIiRvOLMhKJTkCyGFhZI8UYV0lV5Fn0Xg\na5Tkx5qQLpkxWfn5SNcdryP9CkryYkVIl+q5uua34ngDH335KwjJhxUhZUU8B5MV75Ld3X1P\nFVqU5MGKkKpnyZjE7K7CKeqPAl+hJPcEIYmvstofBb5DSM4JQhJOzeso8B1WSc4RUpAoyTVC\nChMlObYqJGsvWfDcr0ZJbhFSoAjJLc61CxYluURIwSIklwgpXJTkECEFjJLcIaSAEZI7hBQy\nSnKGkELGMXBnCClohOQKIYWNkhwhpLCxcecIIQWOkNwgpNBRkhOEFDpCcoKQgkdJLhBS+AjJ\nAUIKH6skBwgpAoRkHyFFgFWSfYQUA0qyjpCiQEi2EVIUWCXZRkhxICTLCCkOrJIsI6RIEJJd\nhBQJVkl2EVIsCMkqQooFqySrCCkahGQTIcWDkiwipHgQkkWEFBFKsoeQIkJI9jgMyTyzMQpM\noyRrHIZ0JCTfCMkal5t21ySzPQpMoyRbnO4jXc3B9igwiZBscXuw4WiutkeBSZRkye8ctZu9\nA4UVmMWW/E5IjkcRqyYjStIipMiwSrLDR0ifn0OeZHsoyQpCig0hWUFI0al3kShJipCiwyrJ\nBkKKDyVZQEjxISQLOPwdIfaS9AgpQrwoq0dIETLtKsn3lISDkGLUbNlRkgwhxYjDDXKEFCX2\nktQIKUqsktQIKU6sksQIKU6sksQIKVK8KKtFSJFilaRFSLGiJClCihUhSRFSrAx7SUqEFK26\nJI6ASxBStOqKWCNJEFK82EsSIqR48W4KIUKKGKskHUKKGCHpEFLMOHVVhpBixipJhpCixouy\nKoQUNVZJKoQUN46AixBS3FgliRBS3AhJhJAix+kNGoQUubIgXkpajZBixxpJgpBix+WLJQgp\nduwkSRBS9HinrAIhRa95pyxzfQ1CAifcCRASuldlfU/IhhESOAIuQEjgPCEBQgJHwAUICayS\nBAgJnN0gQEjIOdywHiEhZ9tuPUJCgVXSSoSEAle4W4mQUOAI+EqEhBIH7tYhJJQ43LAOIaHC\nOeCrEBIqrJJWISTU6oYI6SuEhFp9YS5C+gohocYR8DUICY32RVnfE7JFhIQGhxtWICS0uDDX\n9wgJraYiQlqOkNCpNusMT8ByhIRO+0IST8BShISe5kgDT8BShIQ+0/sTCxAS+uqzG3xPxvYQ\nEp7VZwr5noytISQ8Y+PuK4SEJ+blK+YhJDwhpO8QEp4Q0ncICc/YR/oKIeEZb5P9CiHhVf3+\nPt+TsS2EhHeslRYjJLxjP2kxQsIbjtwtR0h4Q0jLERLeENJyhIR31bEGnoUFCAnvuMLdYi5D\nuu+Nyc71QCaHwhPoW335Yt+TsR0OQ7on5eWedtVACOmXsZe0lMOQDub4qOmYZOVACOmXVRdu\nYNtuPochJdUv3pL0Rkg/rnmTLCXN5TCk5km5Zxkh/brqCuBcB3w2hyGl5t7cygjpx3GFu4Uc\nhnQ0+/rWzWSE9OO4wt0yLg9/H9p6zh92Y3n2vKvPW2UnaSanL8hed82t2/5tKKbv61FApTre\nwBX1Z+LMBgyrK+J4wzyEhDHNhzPzbMzgI6TPzwxP3S8wpv8FkwgJYzhPaAFCwhjWSAsQEsaw\nj7QAIWEUR+3mIySM4rzV+Tj8jQls181FSIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAh\nAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEC\nhAQIEBIgQEiAACEBAoSEZfikl0GEhCX47LERhIQlTO9P9BASFjAvX9EgJCxASGMICcPK58DU\nhxbar/0fooeQMKg6qpBXf3QRsY80gpAwxOQjIXHUbhghYUAdz3tIvI40gpAwYCIkDCIkvDP9\n/0z3FaMICW/6u0T1zlL9FWMICW9Mpbn38hVDCAnD2EdahJAwjJAWISQMGzyzAWMICRAgJECA\nkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAnr8Ja/EiFh\nDa68WiMkrGF6f0aNkLACl+pqEBJmePt4Fz7m5QUh4bPXy3K1ERFSg5Dw2WhI7CM1CAkzDYfE\nUbsKIWGmwZB4HalGSJin2SWq10Hk84yQME9ztI5rgQ8iJMxi+rcI6Q0hYY7e0TlCGuIhpGNi\n0qPdUUDM9L4Q0hCXIV13Jjnmf+WnwWV2RgEr2k/w42NexjgM6Vo+Gwezv+e3nZlcJ/EkYWMc\nhrQ3hzw/mKS4fTepjVEAnjgMqd4o2PXuqEcBeOI8pFO1TVetmNSjADxxumn32