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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<title>Predicting prices of used BMW cars</title>
<meta name="author" content="(Jens Svensmark)"/>
<style type="text/css">
.underline { text-decoration: underline; }
</style>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/reveal.js/dist/reveal.css"/>
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document.getElementsByTagName( 'head' )[0].appendChild( link );
}
</script>
<script src="bmw_fetcher.js"></script>
</head>
<body>
<div class="reveal">
<div class="slides">
<section id="sec-title-slide"><h1 class="title"> Predicting prices of used BMW cars </h1>
<h2 class=\"author\"> Jens Svensmark </h2>
<p class=\"date\"> May 10, 2021 <p>
</section>
<section>
<section id="slide-org7e9eba2">
<h2 id="org7e9eba2">Source</h2>
<p>
Source code for this project available on <a href="https://github.com/jenssss/datacamp-certification">github</a>.
</p>
</section>
</section>
<section>
<section id="slide-org2064619">
<h2 id="org2064619">Problem statement</h2>
<div class="outline-text-2" id="text-org2064619">
</div>
</section>
<section id="slide-org836eb7a">
<h3 id="org836eb7a">Background</h3>
<ul>
<li class="fragment appear">Cars are used throughout the world</li>
<li class="fragment appear">Big resale market (due to cost and durability)</li>
<li class="fragment appear">Many consumers have no clear idea about car prices</li>
<li class="fragment appear">Makes navigating the market and negotiating with car dealers difficult</li>
</ul>
<aside class="notes">
<p>
For most people, car is big investment
</p>
<p>
Lasts many years
</p>
</aside>
</section>
<section id="slide-org334006e">
<h3 id="org334006e">Goal</h3>
<ul>
<li class="fragment appear">Predict resale prices of cars based on historic data
<ul>
<li class="fragment appear">Target variable is continuous</li>
<li class="fragment appear">Will use R-squared (R<sup>2</sup>) metric</li>
<li class="fragment appear">This should be close to 1</li>
</ul></li>
<li class="fragment appear">Make predictions available to consumers</li>
</ul>
<aside class="notes">
<p>
Since target variable is continuous I will use so-called R<sup>2</sup> metric to
assess the model
</p>
</aside>
</section>
</section>
<section>
<section id="slide-orgc5bb50d">
<h2 id="orgc5bb50d">Data</h2>
<div class="outline-text-2" id="text-orgc5bb50d">
</div>
</section>
<section id="slide-org156b92e">
<h3 id="org156b92e">Source</h3>
<ul>
<li class="fragment appear">Provided by Datacamp</li>
<li class="fragment appear">No details about collection known</li>
</ul>
</section>
<section id="slide-org39e7878">
<h3 id="org39e7878">Features</h3>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Feature</th>
<th scope="col" class="org-left">Description</th>
<th scope="col" class="org-left">Type</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">price</td>
<td class="org-left">Price in USD</td>
<td class="org-left">numerical</td>
</tr>
<tr>
<td class="org-left">year</td>
<td class="org-left">Production year</td>
<td class="org-left">numerical</td>
</tr>
<tr>
<td class="org-left">mileage</td>
<td class="org-left">Distance driven</td>
<td class="org-left">numerical</td>
</tr>
<tr>
<td class="org-left">tax</td>
<td class="org-left">Road tax</td>
<td class="org-left">numerical</td>
</tr>
<tr>
<td class="org-left">mpg</td>
