Week6_Lecture1SANDBOX.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>caseid</th><th scope=col>supportgroup</th><th scope=col>treat</th><th scope=col>ally</th><th scope=col>female</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;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 36</td><td>0</td><td>control</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 64</td><td>0</td><td>control</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 56</td><td>0</td><td>control</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 96</td><td>0</td><td>control</td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>101</td><td>0</td><td>control</td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 82</td><td>0</td><td>control</td><td>0.0000000</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & caseid & supportgroup & treat & ally & female\\\\\n",
       "  & <int> & <int> & <chr> & <dbl> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  36 & 0 & control & 0.3333333 & 0\\\\\n",
       "\t2 &  64 & 0 & control & 0.3333333 & 0\\\\\n",
       "\t3 &  56 & 0 & control & 0.3333333 & 0\\\\\n",
       "\t4 &  96 & 0 & control & 0.0000000 & 0\\\\\n",
       "\t5 & 101 & 0 & control & 0.0000000 & 0\\\\\n",
       "\t6 &  82 & 0 & control & 0.0000000 & 1\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 5\n",
       "\n",
       "| <!--/--> | caseid &lt;int&gt; | supportgroup &lt;int&gt; | treat &lt;chr&gt; | ally &lt;dbl&gt; | female &lt;int&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 |  36 | 0 | control | 0.3333333 | 0 |\n",
       "| 2 |  64 | 0 | control | 0.3333333 | 0 |\n",
       "| 3 |  56 | 0 | control | 0.3333333 | 0 |\n",
       "| 4 |  96 | 0 | control | 0.0000000 | 0 |\n",
       "| 5 | 101 | 0 | control | 0.0000000 | 0 |\n",
       "| 6 |  82 | 0 | control | 0.0000000 | 1 |\n",
       "\n"
      ],
      "text/plain": [
       "  caseid supportgroup treat   ally      female\n",
       "1  36    0            control 0.3333333 0     \n",
       "2  64    0            control 0.3333333 0     \n",
       "3  56    0            control 0.3333333 0     \n",
       "4  96    0            control 0.0000000 0     \n",
       "5 101    0            control 0.0000000 0     \n",
       "6  82    0            control 0.0000000 1     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(estimatr)\n",
    "library(ggplot2)\n",
    "data <- read.csv('ps3_lobbying.csv')\n",
    "set.seed(123456789)\n",
    "head(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a quick reminder of what each column means:\n",
    "\n",
    "- `caseid`: Number that identifies each legislator/district\n",
    "- `supportgroup`: This is the *outcome*. It is a measure of whether the legislator agreed to list their name publicly as a \"sponsor\" of the bill.\n",
    "- `treat`: This is the *treatment*. It has several possible values:\n",
    "    - `\"control\"`: the office received no contact from the lobbyist\n",
    "    - `\"officelobby\"`: the legislator was asked to meet to discuss the bill in their office\n",
    "    - `\"sociallobby\"`: the legislator was asked to meet to discuss the bill at a social location (a restaurant or bar)\n",
    "- `ally`: The authors thought that social lobbying might be especially effective among legislators who had supported the group's priorities in the past. To measure this, they asked the lobbyist: \"In your opinion, how well does the phrase ‘ally of the interest group’ describe the legislator?\" This is therefore the lobbyists' rating of whether the legislator is an ally of the interest group (values 0, 1/3, 2/3, and 1).\n",
