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<!-- Unit 3 overview and readiness mini lesson -->
<h4>Distinguish Linear Patterns from Nonlinear Patterns </h4>
<p dir="ltr">A scatter plot is a graph of numerical data with two variables. If two variables vary together in a predictable way, we say there is a statistical relationship between the two variables. </p>
<ul>
<li>When the points of the scatter plot seem to fall along a line, the scatter plot is linear.</li>
<li>Nonlinear patterns seem to follow a curve. </li>
<li>If the scatter plot shows no pattern, it means there is no relationship between the variables.</li>
</ul>
<br>
<br>
<div class="os-raise-d-flex os-raise-justify-content-between">
<div class="os-raise-mx-auto">
<img alt class="img-fluid atto_image_button_text-bottom" height="188" role="presentation" src="https://k12.openstax.org/contents/raise/resources/8644896db99c45a5a5aa3a385530cd3db4bbd03e" width="200">
<br><br>
<p> There is a relationship.</p>
<p> It appears to be an increasing<br> linear pattern.</p>
</div>
<div class="os-raise-mx-auto">
<img alt class="img-fluid atto_image_button_text-bottom" height="186" role="presentation" src="https://k12.openstax.org/contents/raise/resources/083a11a907d6f88ead7c164e77c2fbd33122ecc4" width="200">
<br><br>
<p> There is a relationship.</p>
<p> It appears to be nonlinear.<br> </p>
</div>
<div class="os-raise-mx-auto">
<img alt class="img-fluid atto_image_button_text-bottom" height="190" role="presentation" src="https://k12.openstax.org/contents/raise/resources/d79d914f0d6d3f6c2a64aacaa6234b52474c4e7b" width="200">
<br><br>
<p> There is no relationship.</p>
<p><br> </p>
</div>
</div>
<br>
<h4>Try It: Distinguish Linear Patterns from Nonlinear Patterns</h4>
<p>At a dinner party, every person shakes hands with every other person present. The scatter plot shows the number of people, x, and the number of handshakes, y. </p>
<p><strong><img alt class="img-fluid atto_image_button_text-bottom" height="181" role="presentation" src="https://k12.openstax.org/contents/raise/resources/f75b365e843b9eca4764d2fd68d460e731c50fed" width="200"></strong></p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8872d52c-b89f-4705-96c1-c37f878dad48" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>Is the relationship linear or nonlinear? Be prepared to show your reasoning.</p>
</div>
<div class="os-raise-ib-input-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Here is how to describe the relationship:</p>
<p>The scatter plot shows that the number of handshakes increases as the number of people increases. The increase is not at a constant rate, so the relationship is nonlinear.</p>
</div>
</div>
<!--Interaction End -->
<!--inserted mini review question Begin -->
<h4>Check Your Understanding</h4>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="9da7338b-0f06-476d-a2fb-6fd9a2196fb2" data-retry-limit="0" data-schema-version="1.0">
<div class="os-raise-ib-pset-problem" data-content-id="a5b1e2c2-2618-442e-8d57-5b7e11d8990a" data-problem-type="multiplechoice" data-solution="There is an increasing linear pattern." data-solution-options='["There is an increasing linear pattern.", "There is no pattern.", "There is a decreasing linear pattern.", "There is a nonlinear pattern."]'>
<div class="os-raise-ib-pset-problem-content">
<p>Which statement best describes the scatter plot?</p><br><img alt="scatter plot shows the relationship between crocodiles body mass x, in pounds, and bite force y, in pounds" class="img-fluid atto_image_button_text-bottom" height="285" src="https://k12.openstax.org/contents/raise/resources/cb12a838f9369f40c8fcfbcbe87903c2a3df0d4d" width="300"><br>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response" data-answer="There is no pattern.">
<p>Incorrect. Let’s try again a different way: The points form a linear pattern that increases from left and right. The answer is there is an increasing linear pattern.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response" data-answer="There is a decreasing linear pattern.">
<p>Incorrect. Let’s try again a different way: The points do form a linear pattern but appear to be increasing from left to right. The answer is there is an increasing linear pattern.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response" data-answer="There is a nonlinear pattern.">
<p>Incorrect. Let’s try again a different way: The points cluster in a way that creates a linear pattern and they also increase from left to right. The answer is there is an increasing linear pattern.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>There is an increasing linear pattern.</p>
</div>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>That’s correct! Check yourself: The points on this graph seem to increase from left to right and form a line. There is an increasing linear pattern.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
</div>
</div>
<!--inserted mini review question END -->
<h4>Videos</h4>
<p>Watch the following video to learn more about distinguishing linear patterns from nonlinear patterns based on scatter plots.</p>
<p><strong>Scatter Plots Example</strong></p>
<p>Watch the video to see scatter plots that show the relationship between study time, shoe size, and test score.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/Jpbm5YgciqI;&rel=0" title="Studying, shoe size, and test scores scatter plots | Probability and Statistics | Khan Academy"></iframe></div>
</div>