f668fb6c-7001-47ef-a153-18401e67b33f.html

<h4>Determine the Strength of a Linear Relationship</h4>
<p>Finding a Correlation Coefficient</p>
<ol class="os-raise-noindent" start="1">
  <li>Calculate the correlation coefficient for cricket-chirp data in the table below.</li>
  <li>Tell if the linear relationship is positive or negative and if it is strong, weak, or moderate.</li>
</ol>
<table class="os-raise-horizontaltable">
  <thead>
  </thead>
  <tbody>
    <tr>
      <th scope="row">Chirps</th>
      <td>44</td>
      <td>35</td>
      <td>20.4</td>
      <td>33</td>
      <td>31</td>
      <td>35</td>
      <td>18.5</td>
      <td>37</td>
      <td>26</td>
    </tr>
    <tr>
      <th scope="row">Temperature</th>
      <td>80.5</td>
      <td>70.5</td>
      <td>57</td>
      <td>66</td>
      <td>68</td>
      <td>72</td>
      <td>52</td>
      <td>73.5</td>
      <td>53</td>
    </tr>
  </tbody>
</table>
<br>
<ol class="os-raise-noindent" start="1">
  <li> Using graphing technology, enter the chirps in the \(x\)-column of the table and the temperature in the \(y\)-column of the table. The correlation coefficient is \(r=0.9509\). </li>
  <li>This value is very close to 1, which suggests a strong, positive, linear relationship.</li>
</ol>
<h4>Try It: Determine the Strength of a Linear Relationship</h4>
<p>Calculate the correlation coefficient for data in the table below. Tell if the linear relationship is positive or negative and if it is strong, weak, or moderate.</p>
<table class="os-raise-horizontaltable">
  <thead>
  </thead>
  <tbody>
    <tr>
      <th scope="row">\(x\)</th>
      <td>21</td>
      <td>25</td>
      <td>30</td>
      <td>31</td>
      <td>40</td>
      <td>50</td>
    </tr>
    <tr>
      <th scope="row">\(y\)</th>
      <td>17</td>
      <td>11</td>
      <td>2</td>
      <td>-1</td>
      <td>-18</td>
      <td>-40</td>
    </tr>
  </tbody>
</table>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content"> <br>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work. </p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
  <p>Compare your answer:</p>
  <p>\(r=-0.9985\), The relationship is a strong and negative linear relationship. </p>
</div>