Duq3MvNPP0o\nAE8chnRP2u05M71CIiRsjdPXkQ5NPsnA+sj0fT0KwAvObAAECAkQ8BHS5y03QsLGEBIgQEiA\nACEBAoQECBASIMDhb0CAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECA\nkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAA\nAUICBAgJECAkQICQAAFCAgQICRD40ZCAjfliKdeH424U1oa8wUlmZrgZsscxbnB2bXCSmRlu\nhuxxjBucXRucZGaGmyF7HOMGZ9cGJ5mZ4WbIHse4wdm1wUlmZrgZsscxbnB2bXCSmRluhuxx\njBucXRucZGaGmyF7HOMGZ9cGJ5mZ4WbIHse4wdm1wUlmZrgZsscxbnB2bXCSmRluhuxxjBuc\nXRucZGaGmyF7HOMGZ9cGJ5mZ4WbIvzNGIECEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQE\nCBASIEBIgAAhAQKEBAgQEiBASICA3ZCOqUkO9/LmIWlvioZdT/rXlz3/NGD9JOcWprZiY1IL\nlibX4jy2tlh8YHVMh/LvkhTzKStvprphX+uZdFXPsWbA+knOLUxtxcakFixNrsV5bG2x+MTm\nmK5mfy/+idjn+cUk1/yamIts2Ek7x3aqYT4PWD7J5dDFU1uxMqkFO5NrcR5bWyw+shnSrhp4\n8Vc7mPPj1sn8iQZ9NFk9x46yYb4MWD3J9eClg6tZmdSCncm1N4+tLRafubj4iSmauuXKfybM\nIW/n2FE0zJcBqye5JJ7ampVJLdiZXHvz2NpiMWPU1sdwN1ne/PVk26zXvHsuzvvH/qpouL0B\nqye5JJ7ampVJLdiZXHvz2Npi8Zn9kI7F6tvCU93OsVImH7ClkNRTW7AYko3JzW3OY2uLxafx\n2h7BLSnW2/bmmDGnx1rvIFyT2wxJP7XVUPtfpAO2Mbm5g5CsTfnoeC0P/56U/yjYm2P1aISH\nUG2GVFFObcHipBbUk5s7CKliYcpHx2tjmL0j+Fn1N0k0c6w/5OdhrRzywIBFk/w+fNlAW9JJ\nHWBjVVd+sTDh0sViyXhtDLNdam5pdiu/VR2eua09POMyJNEkvw8/lz+/0kkdYC0kCxMeUkit\nc7uz91e+YHA2wsMo7T9qxYkTyueiHrCFSbYxtQUrk1qwM7m5zXlsbbH4NF6Lw751B00svPbe\nvqZ3KPcqz+oBWzldQD+1BWtnNtiZ3NzmPLa2WHwar8Vh7013wlMqPxpZz7F7Ug5Z/2+ahUm2\nMbUlG5NasDS5NuextcXi03htDrsX0r08zVc79OprMeRUeZSzP2D5S3ryqW2HauXVRzuTa3Me\nW1ssPo3X3aiAcBESIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBI\ngAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAA\nIQEChAQIEJIH1ecYJvvb9IPePpR75ANRpz+6290He0eNuexB85GgyVRJ7yGlI08WIf0A5rIH\n1bJ9zyY/K/g9gLEkCOkHMJc9aD552ySfHzT5nenvz/kpRJjLHjTLdrX1dk/N7nHnmJqk/hTu\nQ/JYV3Wbdo+72a3eIMxHHlm4m7T8mpp7ft6Z+uPCu+G8/vY5MyYb2e/CQoTkQX+NZMxjkX8s\n8buyk6z4flbc2rUBlHeTexvS4CPz6m6x03V7/Oyv2gk75G8hdb99rB5zdPt3DxUheVAt17dy\nH+mxUN8fd87Fl8de02MFcTLJNb8mTQCn4if76qH56CNLJ/P3+PPv8SNjTsVdk7+G1PvtxFyL\nx6Q+5kB4CMmD9qjdvbh9Kb61M0VO92Ijb1d+59wEUN6tV17jj6wHXFTRHdwbCKn328awWadD\nSB70X0eqK2jaMr3vvB4Cb3IYemRl/9i2u1XHAm/nv2wgpN5vHx5bhderk79wBAjJg/6BNGlI\nl8e23aFcTWXNY8ZDyv+ST69lYTZC8mAwpKHvDIc08btJWvy/WDWlx/NtMKT+hJwPKftIGoTk\nwUBIu26Hpbp5aRb77G0faeiRtYM5lgccym+9hHSp9pFedox4mUmD2ejBQEjlAbj8WBwEOD8f\ntTsWx9kO1VG72+gja492yqMJxSGMa7ePlJpjcajOPP12Wh3ZY40kQUgeDIRU79SUeyzlSz37\nt9eRHkt+eSrE4CMbafUC06HeE7o0MbavN3W/fWofgvUIyYOhkIozDkx9Pvjfy5kNjwiKH1zS\n6pyioUc2TvWm26Ou7HKujnJXj9t3ZzbUv12e2UBHGoQECBASIEBIgAAhAQKEBAgQEiBASIAA\nIQEChAQIEJJHIyeMnotLOOT3Q2pM9uGN4B9OOf18RuqON/dpEJJHw8v5rXoTa9K9i3bpEOb+\nuBiN4f1IEoTk0fBynpXvcN2XVw66TV/77rsRPDlkK4aPFiF5NLicn8oVUl69HeKxxljzDM34\n5XvxZgqsRkjuPV227vHfn0n+ynO8y5VPWq0i3s8Qrx5dXAWvu37d437vYnajV7ybkvGGJAVC\nci57eruRMeU16M5ZfR26S32huYPprrHfD6m4Cl53/brH97o7E1e8m3DkHUkKhOTayxtgy+va\nHes/kyKg+sI+jxTSQ7WM90MqroLXv35d787EFe+K4aZloW9H6a6r9sJQIyTXqqsmnLuQiliq\nd5FXl94HTusAAAF7SURBVGhoDtOd98VBu3P+HFKZVnv9uvJ7zZ2pK96VK6v0+ijsdXruhsMN\nAoTk2uBFgkYu83P5S5p3iz/9tL1+XXG/d2f8Ql2Peq/VNuXYBGEVZqJrS0IqNrzSgZ+2168r\n7vfujIdUbtGd0qHNOEJSYCa6Ni+kdukevixdc/268v7TnbeRzJ0grMJMdO1tH6n4ZvdnvY+0\nqw/edRe0u/RDerp+XXNn8op3o9hHkiAk196O2hXf7P6srjhcNHB8FHXJiqC6y9I1ZXTXr+vd\nmbzi3agLR+0UCMm57GlP5jWkS7ly6a5M136S0a4fUnP9uup+fWf6indv6h/+8TqSAiG5V3wC\n32UspObMhvy6f6xQsur8nfaydG0Z9fXrqvvNxewmr3j3pv4hZzZIEJIno3smZ7fnY9/4lCQJ\nQnKt/DC9+258zyRzus/C2d8ahORa/fGu4x9ofjOTb0HS4v1IIoTk3LE8i27iAef3sw+s2bNh\np0FIgAAhAQKEBAj8D4SmMyjT1iuUAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"not plotting observations with leverage one:\n",
      "  679\""
     ]
    },
    {
     "data": {
      "image/png": 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wb0UxASQhBRSGr6L0skBCLekNohXjPgY2MDfIo4pGpYV39+GEskeBZRSMN1JPWj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\nN3KO9Wu3AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VK5IkQCTXDC6ALfe1u9b/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\nWIsAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hMdf9arr6VBH91UNukTqZYL1erfQwMN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\nMziH/ZFZxrAAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(log.model)\n",
    "plot(log.model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see clearly that Sex,Age, and Class are the most significant features. Which makes sense given the women and children first policy.\n",
    "\n",
    "## Predicting using Test Cases\n",
    "Let's make a test set out of our training set, retrain on the smaller version of our training set and check it against the test subset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'caTools' was built under R version 3.6.3\""
     ]
    }
   ],
   "source": [
    "library(caTools)\n",
    "set.seed(101)\n",
    "\n",
    "split = sample.split(df.train$Survived, SplitRatio = 0.70)\n",
    "\n",
    "final.train = subset(df.train, split == TRUE)\n",