    "- `female` : legislator gender, 1 = legislator is female; 0 = not\n",
    "\n",
    "Again, here is what `treat` looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.11617458279846"
      ],
      "text/latex": [
       "0.11617458279846"
      ],
      "text/markdown": [
       "0.11617458279846"
      ],
      "text/plain": [
       "[1] 0.1161746"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# Function to re-randomize, or \"shuffle\", the treatment variable\n",
    "re.randomize <- function(input.data) {\n",
    "    input.data$treat <- sample(input.data$treat)\n",
    "    return(input.data)\n",
    "}\n",
    "\n",
    "# Function to compute the effect of social lobbying\n",
    "compute.social.lobby.effect <- function(input.data) {\n",
    "    estimate <- difference_in_means(supportgroup ~ treat, input.data,\n",
    "                                    condition1 = 'control', condition2 = 'sociallobby')$coefficients\n",
    "    return(as.numeric(estimate))\n",
    "}\n",
    "\n",
    "actual.estimate <- compute.social.lobby.effect(data)\n",
    "actual.estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>caseid</th><th scope=col>supportgroup</th><th scope=col>treat</th><th scope=col>ally</th><th scope=col>female</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;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 36</td><td>0</td><td>control</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 64</td><td>0</td><td>control</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 56</td><td>0</td><td>control</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 96</td><td>0</td><td>control</td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>101</td><td>0</td><td>control</td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 82</td><td>0</td><td>control</td><td>0.0000000</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & caseid & supportgroup & treat & ally & female\\\\\n",
       "  & <int> & <int> & <chr> & <dbl> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  36 & 0 & control & 0.3333333 & 0\\\\\n",
       "\t2 &  64 & 0 & control & 0.3333333 & 0\\\\\n",
       "\t3 &  56 & 0 & control & 0.3333333 & 0\\\\\n",
       "\t4 &  96 & 0 & control & 0.0000000 & 0\\\\\n",
       "\t5 & 101 & 0 & control & 0.0000000 & 0\\\\\n",
       "\t6 &  82 & 0 & control & 0.0000000 & 1\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 5\n",
       "\n",
       "| <!--/--> | caseid &lt;int&gt; | supportgroup &lt;int&gt; | treat &lt;chr&gt; | ally &lt;dbl&gt; | female &lt;int&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 |  36 | 0 | control | 0.3333333 | 0 |\n",
       "| 2 |  64 | 0 | control | 0.3333333 | 0 |\n",
       "| 3 |  56 | 0 | control | 0.3333333 | 0 |\n",
       "| 4 |  96 | 0 | control | 0.0000000 | 0 |\n",
       "| 5 | 101 | 0 | control | 0.0000000 | 0 |\n",
       "| 6 |  82 | 0 | control | 0.0000000 | 1 |\n",
       "\n"
      ],
      "text/plain": [
       "  caseid supportgroup treat   ally      female\n",
       "1  36    0            control 0.3333333 0     \n",
       "2  64    0            control 0.3333333 0     \n",
       "3  56    0            control 0.3333333 0     \n",
       "4  96    0            control 0.0000000 0     \n",
       "5 101    0            control 0.0000000 0     \n",
