Introduction to Data Analysis with R

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<h1>Introduction to Data Analysis with R</h1>
<p>Lecture 7: Stories of Warplanes, Correlation and Regression</p>
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Jannik Buhr
<br/>
<span>Heidelberg University, WS20/21</span>
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<div class="talk-date">2020-12-13</div>
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With Artwork by @allison_horst
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## 1943

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## The Story of Abraham Wald

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<p class="caption">Cover of "A method of estimating plane vulnerability based on damage of survivors"</p>
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> Instead of the most-hit parts, the least-hit parts are to be reinforced.

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## Before we go back to R:

<blockquote class="twitter-tweet" data-width="550" data-lang="en" data-dnt="true" data-theme="light"><p lang="en" dir="ltr">weird how every time you see this image on twitter it has a ton of retweets <a href="https://t.co/VALAKdeheP">pic.twitter.com/VALAKdeheP</a></p>— Jake VanderPlas (@jakevdp) <a href="https://twitter.com/jakevdp/status/1336343740235935744?ref_src=twsrc%5Etfw">December 8, 2020</a></blockquote>

... which is why most people you follow on twitter
have more followers than you do.

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### Best Practices

> **Your raw data is sacred!** Do not ever modify it or
  save over it.
  
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## Covariance, Correlation and Regression

![Source: https://xkcd.com/552/](img/correlation.png)

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## Introducing the Dataset

![I guess it is the baby yoda show now.](img/baby_yoda.gif)

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`$$var(X) = \frac{\sum_{i=0}^{n}{(x_i-\bar x)^2}}{(n-1)}$$`

`$$cov(X,Y)=\text{E}\left[(X-\text{E}\left[X\right])(Y-\text{E}\left[Y\right])\right]$$`

`$$corr(X,Y)=\frac{cov(X,Y)}{\sigma_{X}\sigma_{Y}}$$`

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