    "final.test = subset(df.train, split == FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's rerun our model on only our final training set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "glm(formula = Survived ~ ., family = binomial(link = \"logit\"), \n",
       "    data = final.train)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-2.8288  -0.5607  -0.4096   0.6174   2.4898  \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)  1.777e+01  2.400e+03   0.007 0.994091    \n",
       "Pclass2     -1.230e+00  3.814e-01  -3.225 0.001261 ** \n",
       "Pclass3     -2.160e+00  3.841e-01  -5.624 1.87e-08 ***\n",
       "Sexmale     -2.660e+00  2.467e-01 -10.782  < 2e-16 ***\n",
       "Age         -3.831e-02  1.034e-02  -3.705 0.000212 ***\n",
       "SibSp1      -2.114e-02  2.755e-01  -0.077 0.938836    \n",
       "SibSp2      -4.000e-01  6.463e-01  -0.619 0.536028    \n",
       "SibSp3      -2.324e+00  8.994e-01  -2.584 0.009765 ** \n",
       "SibSp4      -1.196e+00  8.302e-01  -1.440 0.149839    \n",
       "SibSp5      -1.603e+01  9.592e+02  -0.017 0.986666    \n",
       "SibSp8      -1.633e+01  1.004e+03  -0.016 0.987019    \n",
       "Parch1       7.290e-01  3.545e-01   2.056 0.039771 *  \n",
       "Parch2       1.406e-01  4.504e-01   0.312 0.754892    \n",
       "Parch3       7.919e-01  1.229e+00   0.645 0.519226    \n",
       "Parch4      -1.498e+01  1.552e+03  -0.010 0.992300    \n",
       "Parch5      -9.772e-03  1.378e+00  -0.007 0.994343    \n",
       "Parch6      -1.635e+01  2.400e+03  -0.007 0.994563    \n",
       "Fare         3.128e-03  3.091e-03   1.012 0.311605    \n",
       "EmbarkedC   -1.398e+01  2.400e+03  -0.006 0.995353    \n",
       "EmbarkedQ   -1.387e+01  2.400e+03  -0.006 0.995386    \n",
       "EmbarkedS   -1.431e+01  2.400e+03  -0.006 0.995243    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 829.60  on 622  degrees of freedom\n",
       "Residual deviance: 530.63  on 602  degrees of freedom\n",
       "AIC: 572.63\n",
       "\n",
       "Number of Fisher Scoring iterations: 15\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"not plotting observations with leverage one:\n",
      "  42, 473\""
     ]
    },
    {
     "data": {