       "6  82    0            control 0.0000000 1     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>caseid</th><th scope=col>supportgroup</th><th scope=col>treat</th><th scope=col>ally</th><th scope=col>female</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;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 36</td><td>0</td><td>sociallobby</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 64</td><td>0</td><td>officelobby</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 56</td><td>0</td><td>sociallobby</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 96</td><td>0</td><td>control    </td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>101</td><td>0</td><td>sociallobby</td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 82</td><td>0</td><td>officelobby</td><td>0.0000000</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & caseid & supportgroup & treat & ally & female\\\\\n",
       "  & <int> & <int> & <chr> & <dbl> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  36 & 0 & sociallobby & 0.3333333 & 0\\\\\n",
       "\t2 &  64 & 0 & officelobby & 0.3333333 & 0\\\\\n",
       "\t3 &  56 & 0 & sociallobby & 0.3333333 & 0\\\\\n",
       "\t4 &  96 & 0 & control     & 0.0000000 & 0\\\\\n",
       "\t5 & 101 & 0 & sociallobby & 0.0000000 & 0\\\\\n",
       "\t6 &  82 & 0 & officelobby & 0.0000000 & 1\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 5\n",
       "\n",
       "| <!--/--> | caseid &lt;int&gt; | supportgroup &lt;int&gt; | treat &lt;chr&gt; | ally &lt;dbl&gt; | female &lt;int&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 |  36 | 0 | sociallobby | 0.3333333 | 0 |\n",
       "| 2 |  64 | 0 | officelobby | 0.3333333 | 0 |\n",
       "| 3 |  56 | 0 | sociallobby | 0.3333333 | 0 |\n",
       "| 4 |  96 | 0 | control     | 0.0000000 | 0 |\n",
       "| 5 | 101 | 0 | sociallobby | 0.0000000 | 0 |\n",
       "| 6 |  82 | 0 | officelobby | 0.0000000 | 1 |\n",
       "\n"
      ],
      "text/plain": [
       "  caseid supportgroup treat       ally      female\n",
       "1  36    0            sociallobby 0.3333333 0     \n",
       "2  64    0            officelobby 0.3333333 0     \n",
       "3  56    0            sociallobby 0.3333333 0     \n",
       "4  96    0            control     0.0000000 0     \n",
       "5 101    0            sociallobby 0.0000000 0     \n",
       "6  82    0            officelobby 0.0000000 1     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(re.randomize(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>caseid</th><th scope=col>supportgroup</th><th scope=col>treat</th><th scope=col>ally</th><th scope=col>female</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;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 36</td><td>0</td><td>officelobby</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 64</td><td>0</td><td>sociallobby</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 56</td><td>0</td><td>sociallobby</td><td>0.3333333</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 96</td><td>0</td><td>control    </td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>101</td><td>0</td><td>officelobby</td><td>0.0000000</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 82</td><td>0</td><td>sociallobby</td><td>0.0000000</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & caseid & supportgroup & treat & ally & female\\\\\n",
       "  & <int> & <int> & <chr> & <dbl> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  36 & 0 & officelobby & 0.3333333 & 0\\\\\n",
       "\t2 &  64 & 0 & sociallobby & 0.3333333 & 0\\\\\n",
       "\t3 &  56 & 0 & sociallobby & 0.3333333 & 0\\\\\n",