<td class="org-left">Miles per gallon</td>
<td class="org-left">numerical</td>
</tr>
<tr>
<td class="org-left">engineSize</td>
<td class="org-left">Size of engine</td>
<td class="org-left">numerical</td>
</tr>
</tbody>
</table>
</section>
<section id="slide-org39e7878-split">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Feature</th>
<th scope="col" class="org-left">Description</th>
<th scope="col" class="org-left">Type</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">model</td>
<td class="org-left">Car model</td>
<td class="org-left">categorical</td>
</tr>
<tr>
<td class="org-left">transmission</td>
<td class="org-left">Type of transmission</td>
<td class="org-left">categorical</td>
</tr>
<tr>
<td class="org-left">fuelType</td>
<td class="org-left">Fuel type</td>
<td class="org-left">categorical</td>
</tr>
</tbody>
</table>
</section>
<section id="slide-org4b6e929">
<h3 id="org4b6e929">Which features are the most important?</h3>
</section>
<section id="slide-org5b2d356">
<h3 id="org5b2d356">Simple data model</h3>
<div class="figure">
<p><object type="image/svg+xml" data="figures/data_model1.svg" class="org-svg" style="width: 70vw; max-height: 50vh">
Sorry, your browser does not support SVG.</object>
</p>
</div>
</section>
<section id="slide-orgd4b8fb1">
<h3 id="orgd4b8fb1">Full data model</h3>
<div class="figure">
<p><object type="image/svg+xml" data="figures/data_model3.svg" class="org-svg">
Sorry, your browser does not support SVG.</object>
</p>
</div>
</section>
</section>
<section>
<section id="slide-orgf5b9382">
<h2 id="orgf5b9382">Exploring the data</h2>
<div class="outline-text-2" id="text-orgf5b9382">
</div>
</section>
<section id="slide-org9535e62">
<h3 id="org9535e62">Year and mileage</h3>
<div class="figure">
<p><img src="figures/price_of_year_mileage.png" alt="price_of_year_mileage.png" class="r-stretch" />
</p>
</div>
<aside class="notes">
<p>
Price depends strongly on year and mileage
</p>
<p>
Linear looking
</p>
</aside>
</section>
<section id="slide-orge5786d9">
<h3 id="orge5786d9">Car model</h3>
<div class="figure">
<p><object type="image/svg+xml" data="figures/price_of_model.svg" class="r-stretch">
Sorry, your browser does not support SVG.</object>
</p>
</div>
<aside class="notes">
<p>
Many models
</p>
<p>
Price depends somewhat on model
</p>
<p>
Will drop categories with fewer than 20 (M6, Z3, i8)
</p>
</aside>
</section>
<section id="slide-org995d6c3">
<h3 id="org995d6c3">Transmission</h3>
<div class="figure">
<p><object type="image/svg+xml" data="figures/price_of_transmission.svg" class="r-stretch">
Sorry, your browser does not support SVG.</object>
</p>
</div>
<aside class="notes">
<p>
Roughly evenly distributed
</p>
<p>
Slight differences in mean, should be distinguishable be linear model
</p>
</aside>
</section>
<section id="slide-org3d4368a">
<h3 id="org3d4368a">Tax, mpg and engine size</h3>
<div class="figure">
<p><img src="figures/price_of_tax_mpg_enginesize.png" alt="price_of_tax_mpg_enginesize.png" class="r-stretch;" style="max-width: 70vw;" />
</p>
</div>
<aside class="notes">
<p>
Price dependence not so clear
</p>
<p>
Will drop outliers in mpg and zero values in tax, engine size (no 0 vals in mpg though)
</p>
<p>
Should follow up with data collection team
</p>
</aside>
</section>
<section id="slide-org8e28e97">
<h3 id="org8e28e97">Fuel type</h3>
<div class="figure">
