Implementing Statistical Tools in R

# Implementing Statistical Tools in R

### Lecture 5

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name: Introduction

## Find me

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---

# About You

Pre-requisite for this lecture.
<br>
<br>
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You know __What is a Hypotheses and the difference between a research hypotheses and a statistical hypotheses__
<br>
<br>
<br>
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You know __t-tests conceptually__
<br>
<br>
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You know __Chi square-tests conceptually__
<br>
<br>
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You know __ANOVA conceptually__
<br>
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You know __Linear regression conceptually__
<br>
<br>
<br>
---
class: center, middle

# Acknowledgements

### Learning Statistics with R by Dr. Danielle Navarro

This lecture is stolen from her book.
---

# The Chi Square test

.yscroll[
.panelset[
.panel[.panel-name[Data]
<div style="border: 1px solid #ddd; padding: 0px; overflow-y: scroll; height:400px; overflow-x: scroll; width:100%; "><table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> id </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> choice_1 </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> choice_2 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> subj1 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj2 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj3 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj4 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj5 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj6 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj7 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj8 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj9 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj10 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj11 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj12 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj13 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj14 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj15 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj16 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj17 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj18 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj19 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj20 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj21 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj22 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj23 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj24 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj25 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj26 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj27 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj28 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj29 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj30 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj31 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj32 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj33 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj34 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj35 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj36 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj37 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj38 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj39 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj40 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj41 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj42 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj43 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj44 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj45 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj46 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj47 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj48 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj49 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj50 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj51 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj52 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj53 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj54 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj55 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj56 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj57 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj58 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj59 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj60 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj61 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj62 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj63 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj64 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj65 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj66 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj67 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj68 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj69 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj70 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj71 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj72 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj73 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj74 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj75 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj76 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj77 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj78 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj79 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj80 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj81 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj82 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj83 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj84 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj85 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj86 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj87 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj88 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj89 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj90 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj91 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj92 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj93 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj94 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj95 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj96 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj97 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj98 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj99 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj100 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj101 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj102 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj103 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj104 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj105 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj106 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj107 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj108 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj109 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj110 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj111 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj112 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj113 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj114 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj115 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj116 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj117 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj118 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj119 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj120 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj121 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj122 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj123 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj124 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj125 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj126 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj127 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj128 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj129 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj130 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj131 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj132 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj133 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj134 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj135 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj136 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj137 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj138 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj139 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj140 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj141 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj142 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj143 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj144 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj145 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj146 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj147 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj148 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj149 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj150 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj151 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj152 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj153 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj154 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj155 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj156 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj157 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj158 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj159 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj160 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj161 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj162 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj163 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj164 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj165 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj166 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj167 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj168 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj169 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj170 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj171 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj172 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj173 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj174 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj175 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj176 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj177 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj178 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj179 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj180 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj181 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj182 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj183 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj184 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj185 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj186 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj187 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj188 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj189 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj190 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj191 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj192 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj193 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj194 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> diamonds </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj195 </td>
   <td style="text-align:left;"> diamonds </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj196 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj197 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> spades </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj198 </td>
   <td style="text-align:left;"> clubs </td>
   <td style="text-align:left;"> clubs </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj199 </td>
   <td style="text-align:left;"> spades </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
  <tr>
   <td style="text-align:left;"> subj200 </td>
   <td style="text-align:left;"> hearts </td>
   <td style="text-align:left;"> hearts </td>
  </tr>
</tbody>
</table></div>

]
.panel[.panel-name[Choice1]

```
## 
##    clubs diamonds   hearts   spades 
##       35       51       64       50
```

]
.panel[.panel-name[Null H]
H0: All four suits are chosen with equal probability<br>
H0: P = ( .25, .25, .25, .25)
]
.panel[.panel-name[Alternative H1]
H1: At least one of the suit-choice probabilities isn’t .25<br>
H1: P != ( .25, .25, .25, .25)