       "\t4 &  96 & 0 & control     & 0.0000000 & 0\\\\\n",
       "\t5 & 101 & 0 & officelobby & 0.0000000 & 0\\\\\n",
       "\t6 &  82 & 0 & sociallobby & 0.0000000 & 1\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 5\n",
       "\n",
       "| <!--/--> | caseid &lt;int&gt; | supportgroup &lt;int&gt; | treat &lt;chr&gt; | ally &lt;dbl&gt; | female &lt;int&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 |  36 | 0 | officelobby | 0.3333333 | 0 |\n",
       "| 2 |  64 | 0 | sociallobby | 0.3333333 | 0 |\n",
       "| 3 |  56 | 0 | sociallobby | 0.3333333 | 0 |\n",
       "| 4 |  96 | 0 | control     | 0.0000000 | 0 |\n",
       "| 5 | 101 | 0 | officelobby | 0.0000000 | 0 |\n",
       "| 6 |  82 | 0 | sociallobby | 0.0000000 | 1 |\n",
       "\n"
      ],
      "text/plain": [
       "  caseid supportgroup treat       ally      female\n",
       "1  36    0            officelobby 0.3333333 0     \n",
       "2  64    0            sociallobby 0.3333333 0     \n",
       "3  56    0            sociallobby 0.3333333 0     \n",
       "4  96    0            control     0.0000000 0     \n",
       "5 101    0            officelobby 0.0000000 0     \n",
       "6  82    0            sociallobby 0.0000000 1     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(re.randomize(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.118100128369705"
      ],
      "text/latex": [
       "0.118100128369705"
      ],
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       "0.118100128369705"
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      "text/plain": [
       "[1] 0.1181001"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "-0.0603337612323492"
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      "text/latex": [
       "-0.0603337612323492"
      ],
      "text/markdown": [
       "-0.0603337612323492"
      ],
      "text/plain": [
       "[1] -0.06033376"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.0410783055198973"
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      "text/latex": [
       "0.0410783055198973"
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      "text/markdown": [
       "0.0410783055198973"
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      "text/plain": [
       "[1] 0.04107831"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compute.social.lobby.effect(re.randomize(data))\n",
    "compute.social.lobby.effect(re.randomize(data))\n",
    "compute.social.lobby.effect(re.randomize(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulations.20000 <- replicate(20000, compute.social.lobby.effect(re.randomize(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0.0186136071887035</li><li>-0.0115532734274711</li><li>-0.0359435173299101</li><li>-0.0115532734274711</li><li>0.0166880616174583</li><li>0.0430038510911425</li></ol>\n"
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       "\\begin{enumerate*}\n",
       "\\item 0.0186136071887035\n",
       "\\item -0.0115532734274711\n",
       "\\item -0.0359435173299101\n",
       "\\item -0.0115532734274711\n",
       "\\item 0.0166880616174583\n",
       "\\item 0.0430038510911425\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.0186136071887035\n",
       "2. -0.0115532734274711\n",
       "3. -0.0359435173299101\n",
       "4. -0.0115532734274711\n",
       "5. 0.0166880616174583\n",
       "6. 0.0430038510911425\n",
       "\n",
       "\n"
      ],