<p><object type="image/svg+xml" data="figures/price_of_fueltype.svg" class="r-stretch">
Sorry, your browser does not support SVG.</object>
</p>
</div>
<aside class="notes">
<p>
Price dependence weak, unlikely to impact model
</p>
<p>
Will drop categories with fewer than 20
</p>
<p>
Includes electric, but with more data could be included
</p>
</aside>
</section>
</section>
<section>
<section id="slide-orgb5a2639">
<h2 id="orgb5a2639">Predictive model</h2>
<div class="outline-text-2" id="text-orgb5a2639">
</div>
</section>
<section id="slide-orga3a4755">
<h3 id="orga3a4755">Linear model</h3>
<div class="figure">
<p><img src="figures/mileage_fit.png" alt="mileage_fit.png" class="r-stretch" style="max-height: 70vh" />
</p>
</div>
<aside class="notes">
<p>
Assume price depends linearly on mileage and year
</p>
<p>
Mention uncertainty
</p>
<p>
Normal distribution around this line
</p>
</aside>
</section>
<section id="slide-orga8bbb78">
<h3 id="orga8bbb78">Feature selection</h3>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Last added feature</th>
<th scope="col" class="org-right">Mean R<sup>2</sup> test score</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">mileage</td>
<td class="org-right">0.543242</td>
</tr>
<tr>
<td class="org-left">year</td>
<td class="org-right">0.643062</td>
</tr>
<tr>
<td class="org-left">model</td>
<td class="org-right">0.885855</td>
</tr>
<tr>
<td class="org-left">engineSize</td>
<td class="org-right">0.918769</td>
</tr>
<tr>
<td class="org-left">transmission</td>
<td class="org-right">0.924562</td>
</tr>
<tr>
<td class="org-left">…</td>
<td class="org-right">…</td>
</tr>
</tbody>
</table>
<aside class="notes">
<p>
Which features are the most important?
</p>
<p>
Add features one-by-one
</p>
<p>
Most important features here
</p>
</aside>
</section>
<section id="slide-orga8bbb78-split">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Last added feature</th>
<th scope="col" class="org-right">Mean R<sup>2</sup> test score</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">…</td>
<td class="org-right">…</td>
</tr>
<tr>
<td class="org-left">transmission</td>
<td class="org-right">0.924562</td>
</tr>
<tr>
<td class="org-left">fuelType</td>
<td class="org-right">0.925534</td>
</tr>
<tr>
<td class="org-left">mpg</td>
<td class="org-right">0.928286</td>
</tr>
<tr>
<td class="org-left">tax</td>
<td class="org-right">0.928287</td>
</tr>
</tbody>
</table>
<aside class="notes">
<p>
Not so important features here
</p>
</aside>
</section>
<section id="slide-orgb11c602">
<h3 id="orgb11c602">Feature selection</h3>
<ul>
<li class="fragment appear">Include: mileage, year, car model, engine size and transmission.</li>
<li class="fragment appear">Exclude: fuel type, mpg and tax.</li>
</ul>
</section>
<section id="slide-org7de4af2">
<h3 id="org7de4af2">Parameter interpretation</h3>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">observable</th>
<th scope="col" class="org-right">10<sup>coef</sup></th>
<th scope="col" class="org-right">10<sup>coef</sup> - 1</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">year</td>
<td class="org-right">1.106</td>
<td class="org-right">11%</td>
</tr>
<tr>
<td class="org-left">engineSize</td>
<td class="org-right">1.206</td>
<td class="org-right">21%</td>
</tr>
<tr>
<td class="org-left">10000*mileage</td>
<td class="org-right">0.941</td>
<td class="org-right">-6%</td>
</tr>
</tbody>
</table>
</section>
