38f079b4-3572-4b71-a020-01e4d0aa8e73.html

<h4>Activity</h4>
<p>Thinking back to the last activity, you learned about the \(r\)-value. Write these characteristics about the \(r\)-value.</p>
<p>The \(r\)-value is called a correlation coefficient. A <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">correlation coefficient</span> is one way to measure the strength of a linear relationship.
</p>
<ul>
  <li>The sign of \(r\) is the same as the sign of the slope of the best fit line.</li>
  <li>The values for \(r\) go from &ndash;1 to 1 and include &ndash;1 and 1.</li>
  <li>The closer \(r\) is to 1 or &ndash;1, the stronger the linear relationship between the variables.</li>
  <li>The closer \(r\) is to 0, the weaker the linear relationship between the variables.</li>
</ul>
<p>Take turns with your partner to match a scatter plot with a correlation coefficient. For each match you find, explain to your partner how you know it&rsquo;s a match. For each match your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.</p>
<p>A <img alt="Graph of a scatter plot, xy-plane, origin O. &nbsp;" height="225" src="https://k12.openstax.org/contents/raise/resources/4c53d9233e5facaf7bcb054d2d85142eef2c6bd8" width="212"><br><br>
  B <img alt="Graph of a scatter plot, xy-plane, origin O.&nbsp; &nbsp;" height="225" src="https://k12.openstax.org/contents/raise/resources/5ebc57ee0437530f65ab99a13714f5ea8bf2b7dc" width="218"><br><br>
  C <img alt="Graph of a scatter plot, xy-plane, origin O.&nbsp; &nbsp;" height="225" src="https://k12.openstax.org/contents/raise/resources/6954ed7ffa8e06e11973f07b56b6de085a1da0cb" width="212"><br><br>
  D <img alt="Graph of a scatter plot, xy-plane, origin O.&nbsp; &nbsp;" height="225" src="https://k12.openstax.org/contents/raise/resources/2e7ba8699798ccce88a043b79d6b66d4598a6801" width="212"><br><br>
  E <img alt="Graph of a scatter plot, xy-plane, origin O.&nbsp;" height="225" src="https://k12.openstax.org/contents/raise/resources/641d84d3c1be5129505b63cb19eeffad481eb553" width="212"><br><br>
  F <img alt="Graph of a scatter plot, xy-plane, origin O." height="225" src="https://k12.openstax.org/contents/raise/resources/335fd30b3cd08424554478293b5f97b4983a3a13" width="212"><br><br>
  G <img alt="Graph of a scatter plot, xy-plane, origin O." height="225" src="https://k12.openstax.org/contents/raise/resources/07b316d510ff94608340a6e72a4b2930ca54101a" width="212"><br><br>
  H <img alt="Graph of a scatter plot, xy-plane, origin O." height="225" src="https://k12.openstax.org/contents/raise/resources/737eb57e3833fc19c6b27a568a44519455b1ebc7" width="218"><br><br>
</p>
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    <p>1. \(r=-1\)</p>
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    <p>Enter your answer here:</p>
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    <p>Compare your answer:</p>
    <p>Scatter Plot F&nbsp;</p>
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    <p>2. \(r=-0.95\)</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Scatter Plot C</p>
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    <p>3. \(r=-0.74\)</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Scatter Plot D</p>
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    <p>4. \(r=-0.06\)</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Scatter Plot G</p>
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    <p>5. \(r=0.48\)</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Scatter Plot H</p>
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    <p>6. \(r=0.65\)</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Scatter Plot E</p>
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    <p>7. \(r=0.9\)</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
  </div>
  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Scatter Plot B</p>
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    <p>8. \(r=1\)</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Scatter Plot A</p>
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<h4>Video: Matching Correlation Coefficients</h4>
<p><span>Watch the following video to learn more about the connections of scatter plots to the correlation coefficient.</span></p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
  <div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
      <source src="https://k12.openstax.org/contents/raise/resources/9dd8ac5e25c9fae8fc5834b6f516c7a2e7e1a691">
      <track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/b119dbcecc68092e35d57f166f623064f23b530b" srclang="en_us">https://k12.openstax.org/contents/raise/resources/9dd8ac5e25c9fae8fc5834b6f516c7a2e7e1a691
    </video></div>
</div>
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    <h4>Making a Real-World Connection</h4>
    <p>Jada wants to know if the speed that people walk is correlated with their texting speed. To investigate this, she measured the distance, in feet, that 5 of her friends walked in 30 seconds and the number of characters they texted during that time. Each of the 5 friends took 4 walks for a total of 20 walks. Here are the results of the first 20 walks.</p>
    <p><img alt="A scatterplot. Horizontal, from 80 to 180, by 20&rsquo;s, labeled distance, feet. Vertical, from 25 to 150, by 25&rsquo;s, number of characters, texted. 19 dots, trend linearly downward and to the right." src="https://k12.openstax.org/contents/raise/resources/22abec8ebfb486dea91ab1aefac6a4d7eb505af3"><br></p>
    <table class="os-raise-wideequaltable">
      <thead>
        <tr>
          <th scope="col">distance (feet)</th>
          <th scope="col">number of characters texted</th>
          <th scope="col">distance (feet)</th>
          <th scope="col">number of characters texted</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>
            105
          </td>
          <td>
            14
          </td>
          <td>
            95
          </td>
          <td>
            138
          </td>
        </tr>
        <tr>
          <td>
            125
          </td>
          <td>
            110
          </td>
          <td>
            125
          </td>
          <td>
            110
          </td>
        </tr>
        <tr>
          <td>
            115
          </td>
          <td>
            120
          </td>
          <td>
            160
          </td>
          <td>
            80
          </td>
        </tr>
        <tr>
          <td>
            140
          </td>
          <td>
            98
          </td>
          <td>
            175
          </td>
          <td>
            64
          </td>
        </tr>
        <tr>
          <td>
            145
          </td>
          <td>
            102
          </td>
          <td>
            130
          </td>
          <td>
            106
          </td>
        </tr>
        <tr>
          <td>
            160
          </td>
          <td>
            89
          </td>
          <td>
            140
          </td>
          <td>
            95
          </td>
        </tr>