]
.panel[.panel-name[Observed and Expected]

```r
probabilities <- c(clubs = .25, diamonds = .25, hearts = .25, spades = .25)
N <- 200
expected <- N * probabilities
observed - expected
```

```
## 
##    clubs diamonds   hearts   spades 
##      -15        1       14        0
```

```r
(observed - expected)^2
```

```
## 
##    clubs diamonds   hearts   spades 
##      225        1      196        0
```

```r
(observed - expected)^2/expected
```

```
## 
##    clubs diamonds   hearts   spades 
##     4.50     0.02     3.92     0.00
```

```r
sum((observed - expected)^2/expected)
```

```
## [1] 8.44
```
]
.panel[.panel-name[Critical Value]

```r
qchisq(p = 0.95,df = 3) # df = k-1
```

```
## [1] 7.814728
```

```r
## exact p - value
pchisq(q = 8.44,df = 3, lower.tail = FALSE)
```

```
## [1] 0.03774185
```

]
.panel[.panel-name[Silver bullet]

```r
goodnessOfFitTest(cards$choice_1) # the function is from the lsr package
```

```
## 
##      Chi-square test against specified probabilities
## 
## Data variable:   cards$choice_1 
## 
## Hypotheses: 
##    null:        true probabilities are as specified
##    alternative: true probabilities differ from those specified
## 
## Descriptives: 
##          observed freq. expected freq. specified prob.
## clubs                35             50            0.25
## diamonds             51             50            0.25
## hearts               64             50            0.25
## spades               50             50            0.25
## 
## Test results: 
##    X-squared statistic:  8.44 
##    degrees of freedom:  3 
##    p-value:  0.038
```

```r
# one could also us the funciton chisq.test()
```

]
]
]
 
---
class: left, top

# The t-test

```r
grades
```

```
##  [1] 50 60 60 64 66 66 67 69 70 74 76 76 77 79 79 79 81 82 82 89
```

]
.panel[.panel-name[One Sample]

```r
oneSampleTTest(x = grades, mu = 67.5)
```

```
## 
##    One sample t-test 
## 
## Data variable:   grades 
## 
## Descriptive statistics: 
##             grades
##    mean     72.300
##    std dev.  9.521
## 
## Hypotheses: 
##    null:        population mean equals 67.5 
##    alternative: population mean not equal to 67.5 
## 
## Test results: 
##    t-statistic:  2.255 
##    degrees of freedom:  19 
##    p-value:  0.036 
## 
## Other information: 
##    two-sided 95% confidence interval:  [67.844, 76.756] 
##    estimated effect size (Cohen's d):  0.504
```

]
.panel[.panel-name[Independent Samples test - Data]
<div style="border: 1px solid #ddd; padding: 0px; overflow-y: scroll; height:400px; overflow-x: scroll; width:100%; "><table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> grade </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> tutor </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 65 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 72 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 66 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 73 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 71 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 66 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 76 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 69 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 79 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 73 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 62 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 83 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 76 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 69 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 68 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 65 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 86 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 70 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 80 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 73 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 68 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 55 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 78 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 78 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 90 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 77 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 56 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 68 </td>
   <td style="text-align:left;"> Anastasia </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:left;"> Bernadette </td>
  </tr>
</tbody>
</table></div>

]
.panel[.panel-name[Independent Samples test - Code]

```r
independentSamplesTTest(
  formula = grade ~ tutor,
  data = harpo,
  var.equal = TRUE
)
```

```
## 
##    Student's independent samples t-test 
## 
## Outcome variable:   grade 
## Grouping variable:  tutor 
## 
## Descriptive statistics: 
##             Anastasia Bernadette
##    mean        74.533     69.056
##    std dev.     8.999      5.775
## 
## Hypotheses: 
##    null:        population means equal for both groups
##    alternative: different population means in each group
## 
## Test results: 
##    t-statistic:  2.115 
##    degrees of freedom:  31 
##    p-value:  0.043 
## 
## Other information: 
##    two-sided 95% confidence interval:  [0.197, 10.759] 
##    estimated effect size (Cohen's d):  0.74
```

]
]
]
---
class: left, top

# The ANOVA* test

]
.panel[.panel-name[Drug and mood gain]

```
## # A tibble: 3 x 2
##   drug     mean.mood.gain
##   <fct>             <dbl>
## 1 placebo           0.45 
## 2 anxifree          0.717
## 3 joyzepam          1.48
```