      "image/png": 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6ZMm8XHN82/Pp2C0k5B5u1n6KCjaarN\n0+B/5edaGtLbAcznjxv//Zemw39M9q8p/q3ua/7999+/6k95n/afsenxhz+r/2h27W7JhJO/\nZVukap/OpPV13LtbnS9bKzTYHE02/iQSHSM9J7yO9DpGuj7yr5YfIxV/zz1G6t0X3K6va3oG\nOprO5jFS880JE0paO2/xc/YsGLUrCVuioxlcjNqdx3fVSrdT/jpSdPjjdaR1RCnR0Tz2Xkdq\ntgt/C5Zr0izQS7FZoiMdUUjxWbZE77PAkLUpMdAg5PQUoV+axS6s2izRkRIhbdziluhIakVI\npsvzUoVrWUp0pEVIezC/CjoSW7trd4iyywfdIun7+ghptpmbJTpSWxnSqTzt5659Zx8hDRre\n9s9oiY7kVg9/v38hQUgDvpyhMbElOtJbGVJUb5GmnNmwaBZo+f6+qgkn45GRBat37aLsbJ9r\nxJkNLnTGeQbvNX5mK5sjK9YONlQnokqvoU9IA5ozDb+dPDgQk/jccdRWvyB7yc5DPUiv/E1I\nQ+qQ0m9bpUznjRcW3oKBFs5s2JR8xVSfIz755TsSso+QNqV5S1ZqJmyT4MyqMxs6Zzd4XqpQ\nFOu6fJ998xZheEZIG2TqhEzKVuk3sGu3QeV7f037K/hFSJtk6o5s7BBgvrUhneM0fcQmln5g\nHyF9Zapt0YTXlODAypDyj3WJskeTj750rL0tYpPk3cqQEnNJ7yZOL3z0pXtVSOzd/QDB2d/5\nWygYtfPh/UjJ9/IETBDSwVwJyZP2aAMl+bR61+5+zd5Bwa6dL6bL9+IEa/1gQ35tSGOkp63y\nfJiOkn7C6uHv4nL48UW0PD2zwBek9AN4QXb7COkHENIekJJ3q0O6HvKRu4doefpmga8oyTfJ\nW81f34ukJfFMmI2S/FoZ0tkkz+xhO0/4xL6Fs8AkbJP8Wn05rqeNT8PjebAAr8z6JDizgZB+\nBNskj1aGFJdbpOzEVSGeBYvU2yNKck5zjHSNjPQj+3gSLMMmyZu1o3aH8lGTnmpHSEtRki+S\n15HMQXuGECEtRkmecGbDzlCSH4S0N5TkhSqku/Qq+jwBVqAkH9aEdEuMSfLPR7ofeB3pdxCS\nBytCuhUP1T19ZOMNfPTl76Ak91aElGTxnEySvUv28PS9VGiwc+feipCKx8iYyBzuwiVqzwLL\nEJJzgpDEV1ltzwILsU1yTRCScGneZ4GlCMkxQtopSnKLkPaKkpxaFZK1PXEe+fUIySlC2i1K\ncolz7faLkhwipB0jJHcIac8oyRlC2jN27pwhpF0jJFcIad8oyRFC2jd27hwhpJ0jJDcIae8o\nyQlC2j1KcoGQdo+QXCCk/aMkBwgpAFVFhGQPIQWATZJ9hBQCSrKOkEJASNYRUhAoyTZCCgIh\n2UZIYaAkywgpENUAOCHZQUiBYJNkFyGFgpCsIqRgVCc3UJINhBQMNkk2EVI4GG6wiJDCwXiD\nRYQUEEKyh5ACUldESXKEFJL6KIkVrEZIITGUZAshBYUThWwhpKAwcGeLw5BMl41Z4BtCssRh\nSGdC8o9NkiUud+3uUWJ7FvimPEpiBFzM6THS3ZxszwJfNON2rGQlt4MNZ3O3PQt8wb6dFb8z\najf5AArrsJZt+J2QHM8iXIRkAyGFpzxMYrxByUdI3x9AHmGb2CRZQEgBoiQ9QgoQIekRUoia\nF5N8L8luEFKIqu0RIckQUohMvUnyvSS7wfB3kOrThFjTIoQUJIYb1AgpTBwliRFSmOoNEqta\ng5ACxXlCWoQUqPIAiaMkEUIKVV4Qww0qhBQqBu6kCClYlKRESOHi9AYhQgpXtTWiJAFCClf1\nKhIhCRBSuMqdOnbuFAgpYPUIOOt7NUIKGNc/0yGkkBGSDCEFjfecqxBS2NgkiRBS2EzKS0kS\nhBS2egjc94JsHSGFrXovBSWtREiBY+BOg5ACR0gahBQ6RsAlCCl0bJIkCCl0vJlCgpCCx8Cd\nAiEFj307BUICIQkQEtgkCRASuAqKACGBTZIAIaEas+NC4CsQEsrrCXFF/TUICWl1JSFKWo6Q\nkNbXEyKkxQgJGQbuViIkZPh05pUICTlGwNchJBRMdfKq7wXZJkJCgU/wW4WQUDDN2B3mIyQU\nyhdl2SQtQ0goGC7esAYhocSpq2sQEkpVRYS0BCGhwr7dCoSESnOU5HtJNoiQUMsr4hzwRQgJ\nNUbAlyMkNDhKWoyQ0GDgbjFCQkv9TlnfC7I5hIQWzlxdipDQUo+A+16QzSEktFVvlPW9HJtD\nSGjjLecLERK6DO9KWoKQ0FUmREnzEBK68nXPvt1chIQu3nK+CCGhyxQvx7JJmoeQ8KbeHvEo\nzEBIeFMPf/MozEBIeFeNNPAozEBI