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243ecee5-944c-4da2-a2d0-bd670e71d65e.html
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<h4>Activity</h4>
<p>For each situation, describe the linear relationship between the variables, based on the correlation coefficient. Make sure to mention whether there is a <strong>strong relationship</strong> or not as well as whether it is a <strong>positive relationship</strong> or <strong>negative relationship</strong>.</p>
<!--Question 1 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="0e62a990-bbb6-42c0-b9d5-c6a48e52329d" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>Number of steps taken per day and number of kilometers walked per day. \(r = 0.92\)
</li>
</ol>
</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:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>There is a strong, positive linear relationship. An increase in the number of kilometers walked tends to go along with an increase in the number of steps taken per day.</p>
</div>
</div>
<br>
<!--Question 2 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a445eeb5-8b55-4a21-b7e7-4113f346ae5f" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Temperature of a rubber band and distance the rubber band can stretch. \(r = 0.84\)
</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-prompt">
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>There is a strong, positive linear relationship. An increase in temperature tends to go along with an increase in the distance a rubber band can stretch.</p>
</div>
</div>
<br>
<!--Question 3 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5754c2f4-e4fd-45df-8e60-8dea69fdcaa8" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Car weight and distance traveled using a full tank of gas. \(r = - 0.86\)
</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-prompt">
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>There is a strong, negative relationship. An increase in the weight of a car tends to go along with a decrease in the distance it can travel on a full tank of gas.</p>
</div>
</div>
<br>
<!--Question 4 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d9302011-f268-4768-868a-e02c461c3ccb" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>Average fat intake per citizen of a country and average cancer rate of a country. \(r = 0.73\)
</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-prompt">
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>There is a moderate positive linear relationship. An increase in the fat intake per citizen of a country tends to go along with an increase in the average cancer rate of a country, but it is not a strong relationship.</p>
</div>
</div>
<br>
<!--Question 5 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="acc7f7b4-7452-48b0-9135-f338e1bd71cb" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>Score on science exam and number of words written on the essay question. \(r = 0.28\)
</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-prompt">
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>There is a weak, positive linear relationship. An increase in the number of words written on the essay question tends to go along with an increase on the score for a science exam, but the relationship is weak.</p>
</div>
</div>
<br>
<!--Question 6 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b0acde4c-cec4-4d02-9772-7cae87beeccf" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li>Average time spent listening to music per day and average time spent watching TV per day. \(r = - 0.17\)
</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-prompt">
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>There is a weak, negative relationship. An increase in the average time spent listening to music per day tends to go along with a decrease in the average time spent watching TV per day, although the relationship is weak.</p>
</div>
</div>
<br>
<br>
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<!--Start interaction. If multiple interactions appear under "are you ready for more?, they should all have matching "data-wait-for-event", which should also match the "data-fire-event" for the button. Note in this sample, they are all RFM1-->
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="17f14905-8ee3-4dff-ba31-3da72c54768e" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>A biologist is trying to determine if a group of dolphins is a new species of dolphin or if it is a new group of individuals within the same species of dolphin. The biologist measures the width (in millimeters) of the largest part of the skull, zygomatic width, and the length (in millimeters) of the snout, rostral length, of 10 dolphins from the same group of individuals.</p>
<table class="os-raise-wideequaltable">
<thead>
<tr>
<th scope="col">\(x\), rostral length (mm)</th>
<th scope="col">\(y\), zygomatic width (mm)</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>288</p>
</td>
<td>
<p>147</p>
</td>
</tr>
<tr>
<td>
<p>247</p>
</td>
<td>
<p>147</p>
</td>
</tr>
<tr>
<td>
<p>268</p>
</td>
<td>
<p>171</p>
</td>
</tr>
<tr>
<td>
<p>278</p>
</td>
<td>
<p>177</p>
</td>
</tr>
<tr>
<td>
<p>258</p>
</td>
<td>
<p>168</p>
</td>
</tr>
<tr>
<td>
<p>272</p>
</td>
<td>
<p>184</p>
</td>
</tr>
<tr>
<td>
<p>272</p>
</td>
<td>
<p>161</p>
</td>
</tr>
<tr>
<td>
<p>258</p>
</td>
<td>
<p>159</p>
</td>
</tr>
<tr>
<td>
<p>273</p>
</td>
<td>
<p>168</p>
</td>
</tr>
<tr>
<td>
<p>277</p>
</td>
<td>
<p>166</p>
</td>
</tr>
</tbody>
</table><br>
<p>The data appears to be linear and the equation of the line of best fit is \(𝑦=0.201𝑥+110.806\) and the \(r\) -value is 0.201.</p>
<ol class="os-raise-noindent">
<li>After checking the data, the biologist realizes that the first zygomatic width listed as 147 mm is an error. It is supposed to be 180 mm. Use technology to find the equation of a line of best fit and the correlation coefficient for the corrected data. What is the equation of the line of best fit and the correlation coefficient?
</li>
</ol>
</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:</p>
<p>\(y=0.693\) \(x−18.373\) and \(r=0.76\)</p>
</div>
</div>
<br>
<!--Q2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="ce106368-f29f-46c5-914e-98cc0da1e5e5" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Compare the new equation of the line of best fit with the original. What impact did changing one data point have on the slope, \(y\) -intercept, and correlation coefficient on the line of best fit?</li>
</ol>
</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:</p>
<p>Your answer may vary, but here is a sample.</p>
<p> The slope increased and the correlation coefficient got closer to 1. The \(y\) -intercept also change significantly.</p>
</div>
</div>
<br>
<!--Q3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dd6e076e-7a80-49ea-8f05-59b2fba52c2f" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Why do you think that weak positive association became a moderately strong association? Be prepared to show your reasoning.</li>
</ol>
</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:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>I think it became moderately strong because the data point that was changed did not follow the roughly linear pattern of the other 9 data points, and when it was changed, it did follow the linear pattern more closely.</p>
</div>
</div>
<br>
<!--Q4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="ce40e9dd-af58-4aa1-b769-bfeae4ef4da6" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<p>For questions 4—6, use technology to change the \(y\)-value for the first and second entries in the table.</p>
<li>How does changing each point's \(y\)-value impact the correlation coefficient?</li>
</ol>
</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:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>Changing the points to numbers well above or below the existing linear trend in the data makes the correlation coefficient get closer to zero.</p>
</div>
</div>
<br>
<!--Q5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d3166fb2-a015-4f79-829e-5bde3a873f61" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>Can you change two values to get the correlation coefficient closer to 1? Use data to support your answer.</li>
</ol>
</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:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>For example: I managed to get the \(r\) -value to 0.86 by changing the 2 values that appeared furthest from the line of best fit, \((272 , 184)\) and \((272,161)\), to values that are very close to the existing line of best fit, \((272,168)\) and \((272,168)\).</p>
</div>
</div>
<br>
<!--Q6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="9cba8869-9ecf-499c-8117-662ed73d42ad" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li>By leaving (288,180), can you change a value to get the relationship to change from a positive one to a negative one? Use data to support or refute your answer.</li>
</ol>
</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:</p>
<p>Your answer may vary, but here is a sample.</p>
<p>By changing \((247,147)\) to \((247,1000)\), I was able to change the relationship to a negative one because the line of best fit had a negative slope, \(y = - 14.187 x + 4071.1\).</p>
</div>
</div>