]
.panel[.panel-name[Code]

```r
aov(formula = mood.gain ~ drug, data = clin.trial) -> anova_test

anova_test
```

```
## Call:
##    aov(formula = mood.gain ~ drug, data = clin.trial)
## 
## Terms:
##                     drug Residuals
## Sum of Squares  3.453333  1.391667
## Deg. of Freedom        2        15
## 
## Residual standard error: 0.3045944
## Estimated effects may be unbalanced
```

```r
summary(anova_test)
```

```
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## drug         2  3.453  1.7267   18.61 8.65e-05 ***
## Residuals   15  1.392  0.0928                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

]
]
]
---

# Linear Regresison

.yscroll[
.panelset[
.panel[.panel-name[DATA]
<div style="border: 1px solid #ddd; padding: 0px; overflow-y: scroll; height:400px; overflow-x: scroll; width:100%; "><table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> dan.sleep </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> baby.sleep </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> dan.grump </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> day </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 7.59 </td>
   <td style="text-align:right;"> 10.18 </td>
   <td style="text-align:right;"> 56 </td>
   <td style="text-align:right;"> 1 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.91 </td>
   <td style="text-align:right;"> 11.66 </td>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:right;"> 2 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.14 </td>
   <td style="text-align:right;"> 7.92 </td>
   <td style="text-align:right;"> 82 </td>
   <td style="text-align:right;"> 3 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.71 </td>
   <td style="text-align:right;"> 9.61 </td>
   <td style="text-align:right;"> 55 </td>
   <td style="text-align:right;"> 4 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.68 </td>
   <td style="text-align:right;"> 9.75 </td>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:right;"> 5 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.99 </td>
   <td style="text-align:right;"> 5.04 </td>
   <td style="text-align:right;"> 72 </td>
   <td style="text-align:right;"> 6 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.19 </td>
   <td style="text-align:right;"> 10.45 </td>
   <td style="text-align:right;"> 53 </td>
   <td style="text-align:right;"> 7 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.19 </td>
   <td style="text-align:right;"> 8.27 </td>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:right;"> 8 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.40 </td>
   <td style="text-align:right;"> 6.06 </td>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:right;"> 9 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.58 </td>
   <td style="text-align:right;"> 7.09 </td>
   <td style="text-align:right;"> 71 </td>
   <td style="text-align:right;"> 10 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.49 </td>
   <td style="text-align:right;"> 11.68 </td>
   <td style="text-align:right;"> 72 </td>
   <td style="text-align:right;"> 11 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.27 </td>
   <td style="text-align:right;"> 6.13 </td>
   <td style="text-align:right;"> 65 </td>
   <td style="text-align:right;"> 12 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.95 </td>
   <td style="text-align:right;"> 7.83 </td>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:right;"> 13 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.65 </td>
   <td style="text-align:right;"> 5.60 </td>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:right;"> 14 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.41 </td>
   <td style="text-align:right;"> 6.03 </td>
   <td style="text-align:right;"> 66 </td>
   <td style="text-align:right;"> 15 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.33 </td>
   <td style="text-align:right;"> 8.19 </td>
   <td style="text-align:right;"> 69 </td>
   <td style="text-align:right;"> 16 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.30 </td>
   <td style="text-align:right;"> 6.38 </td>
   <td style="text-align:right;"> 73 </td>
   <td style="text-align:right;"> 17 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.47 </td>
   <td style="text-align:right;"> 11.11 </td>
   <td style="text-align:right;"> 52 </td>
   <td style="text-align:right;"> 18 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.21 </td>
   <td style="text-align:right;"> 5.51 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 19 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.53 </td>
   <td style="text-align:right;"> 6.69 </td>
   <td style="text-align:right;"> 53 </td>
   <td style="text-align:right;"> 20 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.00 </td>
   <td style="text-align:right;"> 9.74 </td>
   <td style="text-align:right;"> 54 </td>
   <td style="text-align:right;"> 21 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.35 </td>
   <td style="text-align:right;"> 9.02 </td>
   <td style="text-align:right;"> 63 </td>