+GBaf2MaQsIHRu3mIyT0YMxuLkICBAgJECAkQICQAAFC\nAgQICRAgJECAkAABlyE9j8Yk13Iio1MhJGyMw5CeUX5W8aGYCCFhTxyGdDLnV03nKMknQkjY\nE4chRcUvPqL4QUjYGYchVe08k4SQsDMOQ4rNs/oqISTsi8OQzuZYfvUwCSFhV1wOf5/qeq5f\n3u9CSNgYpy/I3g/VV4/jx1RM2+JZQI1HYxLObMAYPuZ8IkLCGC6pP5GPkL4/LDxuP4KPOZ+K\nkDCiulQkJX1DSBhRXyuSR+QLQsKY6pqrlPQFIWFM/THnPCTjCAlj6o855yEZx/A3RlUl+V6O\nX0dIGMWo3TSEhC/Yr5uCkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECA\nkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAA\nAUICBAgJECAkLMBHJr0jJMxWfkKz78X4KYSE2UzrbxQICXOZt3+REhLmI6QehIQR+QNRfRpz\n/W/7hygQEoYVowpp8VcTEcdInwgJg0w6EBKjdh8ICUPKeD5D4nWkT4SEISMh4R0hYYBp/zHN\nv+hDSOjXPiQqD5bKf9GDkNDPFKpbb//iDSFhBMdIUxESRhDSVISEEb1nNqAHIQEChAQIEBIg\nQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIEeIMFIWE1rnNHSBAwrb9D\nRUhYiwujpISE6T4ups9F9RuEhIneL4JSR0RIKSFhssGQOEZKCQnz9IfEqB0hYZbekHgdiZAw\nS3VIVG6Dgs+nQUiYoRqt48qr7wgJ05n2V4TU5iGkc2Tis91ZwIrW6BwhvXEZ0v1gonP6l39a\nSGJnFrDItP4hpDcOQ7rnBZ3M8Zk+DmZ0m8TD84Pqz0viovo9HIZ0NKc0PZko+/ppYhuzADxx\nGFL5n7FD64Z6FoAnzkO6FPt0xYZJPQvAE6e7dq+jo8Iz383TzwLwxGFIz6j5aN/xDRIhYWuc\nvo50qvKJerZHpm3xLAAvOLMBECAkQMBHSN/33AgJG0NIgAAhAQKEBAgQEiBASIAAw9+AACEB\nAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKE\nBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQI\nEBIgQEiAwI+GBGzMgme5PhwnbC4302bavzsjsa2ufKa9n2n7mZHYVlc+097PtP3MSGyrK59p\n72fafmYkttWVz7T3M20/MxLb6spn2vuZtp8ZiW115TPt/Uzbz4zEtrrymfZ+pu1nRmJbXflM\nez/T9jMjsa2ufKa9n2n7mZHYVlc+097PtP3MSGyrK59p72fafmYE7BkhAQKEBAgQEiBASIAA\nIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiCwyZDO5VIvvuL5hGmnp8hEp6d0\n2qmdRc7ZWdyctWW2urJtPkl6bDGke7la7hbWUTXtNMknHSunndpZ5Jydxc1ZW2arK9vmk6TP\nBkO6R/U6Olib9s1E9+zWTTx9/SLnLC1uztYyW13ZNp8kvbYX0tkk5To6mz9r0z6Z6+vvi3oO\n+kUuWFrcnK1ltrmybT5J+m0vJHNK63V0tjbtg3mkFv5zpl/kgqXFzdlaZpsr2+aTZGCOTuai\ndE+b9X89vo5RrUy7+4+MfpELlhY3Z2uZba5sm0+SftsLKW2to1xiY9rWQrKwyKntkOwsc2p3\nZdt8kvTNzvYMbKhX/CVNnyfttttuSFYWObUbkq1lTp2EZHHpu7OzPH0rOmv8qR02tRtSQbzI\nqeXFzemXOXUSUsHK0ndnZ3n6Mu1XA7prfP3675l2pH1s317LkD/hxYvbx8a07azszrR7b1lA\nSP3TLgaSHqqBJNshiRe3j8WQrCw9IX1X/4csO6nEzvr/y1/auBrxcI+VRU6tLW7O1jKndle2\nzSdJ3+wsT9+K+nW8U34cebUwbUunClhZ5NTumQ22ljm1u7JtPkn6Zmd5+laU6+gZ5TtM2v8K\nV/sAsZVRUyuLnLGzuDlry2x3Zdt8kvTNzvYMbKjW//MUmVg8rtmetoXX8WwscjVdWy872lpm\nuyvb5pOkb3bW5wAEgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAA\nAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFC\nAgQICRAgJECAkDwoPuM8Oj7G7/TxWdwDn4M6/ond1j/PGxnWsgemFI2V9BlSPPBgEdIPYC17\nUDy3n8noRwR/BjCUBCH9ANayB9UHbpvo+51GvzP+/Sk/hQhr2YPquV3svT1jc3jdOMcmKj98\n+xS9tlXNr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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"not plotting observations with leverage one:\n",