<section id="slide-orge1016a5">
<h3 id="orge1016a5">Parameter interpretation</h3>
<p>
Price relative to "Automatic"
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">transmission</th>
<th scope="col" class="org-right">10<sup>coef</sup></th>
<th scope="col" class="org-right">10<sup>coef</sup> - 1</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Manual</td>
<td class="org-right">0.913</td>
<td class="org-right">-9%</td>
</tr>
<tr>
<td class="org-left">Semi-Auto</td>
<td class="org-right">1.02</td>
<td class="org-right">2%</td>
</tr>
</tbody>
</table>
</section>
<section id="slide-org53b408e">
<h3 id="org53b408e">Parameter interpretation</h3>
<p>
Price relative to "1 Series"
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">model</th>
<th scope="col" class="org-right">10<sup>coef</sup></th>
<th scope="col" class="org-right">10<sup>coef</sup> - 1</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">2 Series</td>
<td class="org-right">1.027</td>
<td class="org-right">3%</td>
</tr>
<tr>
<td class="org-left">3 Series</td>
<td class="org-right">1.13</td>
<td class="org-right">13%</td>
</tr>
<tr>
<td class="org-left">4 Series</td>
<td class="org-right">1.151</td>
<td class="org-right">15%</td>
</tr>
<tr>
<td class="org-left">5 Series</td>
<td class="org-right">1.228</td>
<td class="org-right">23%</td>
</tr>
<tr>
<td class="org-left">6 Series</td>
<td class="org-right">1.302</td>
<td class="org-right">30%</td>
</tr>
<tr>
<td class="org-left">…</td>
<td class="org-right">…</td>
<td class="org-right">…</td>
</tr>
</tbody>
</table>
</section>
<section id="slide-org5790b2e">
<h3 id="org5790b2e">Web interface prototype</h3>
<div style="text-align:left">
<form>
</form>
</div>
<aside class="notes">
<p>
Live demo is dangerous
</p>
<p>
Mention prediction interval - shows uncertainty
</p>
</aside>
</section>
<section id="slide-org6ebb31a">
<h3 id="org6ebb31a">Web interface prototype</h3>
<p> <a href="https://svensmark.jp/dc_cert/predict_price/" target="_blank">https://svensmark.jp/dc_cert/predict_price/</a> </p>
<div class="figure">
<p><img src="figures/web_page_screenshot.png" alt="web_page_screenshot.png" />
</p>
</div>
</section>
</section>
<section>
<section id="slide-org23aa22e">
<h2 id="org23aa22e">Conclusion</h2>
<ul>
<li class="fragment appear">Built a linear model for predicting resale prices of BMW cars</li>
<li class="fragment appear">Works fairly well</li>
<li class="fragment appear">Model coefficients are explainable</li>
<li class="fragment appear">Demonstrated web interface prototype</li>
</ul>
</section>
<section id="slide-org127ffeb">
<h3 id="org127ffeb">Going forward</h3>
<p style="text-align:left">
Follow up with data collection team
</p>
<ul>
<li class="fragment appear">Suspicious values in mpg, engine size and tax</li>
</ul>
<p class="fragment (appear)" style="text-align:left">
If more accuracy is required
</p>
<ul>
<li class="fragment appear">More complex model might help</li>
<li class="fragment appear">But risk of overfitting and less explainability</li>
</ul>
<p class="fragment (appear)" style="text-align:left">
Web interface
</p>
<ul>
<li class="fragment appear">Improve design of web front end</li>
<li class="fragment appear">Ensure scalability of back end depending on expected usage</li>
</ul>
</section>
<section id="slide-orgea7e098">
<h3 id="orgea7e098">Thank you for your attention</h3>
<p>
Any questions?