   <td style="text-align:right;"> 22 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.86 </td>
   <td style="text-align:right;"> 6.44 </td>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:right;"> 23 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.86 </td>
   <td style="text-align:right;"> 9.43 </td>
   <td style="text-align:right;"> 56 </td>
   <td style="text-align:right;"> 24 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4.86 </td>
   <td style="text-align:right;"> 3.46 </td>
   <td style="text-align:right;"> 82 </td>
   <td style="text-align:right;"> 25 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.87 </td>
   <td style="text-align:right;"> 6.32 </td>
   <td style="text-align:right;"> 72 </td>
   <td style="text-align:right;"> 26 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.40 </td>
   <td style="text-align:right;"> 7.95 </td>
   <td style="text-align:right;"> 59 </td>
   <td style="text-align:right;"> 27 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.93 </td>
   <td style="text-align:right;"> 7.69 </td>
   <td style="text-align:right;"> 66 </td>
   <td style="text-align:right;"> 28 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.21 </td>
   <td style="text-align:right;"> 7.45 </td>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:right;"> 29 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.99 </td>
   <td style="text-align:right;"> 7.56 </td>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:right;"> 30 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.17 </td>
   <td style="text-align:right;"> 7.95 </td>
   <td style="text-align:right;"> 44 </td>
   <td style="text-align:right;"> 31 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.85 </td>
   <td style="text-align:right;"> 11.61 </td>
   <td style="text-align:right;"> 53 </td>
   <td style="text-align:right;"> 32 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.27 </td>
   <td style="text-align:right;"> 4.70 </td>
   <td style="text-align:right;"> 76 </td>
   <td style="text-align:right;"> 33 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.66 </td>
   <td style="text-align:right;"> 8.52 </td>
   <td style="text-align:right;"> 41 </td>
   <td style="text-align:right;"> 34 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4.98 </td>
   <td style="text-align:right;"> 4.70 </td>
   <td style="text-align:right;"> 86 </td>
   <td style="text-align:right;"> 35 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.19 </td>
   <td style="text-align:right;"> 8.32 </td>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:right;"> 36 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.41 </td>
   <td style="text-align:right;"> 9.38 </td>
   <td style="text-align:right;"> 63 </td>
   <td style="text-align:right;"> 37 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4.84 </td>
   <td style="text-align:right;"> 4.18 </td>
   <td style="text-align:right;"> 89 </td>
   <td style="text-align:right;"> 38 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.03 </td>
   <td style="text-align:right;"> 5.98 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 39 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.66 </td>
   <td style="text-align:right;"> 9.29 </td>
   <td style="text-align:right;"> 57 </td>
   <td style="text-align:right;"> 40 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.51 </td>
   <td style="text-align:right;"> 6.01 </td>
   <td style="text-align:right;"> 59 </td>
   <td style="text-align:right;"> 41 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.92 </td>
   <td style="text-align:right;"> 10.54 </td>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:right;"> 42 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.12 </td>
   <td style="text-align:right;"> 11.78 </td>
   <td style="text-align:right;"> 48 </td>
   <td style="text-align:right;"> 43 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.47 </td>
   <td style="text-align:right;"> 11.60 </td>
   <td style="text-align:right;"> 53 </td>
   <td style="text-align:right;"> 44 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.99 </td>
   <td style="text-align:right;"> 11.35 </td>
   <td style="text-align:right;"> 50 </td>
   <td style="text-align:right;"> 45 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.44 </td>
   <td style="text-align:right;"> 5.63 </td>
   <td style="text-align:right;"> 72 </td>
   <td style="text-align:right;"> 46 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.16 </td>
   <td style="text-align:right;"> 6.98 </td>
   <td style="text-align:right;"> 57 </td>
   <td style="text-align:right;"> 47 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.62 </td>
   <td style="text-align:right;"> 6.03 </td>
   <td style="text-align:right;"> 60 </td>
   <td style="text-align:right;"> 48 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.87 </td>
   <td style="text-align:right;"> 4.66 </td>
   <td style="text-align:right;"> 70 </td>
   <td style="text-align:right;"> 49 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 9.00 </td>
   <td style="text-align:right;"> 9.81 </td>