        <tr>
          <td>
            170
          </td>
          <td>
            72
          </td>
          <td>
            150
          </td>
          <td>
            95
          </td>
        </tr>
        <tr>
          <td>
            140
          </td>
          <td>
            100
          </td>
          <td>
            155
          </td>
          <td>
            90
          </td>
        </tr>
        <tr>
          <td>
            130
          </td>
          <td>
            107
          </td>
          <td>
            160
          </td>
          <td>
            74
          </td>
        </tr>
        <tr>
          <td>
            105
          </td>
          <td>
            113
          </td>
          <td>
            135
          </td>
          <td>
            108
          </td>
        </tr>
      </tbody>
    </table><br>
    <p>Over the next few days, the same 5 friends practiced walking and texting to see if they could walk faster and text more characters. They did not record any more data while practicing. After practicing, each of the 5 friends took another 4 walks. Here are the results of the final 20 walks.</p>
    <p><img alt="A scatterplot. Horizontal, from 120 to 240, by 20&rsquo;s, labeled distance, feet. Vertical, from 25 to 200, by 25&rsquo;s, number of characters, texted. 19 dots, trend slightly downward and right." src="https://k12.openstax.org/contents/raise/resources/80f714383377d80c86e2118803fac90afacdda3c"></p>
    <table class="os-raise-wideequaltable">
      <thead>
        <tr>
          <th scope="col">distance (feet)</th>
          <th scope="col">number of characters texted</th>
          <th scope="col">distance (feet)</th>
          <th scope="col">number of characters texted</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>
            140
          </td>
          <td>
            410
          </td>
          <td>
            165
          </td>
          <td>
            151
          </td>
        </tr>
        <tr>
          <td>
            150
          </td>
          <td>
            155
          </td>
          <td>
            170
          </td>
          <td>
            136
          </td>
        </tr>
        <tr>
          <td>
            160
          </td>
          <td>
            151
          </td>
          <td>
            190
          </td>
          <td>
            143
          </td>
        </tr>
        <tr>
          <td>
            155
          </td>
          <td>
            170
          </td>
          <td>
            205
          </td>
          <td>
            132
          </td>
        </tr>
        <tr>
          <td>
            180
          </td>
          <td>
            125
          </td>
          <td>
            205
          </td>
          <td>
            128
          </td>
        </tr>
        <tr>
          <td>
            205
          </td>
          <td>
            130
          </td>
          <td>
            210
          </td>
          <td>
            140
          </td>
        </tr>
        <tr>
          <td>
            225
          </td>
          <td>
            95
          </td>
          <td>
            215
          </td>
          <td>
            109
          </td>
        </tr>
        <tr>
          <td>
            175
          </td>
          <td>
            161
          </td>
          <td>
            220
          </td>
          <td>
            105
          </td>
        </tr>
        <tr>
          <td>
            195
          </td>
          <td>
            108
          </td>
          <td>
            230
          </td>
          <td>
            126
          </td>
        </tr>
        <tr>
          <td>
            155
          </td>
          <td>
            142
          </td>
          <td>
            225
          </td>
          <td>
            138
          </td>
        </tr>
      </tbody>
    </table><br>
    <span>1.&nbsp;What do you notice about the 2 scatter plots?</span><br>
  </div>
  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
  </div>
  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:Your answer may vary, but here is a sample.</p>
    <p>I noticed that in the second scatter plot, the students traveled longer distances. In addition, the students seemed to type more characters for any given distance in the second scatter plot than in the first scatter plot.</p>
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</div>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="cceb3a3d-0369-4877-94b1-c1ebea482ef3" data-schema-version="1.0" data-wait-for-event="RFM1">
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    <p>2.&nbsp;Jada noticed that her friends walked farther and texted faster during the last 20 walks than they did during the first 20 walks. Since both were faster, she predicts that the correlation coefficient of the line of best fit for the last 20 walks will be closer to &ndash;1 than the correlation coefficient of the line of best fit for the first 20 walks. Do you agree with Jada? Be prepared to show your reasoning.</p>
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  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer: You answer may vary, but here is a sample.</p>
    <p>I do not agree with Jada. The correlation coefficient deals with the strength and direction of a linear relationship. The comparison bewteen walking distrance and the number of characters texted relates to the slope of the line, because it compares rates of number of characters texted over the distanced walked.</p>
  </div>
</div>
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    <p>3. Use technology to find an equation of the line of best fit for each data set.
    </p>
    <div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
  </div>
  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer: You answer may vary, but here is a sample.</p>
    <p>The line of best fit for scatter plot 1 is \(y=-0.8547x +218.6053\). The line of best fit for scatter plot 2 is \(y=-0.4658x +222.1704\). </p>
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  <div class="os-raise-ib-input-content">
    <p>4.&nbsp;The correlation coefficient for the first line of best fit is \(-0.95\) and the second line of best fit is \(-0.68\). Was your answer to question 2 correct? Why do you think the correlation coefficients for the two data sets are so different? Be prepared to show your reasoning.</p>
  </div>
  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
  </div>
  <div class="os-raise-ib-input-ack">
    <p>Compare your answer: You answer may vary, but here is a sample.</p>
    <p>I think the correlation coefficients are different because the data in the second scatter plot are more scattered than the data in the first scatter plot. On average, the data in the first scatter plot are much closer to the line of best fit than the data in the second scatter plot.</p>
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