</p>
</section>
</section>
<section>
<section id="slide-org8426c58">
<h2 id="org8426c58">Additional background</h2>
</section>
</section>
<section>
<section id="slide-org38fc437">
<h2 id="org38fc437">Metric</h2>
<div class="outline-text-2" id="text-org38fc437">
</div>
</section>
<section id="slide-org7c71588">
<h3 id="org7c71588">R-squared (R<sup>2</sup>)</h3>
<ul>
<li class="fragment appear">A number</li>
<li class="fragment appear">Measure of how well the model describes the data</li>
<li class="fragment appear">The closer to one the better</li>
</ul>
</section>
</section>
<section>
<section id="slide-org18856e2">
<h2 id="org18856e2">Data</h2>
<div class="outline-text-2" id="text-org18856e2">
</div>
</section>
<section id="slide-org83e3872">
<h3 id="org83e3872">Data model 2</h3>
<div class="figure">
<p><object type="image/svg+xml" data="figures/data_model2.svg" class="org-svg">
Sorry, your browser does not support SVG.</object>
</p>
</div>
</section>
</section>
<section>
<section id="slide-org3b56c68">
<h2 id="org3b56c68">Predictive model</h2>
<div class="outline-text-2" id="text-org3b56c68">
</div>
</section>
<section id="slide-orgda2cad9">
<h3 id="orgda2cad9">Additional assumption</h3>
<ul>
<li>All car prices fall at the same rate with age and mileage,
independent on car model and other factors</li>
</ul>
<aside class="notes">
<p>
Since the same model is applied across these variables
</p>
</aside>
</section>
<section id="slide-orgf5ea89c">
<h3 id="orgf5ea89c">Parameter interpretation</h3>
<p>
Price relative to "1 Series"
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">model</th>
<th scope="col" class="org-right">10<sup>coef</sup></th>
<th scope="col" class="org-right">10<sup>coef</sup> - 1</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">2 Series</td>
<td class="org-right">1.027</td>
<td class="org-right">3%</td>
</tr>
<tr>
<td class="org-left">3 Series</td>
<td class="org-right">1.13</td>
<td class="org-right">13%</td>
</tr>
<tr>
<td class="org-left">4 Series</td>
<td class="org-right">1.151</td>
<td class="org-right">15%</td>
</tr>
<tr>
<td class="org-left">5 Series</td>
<td class="org-right">1.228</td>
<td class="org-right">23%</td>
</tr>
<tr>
<td class="org-left">6 Series</td>
<td class="org-right">1.302</td>
<td class="org-right">30%</td>
</tr>
<tr>
<td class="org-left">7 Series</td>
<td class="org-right">1.542</td>
<td class="org-right">54%</td>
</tr>
<tr>
<td class="org-left">…</td>
<td class="org-right">…</td>
<td class="org-right">…</td>
</tr>
</tbody>
</table>
</section>
<section id="slide-orgf5ea89c-split">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<tbody>
<tr>
<td class="org-left">…</td>
<td class="org-right">…</td>
<td class="org-right">…</td>
</tr>
<tr>
<td class="org-left">8 Series</td>
<td class="org-right">2.07</td>
<td class="org-right">107%</td>
</tr>
<tr>
<td class="org-left">X1</td>
<td class="org-right">1.162</td>
<td class="org-right">16%</td>
</tr>
<tr>
<td class="org-left">X2</td>
<td class="org-right">1.204</td>
<td class="org-right">20%</td>
</tr>
<tr>
<td class="org-left">X3</td>
<td class="org-right">1.435</td>
<td class="org-right">44%</td>
</tr>
<tr>
<td class="org-left">X4</td>
<td class="org-right">1.492</td>
<td class="org-right">49%</td>
</tr>
<tr>
<td class="org-left">X5</td>
<td class="org-right">1.762</td>
<td class="org-right">76%</td>
</tr>
<tr>
<td class="org-left">X6</td>
<td class="org-right">1.791</td>
<td class="org-right">79%</td>
</tr>
<tr>
<td class="org-left">…</td>
<td class="org-right">…</td>
<td class="org-right">…</td>
</tr>
</tbody>
</table>
</section>
<section id="slide-orgf5ea89c-split">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<tbody>
<tr>
<td class="org-left">…</td>
<td class="org-right">…</td>
<td class="org-right">…</td>
</tr>
<tr>
<td class="org-left">X7</td>
<td class="org-right">2.382</td>
<td class="org-right">138%</td>
</tr>
<tr>
<td class="org-left">M2</td>
<td class="org-right">1.488</td>
<td class="org-right">49%</td>
</tr>
<tr>
<td class="org-left">M3</td>
<td class="org-right">2.183</td>
<td class="org-right">118%</td>
</tr>