   <td style="text-align:right;"> 46 </td>
   <td style="text-align:right;"> 50 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.31 </td>
   <td style="text-align:right;"> 12.07 </td>
   <td style="text-align:right;"> 58 </td>
   <td style="text-align:right;"> 51 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.71 </td>
   <td style="text-align:right;"> 7.57 </td>
   <td style="text-align:right;"> 68 </td>
   <td style="text-align:right;"> 52 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.43 </td>
   <td style="text-align:right;"> 11.35 </td>
   <td style="text-align:right;"> 58 </td>
   <td style="text-align:right;"> 53 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.90 </td>
   <td style="text-align:right;"> 5.47 </td>
   <td style="text-align:right;"> 71 </td>
   <td style="text-align:right;"> 54 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.52 </td>
   <td style="text-align:right;"> 8.29 </td>
   <td style="text-align:right;"> 52 </td>
   <td style="text-align:right;"> 55 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.03 </td>
   <td style="text-align:right;"> 6.80 </td>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:right;"> 56 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.29 </td>
   <td style="text-align:right;"> 10.63 </td>
   <td style="text-align:right;"> 59 </td>
   <td style="text-align:right;"> 57 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.32 </td>
   <td style="text-align:right;"> 8.59 </td>
   <td style="text-align:right;"> 59 </td>
   <td style="text-align:right;"> 58 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.88 </td>
   <td style="text-align:right;"> 7.82 </td>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:right;"> 59 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.22 </td>
   <td style="text-align:right;"> 7.18 </td>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:right;"> 60 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.94 </td>
   <td style="text-align:right;"> 8.29 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 61 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.01 </td>
   <td style="text-align:right;"> 11.08 </td>
   <td style="text-align:right;"> 64 </td>
   <td style="text-align:right;"> 62 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.20 </td>
   <td style="text-align:right;"> 6.46 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 63 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.30 </td>
   <td style="text-align:right;"> 3.25 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 64 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.72 </td>
   <td style="text-align:right;"> 9.74 </td>
   <td style="text-align:right;"> 54 </td>
   <td style="text-align:right;"> 65 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.82 </td>
   <td style="text-align:right;"> 8.75 </td>
   <td style="text-align:right;"> 62 </td>
   <td style="text-align:right;"> 66 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.14 </td>
   <td style="text-align:right;"> 11.75 </td>
   <td style="text-align:right;"> 52 </td>
   <td style="text-align:right;"> 67 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.27 </td>
   <td style="text-align:right;"> 9.31 </td>
   <td style="text-align:right;"> 64 </td>
   <td style="text-align:right;"> 68 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.70 </td>
   <td style="text-align:right;"> 7.73 </td>
   <td style="text-align:right;"> 65 </td>
   <td style="text-align:right;"> 69 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.55 </td>
   <td style="text-align:right;"> 8.68 </td>
   <td style="text-align:right;"> 65 </td>
   <td style="text-align:right;"> 70 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.38 </td>
   <td style="text-align:right;"> 9.77 </td>
   <td style="text-align:right;"> 57 </td>
   <td style="text-align:right;"> 71 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.73 </td>
   <td style="text-align:right;"> 9.71 </td>
   <td style="text-align:right;"> 59 </td>
   <td style="text-align:right;"> 72 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.32 </td>
   <td style="text-align:right;"> 4.17 </td>
   <td style="text-align:right;"> 79 </td>
   <td style="text-align:right;"> 73 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.86 </td>
   <td style="text-align:right;"> 10.18 </td>
   <td style="text-align:right;"> 53 </td>
   <td style="text-align:right;"> 74 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.35 </td>
   <td style="text-align:right;"> 9.28 </td>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:right;"> 75 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.11 </td>
   <td style="text-align:right;"> 7.23 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 76 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.45 </td>
   <td style="text-align:right;"> 6.38 </td>
   <td style="text-align:right;"> 82 </td>
   <td style="text-align:right;"> 77 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.80 </td>
   <td style="text-align:right;"> 9.20 </td>