      "  42, 473\""
     ]
    },
    {
     "data": {
      "image/png": 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L/iCqn7zJbpweo4aB08iykkVR0jf/bTwwgJnkUV0vg8QkI4IgrpODmTkBCOeELS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",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3NLh/hbODG8BYS0P88tDTrHvgZ9Kwhpd55Kb2Ho29hQ1DER0u48Iz0UcsKWoo6I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\nRK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0w1iBo+p/g/4/RIy9kW0A2yUaRAPeNIfb+R5VvNy920CXetg1VbqL5iBGbtdFTr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\nAZEADIBIAAZAJAAD/B92wN8Bssn1ZAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final.log.model <- glm(formula=Survived ~ . , family = binomial(link='logit'),data = final.train)\n",
    "summary(final.log.model)\n",
    "plot(final.log.model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Accuracy 0.798507462686567\"\n"
     ]
    }
   ],
   "source": [
    "fitted.probabilities <- predict(final.log.model,newdata=final.test,type='response')\n",
    "\n",
    "fitted.results <- ifelse(fitted.probabilities > 0.5,1,0)\n",
    "misClasificError <- mean(fitted.results != final.test$Survived)\n",
    "\n",
    "print(paste('Accuracy',1-misClasificError))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like we were able to achieve around 80% accuracy, where as random guessing would have just been 50% accuracy. Let's plot the results and see the confusion matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jtaQ6rQth2EdrSGVKFtOwjtaA2pQtt2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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final.test$prediction <- fitted.probabilities\n",
    "\n",
    "ggplot(data = final.test, aes( x = Survived, y = prediction)) +geom_boxplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   \n",
       "    FALSE TRUE\n",
       "  0   140   25\n",
       "  1    29   74"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(final.test$Survived, fitted.probabilities > 0.5)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}