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       "[1]  0.01861361 -0.01155327 -0.03594352 -0.01155327  0.01668806  0.04300385"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(simulations.20000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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EAQwg4AIAhhBwAQhLADAAhC2AEABCHs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\nRK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(simulations.20000, binwidth = .025) + \n",
    "                             geom_vline(xintercept = actual.estimate, color = 'red') +\n",
    "theme(axis.title.x = element_text(size = 16), \n",
    "      axis.text.x = element_text(size = 16), \n",
    "      axis.text.y = element_text(size = 16))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rSo37dJQThjBwAQhLADAAhC2AEABCHsAACCEHYAAEEIOwCAIIQdAEAQwg4AIAhh\nBwAQhLADAAhC2AEABCHsAACCKC70BApj8+bNt99++9q1a3ft2jV27NiZM2fOnTu3vLy80PMC\nAOi9AzHsVq5cecMNNzQ2Nua/3bJlyx133LFq1aoFCxaMHTu2sHMDAOi1Ay7s1qxZs3Dhwlwu\nN23atDlz5kyYMGHt2rW33Xbbxo0br7jiisWLF5eWlhZ6jgAAvXHAhd33vve9XC43efLkK6+8\nMn/tddKkSbW1tQsWLNi6des999xz9tlnF3qOAAC9cWC9eGLTpk3PP/98SumCCy7o/Iy6Y445\nZubMmSmlBx98sGCTAwDomwPrjN2qVatSSqWlpTNmzOiy6MQTT3z00Uc3b9782muv1dTUFGJ2\nw8n8+fMLPQUA+s1APKovWrSo37fJPh1YZ+w2b96cUqqtre3+AtipU6fmv3jhhRcGe1oAAP3h\nwAq7l19+OaU0evTo7otGjRrVeQwAwLBzYF2Kzb/FyciRI7svKi0tLS0tbW5ubmho6Hz7I488\nsnHjxvzX5eXlc+bM6cXPLSoqymazFRUVvVi3X1x88cWF+tEAHJj6/fLujTfe2L8b3H/FxcWZ\nTCabzRZqAp1lMpm9LD2wwq6pqSmltKfAqqqqam5uzo/p8Mtf/vLee+/Nfz1mzJi5c+f2+qdX\nVVX1et0++vGPf1yoH81g+PnP06OPzp07d+6//VuhpwKFcPvt6bHHLrzwwgv/5V8KPRXCKi4u\nLisrK/QsUkqpvb19L0sPrLDLv0ddx1sTd9Ha2ppSKikp6XzjP/3TP5155pn5r4uLi7dv396L\nn5vNZsvLy3ft2tWLdeli9OjRra2tdmZnJfX1lSk1NjY29fD4HDVqVF1d3QDN6oAyYsSIoqIi\nO7NfjBgxor6+fu//dHXR61+B2CoqKkpLS3fs2NGjncluVVRUtLa2trS0FHoiKaVUVFS022uP\neQdW2OXP1e3cubP7olwul78I2+V83uGHH3744Yd3fPvaa6/14ue2t7eXlpYOkQMigFwuZ2d2\nlmltTSm1tbX1dLfYk/0ll8ullOzMfpE/LHvUIkVtbalXvwKx5U8vtba2trW1FXouw15ZWdnQ\nCbu9XxE+sF48MX78+JTSbv+qrqury5+xy48BABh2DqywO/TQQ1NKGzZsyDdcZ+vWres8BgBg\n2Dmwwu64445LKTU2Nq5Zs6bLoqeeeiqlNHHixHHjxhVgZgAAfXZghV1tbe2kSYAdUZ0AABVf\nSURBVJNSSkuXLu38BI4tW7Y8/vjjKaXTTjutYJMDAOibAyvsUkrz5s1LKa1evXrRokUvvvhi\nc3Pz6tWrr7766vr6+pqamt69TR0AwFBwYL0qNqV0/PHHX3jhhbfeeuvy5cuXL19eVFSUP3U3\natSoBQsWdP+oMQCA4eKAC7uU0nnnnTdlypRly5atX7++vr5+3LhxJ5xwwrnnnjtmzJhCTw0A\noPcOxLBLKU2fPn369OmFngUAQH864J5jBwAQlbADAAhC2AEABCHsAACCEHYAAEEIOwCAIIQd\nAEAQwg4AIAhhBwAQhLADAAhC2AEABCHsAACCEHYAAEEIOwCAIIQdAEAQwg4AIAhhBwAQhLAD\nAAhC2AEABCHsAACCEHYAAEEIOwCAIIQdAEAQxYWewDBTUlLSi7WKiopyuVzv1qWzXC63cuXK\nioqKyZMnF3ouQ0jR+PGtp56aqa3t6THW1tbmsOwXv/vd71paWo4++uhCTySC9vb24uLiXC63\n/6sUvfWtraeemjnsMMdzZxs3bnzzzTePOOKI0tLSQs9l2MvlckVFRUPkACsq2ttZuUyPfnmg\nsFpbW2fOnHncccfdeOONhZ4L/MX555+/ZcuWRx99tNATgb/493//91/84hdLliw57LDDCj0X\nBo9LsQAAQQg7AIAghB0AQBCeY8dw0t7evnz58urq6uOPP77Qc4G/+PWvf93Q0HDaaacVeiLw\nF+vWrXvppZdOOumkysrKQs+FwSPsAACCcCkWACAIYQcAEISwAwAIwidPMBRt3rz59ttvX7t2\n7a5du8aOHTtz5sy5c+eWl5fv/xYeeeSRhx56aOPGjTt27Bg7duyECRM+8IEPnHjiiQM3Z0Lq\n+6HY9y1AFx4h2QsvnmDIWbly5Q033NDY2Nj5xsmTJy9YsGDs2LH7XL25ufnaa69dtWpV90XH\nH3/85Zdf7tN12E99PBT7ZQvQhUdI9k7YMbSsWbNmwYIFuVxu2rRpc+bMmTBhwtq1a2+77ba6\nurqDDz548eLF+3zQ+fa3v33fffellGbOnPme97zniCOO2Lp169133/3YY4+llM4444yLL754\nMO4Jw1zfD8W+bwG68AjJPmWvuuqqQs8B/uK666574403Jk+efM0110yePLm6uvqoo4465phj\nVqxYUVdXN2LEiL1/zvq2bdu+8Y1v5HK5U0899bLLLps4cWJlZeW4ceNOOeWUXbt2Pfvss889\n99xJJ51UXV09aPeIYaqPh2K/bAG68AjJPnnxBEPIpk2bnn/++ZTSBRdc0Pn5Isccc8zMmTNT\nSg8++ODet7By5cq2trbi4uJPfvKTmUym86KLLroom83mcrlnnnlmAOZOKH0/FPu+BejCIyT7\nQ9gxhOSf9lFaWjpjxowui/LP6t28efNrr722ly288sorKaVJkyZVVVV1WVRWVva2t70tpbRp\n06b+mzIx9f1Q7PsWoAuPkOwPYccQsnnz5pRSbW1t95d3TZ06Nf/FCy+8sJctHHrooR/60Idm\nz57dfVEul9u+fXtKacyYMf0zXeLq+6HY9y1AFx4h2R/e7oQh5OWXX04pjR49uvuiUaNGdR6z\nJ7Nnz97tY1ZK6bHHHqurq0spTZs2ra8TJbq+H4p93wJ04RGS/eGMHUNI/gX8I0eO7L6otLQ0\n/2qvhoaGXmx5/fr1ixcvTilNnz792GOP7ds0ia/vh+LAHcwcsDxCsj+csWMIaWpqSilVVFTs\ndmlVVVVzc3N+TI+2uWTJkiVLlrS1tU2YMOFLX/pSP0yU6Pp+KA7EwcwBziMk+0PYMYTk/+Ls\n8sabHVpbW1NKJSUl+7/BFStW3HzzzflnE5944omf/exnd3sVA7ro+6HY7wczeIRkfwg7Bttl\nl1327LPPdr7lzDPP/MQnPpH+7y/RnTt3dl8rl8vlLzHs6a/VLl577bXFixfnX0Q2bty4efPm\nzZo1q++T5wDR90OxHw9myPMIyf4Qdgy2qqqqjuf55nW8wmv8+PHr1q3LP4G3i7q6uvzfo+PH\nj9/nj3jyySe//vWv19fXV1ZWnn/++aeffrpTI/RI3w/F/jqYoYNHSPaHsGOw7eXDTg499NCU\n0oYNG1pbW4uL/+rgXLduXecxe7FmzZqvfe1rLS0t06dPv/TSS2tqavo6Yw48fT8U++Vghs48\nQrI/vCqWIeS4445LKTU2Nq5Zs6bLoqeeeiqlNHHixHHjxu1lC42Njdddd11LS8usWbOuuuoq\nj1n0Tt8Pxb5vAbrwCMn+EHYMIbW1tZMmTUopLV26tL29veP2LVu2PP744yml0047be9bePjh\nh3fu3FldXf25z30um80O6GwJrO+HYt+3AF14hGR/ZPdyXQwG37hx41asWPHyyy+/8sorhxxy\nSHl5+dq1a6+//vo33nijpqbmC1/4QucLELfccsttt932wAMPvPOd7ywrK0spff/733/llVeO\nPPLIsWPH/nkPMpnMiBEjCncXGR76eCj2dAuwPzxCsk+ZXC5X6DnAX7n99ttvvfXW/JFZVFSU\n/8N01KhRV199dW1tbeeR11577a9//euU0i233FJdXZ1S+tjHPvb666/vffsXXnjheeedN1Cz\nJ5C+HIo93QLsJ4+Q7J2/FxlyzjvvvClTpixbtmz9+vX19fXjxo074YQTzj333H1+gmFzc/Mb\nb7wxOJPkQNDrQ7EftwBdeIRk75yxAwAIwosnAACCEHYAAEEIOwCAIIQdAEAQwg4AIAhhBwAQ\nhLADAAhC2AEABCHsAACCEHYAAEEIO2BArFixIpPJZDKZQk1g9erV+Qns2rWrv7ZZ8DsFsHfC\nDiCs22677cMf/vCECRPKy8uPOuqoM844Y9myZXsavHbt2gsuuOCtb31rRUXFlClTLr/88r00\n8RAZDHSVAxgATz/99IwZM2bMmFGoCfz2t7/NP8rt3Lmzd1v4xCc+MW3atJtuuqnjloLfqf3X\n0NDwgQ98YLcP+6effnpDQ0OX8UuXLh0xYkSXkdOnT9+8eXP3jQ+RwUB3wg6Iqe9hN3v27JTS\nwoUL+3dig+Piiy/O3/2zzz77Zz/72QsvvPDwww+fe+65+RsvvfTSzoMfeuih/PXld7/73UuW\nLFmzZs3ixYtrampSSrW1tV0qcIgMBnZL2AExHchh9+KLLxYXF6eULrzwwra2ts6LPv/5z6eU\nMpnMmjVrOm6cMWNG/sTYjh07Om781a9+VVZWllK6/vrrO29hiAwGdstz7IDCaGlp8dypfHT2\n+2aXLl3a2tpaWlr6rW99q6jorx7n/+M//qOkpCSXyz3++OP5W373u9/lI/iqq67qfBn05JNP\nPvvss1NKN998c8eNQ2QwsCfCDuiNFStWnHPOOUcffXRlZeVhhx02e/bsJUuWdG6UJ554ossL\nSDds2JDJZN761rc2NjZ+/vOff8tb3jJixIiKioq/+Zu/+e///u/8mIcffviDH/zgQQcdNGLE\niBkzZtxwww2tra0dW7jvvvsymcyYMWO6z+fWW2/NZDLHHHPMPmfe1NS0cOHC008//fDDD6+o\nqKitrZ09e/att97a0tLSMeaiiy7KZDIPPPBASunyyy/PZDKzZs3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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(simulations.20000, binwidth = .025) + \n",
    "                             geom_vline(xintercept = actual.estimate, color = 'red') +\n",
    "geom_vline(xintercept = -1*actual.estimate, color = \"red\") +\n",
    "theme(axis.title.x = element_text(size = 16), \n",
    "      axis.text.x = element_text(size = 16), \n",
    "      axis.text.y = element_text(size = 16))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0749"
      ],
      "text/latex": [
       "0.0749"
      ],
      "text/markdown": [
       "0.0749"
      ],
      "text/plain": [
       "[1] 0.0749"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(ifelse(simulations.20000 >= actual.estimate, 1, 0))/20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.12275"
      ],
      "text/latex": [
       "0.12275"
      ],
      "text/markdown": [
       "0.12275"
      ],
      "text/plain": [
       "[1] 0.12275"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(ifelse(simulations.20000 >= actual.estimate | \n",
    "           simulations.20000 <= -1*actual.estimate, 1, 0))/20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code here"
   ]
  }
 ],
 "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": "4.0.5"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}