   <td style="text-align:right;"> 68 </td>
   <td style="text-align:right;"> 78 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.13 </td>
   <td style="text-align:right;"> 8.20 </td>
   <td style="text-align:right;"> 67 </td>
   <td style="text-align:right;"> 79 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.35 </td>
   <td style="text-align:right;"> 10.16 </td>
   <td style="text-align:right;"> 54 </td>
   <td style="text-align:right;"> 80 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.93 </td>
   <td style="text-align:right;"> 8.95 </td>
   <td style="text-align:right;"> 53 </td>
   <td style="text-align:right;"> 81 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.07 </td>
   <td style="text-align:right;"> 6.80 </td>
   <td style="text-align:right;"> 62 </td>
   <td style="text-align:right;"> 82 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.66 </td>
   <td style="text-align:right;"> 8.34 </td>
   <td style="text-align:right;"> 50 </td>
   <td style="text-align:right;"> 83 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.09 </td>
   <td style="text-align:right;"> 6.25 </td>
   <td style="text-align:right;"> 80 </td>
   <td style="text-align:right;"> 84 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4.91 </td>
   <td style="text-align:right;"> 6.75 </td>
   <td style="text-align:right;"> 91 </td>
   <td style="text-align:right;"> 85 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.03 </td>
   <td style="text-align:right;"> 9.09 </td>
   <td style="text-align:right;"> 62 </td>
   <td style="text-align:right;"> 86 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.02 </td>
   <td style="text-align:right;"> 10.42 </td>
   <td style="text-align:right;"> 64 </td>
   <td style="text-align:right;"> 87 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.67 </td>
   <td style="text-align:right;"> 8.89 </td>
   <td style="text-align:right;"> 57 </td>
   <td style="text-align:right;"> 88 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 8.15 </td>
   <td style="text-align:right;"> 9.43 </td>
   <td style="text-align:right;"> 54 </td>
   <td style="text-align:right;"> 89 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.88 </td>
   <td style="text-align:right;"> 6.79 </td>
   <td style="text-align:right;"> 72 </td>
   <td style="text-align:right;"> 90 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.72 </td>
   <td style="text-align:right;"> 6.91 </td>
   <td style="text-align:right;"> 78 </td>
   <td style="text-align:right;"> 91 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.66 </td>
   <td style="text-align:right;"> 6.05 </td>
   <td style="text-align:right;"> 63 </td>
   <td style="text-align:right;"> 92 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.85 </td>
   <td style="text-align:right;"> 6.32 </td>
   <td style="text-align:right;"> 59 </td>
   <td style="text-align:right;"> 93 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.57 </td>
   <td style="text-align:right;"> 8.62 </td>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:right;"> 94 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.16 </td>
   <td style="text-align:right;"> 7.84 </td>
   <td style="text-align:right;"> 76 </td>
   <td style="text-align:right;"> 95 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.31 </td>
   <td style="text-align:right;"> 5.89 </td>
   <td style="text-align:right;"> 79 </td>
   <td style="text-align:right;"> 96 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.77 </td>
   <td style="text-align:right;"> 9.77 </td>
   <td style="text-align:right;"> 51 </td>
   <td style="text-align:right;"> 97 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5.38 </td>
   <td style="text-align:right;"> 6.97 </td>
   <td style="text-align:right;"> 82 </td>
   <td style="text-align:right;"> 98 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7.02 </td>
   <td style="text-align:right;"> 6.56 </td>
   <td style="text-align:right;"> 55 </td>
   <td style="text-align:right;"> 99 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6.45 </td>
   <td style="text-align:right;"> 7.93 </td>
   <td style="text-align:right;"> 74 </td>
   <td style="text-align:right;"> 100 </td>
  </tr>
</tbody>
</table></div>

]
.panel[.panel-name[Code]

```r
model1 <- lm(dan.grump ~ dan.sleep,
             data = parenthood)

model1
```

```
## 
## Call:
## lm(formula = dan.grump ~ dan.sleep, data = parenthood)
## 
## Coefficients:
## (Intercept)    dan.sleep  
##     125.956       -8.937
```

```r
summary(model1)
```

```
## 
## Call:
## lm(formula = dan.grump ~ dan.sleep, data = parenthood)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.025  -2.213  -0.399   2.681  11.750 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 125.9563     3.0161   41.76   <2e-16 ***
## dan.sleep    -8.9368     0.4285  -20.85   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.332 on 98 degrees of freedom
## Multiple R-squared:  0.8161,	Adjusted R-squared:  0.8142 
## F-statistic: 434.9 on 1 and 98 DF,  p-value: < 2.2e-16
```

]
]
]
---

<br><br>
.big[Feedback is welcome at: _ayush.ap58@gmail.com_]