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<h4>Activity</h4>
<br>
<!--Q#1-->
<ol class="os-raise-noindent">
<li> Click on the "\(+\)" sign and choose to add a table in the Desmos graphing tool. This will generate a table for entering a data set. </li>
</ol>
<p><strong>Desmos: Correlation Data Set Table</strong></p>
<br>
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="c04ae120-0680-4b06-b550-dd2f0d767550" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<!--QUESTION IS OUTSIDE OF INTERACTION DUE TO DESMOS-->
</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><strong>Answer:</strong> Your answers may vary</p>
</div>
</div>
<!--Interaction End -->
<ol class="os-raise-noindent" start="2">
<li> Enter the data set shown in the table below into the corresponding \(x_1\) and \(y_1\) columns. </li>
</ol>
<p>(If preferred, the data can be copied and pasted into Desmos from a spreadsheet using keyboard shortcuts. Windows: Ctrl+C for copy and Ctrl+V for paste. Mac: Command+C for copy and Command+V for paste.)</p>
<table class="os-raise-skinnytable">
<thead>
<tr>
<th scope="col">\(x_1\)</th>
<th scope="col">\(y_1\)</th>
</tr>
</thead>
<tbody>
<tr>
<td>2</td>
<td>12</td>
</tr>
<tr>
<td>9</td>
<td>11</td>
</tr>
<tr>
<td>15</td>
<td>6</td>
</tr>
<tr>
<td>21</td>
<td>3</td>
</tr>
<tr>
<td>22</td>
<td>-1</td>
</tr>
</tbody>
</table>
<br>
<p>The window should be appropriately set to display the points in the table, but sometimes it will be necessary to adjust the window of the graph in order to properly view your data set. Use the mouse to drag and change the viewing window. To zoom in or out, use the buttons in the top right or the scrolling wheel on the mouse.</p>
<ol class="os-raise-noindent" start="3">
<li> Hit return to enter a new item. Enter the command corr(\(x_1, y_1\)). You do not have to enter anything special to get the subscripts to appear – simply type \(x\) and then 1 and it will automatically fill in \(x_1\). </li>
</ol>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="a9b9f8f9-04e8-4732-b749-1d1f444d093d" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"><!--Q#4-->
<div class="os-raise-ib-pset-problem" data-content-id="6c0e897a-09c2-448d-861c-3df8564945cb" data-problem-comparator="text" data-problem-type="input" data-solution="-0.948">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li> A number between -1 and 1 will appear after an equal sign in the bottom right-hand corner of the same box. What is the number rounded to the thousandths place? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -0.948</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct value of the correlation coefficient is -0.948.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Q#5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2d7984ad-ea4c-44e1-ab5f-882739572038" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li> What does this number tell you about the strength of the linear relationship? </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>These data have a strong negative linear relationship. This means that as the \(x\)-values increase, the \(y\)-values decrease.</p>
</div>
</div>
<!--Interaction End -->
<br>
<h4>Activity</h4>
<blockquote>
<p>Use the following data to answer questions 1-5.</p>
<table class="os-raise-skinnytable">
<thead>
<tr>
<th scope="col">\(x_1\)</th>
<th scope="col">\(y_1\)</th>
</tr>
</thead>
<tbody>
<tr>
<td>2</td>
<td>12</td>
</tr>
<tr>
<td>9</td>
<td>11</td>
</tr>
<tr>
<td>15</td>
<td>6</td>
</tr>
<tr>
<td>21</td>
<td>3</td>
</tr>
<tr>
<td>22</td>
<td>-1</td>
</tr>
</tbody>
</table>
</blockquote>
<br>
<ol class="os-raise-noindent" >
<li> Use the Desmos graphing tool below to create a table for entering this data. Click on the “\(+\)” symbol and select the table from the drop-down menu.</li>
</ol>
<br>
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="cd29d7d3-1f5f-426c-a316-0d94f2489854" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<!--QUESTION IS OUTSIDE OF INTERACTION DUE TO DESMOS-->
</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><strong>Answer:</strong> Your answers may vary</p>
</div>
</div>
<!--Interaction End -->
<ol class="os-raise-noindent" start="2">
<li> Enter the data into the corresponding \(x_1\) and \(y_1\) columns in the table you created in Question 1. Press Enter or use arrow keys to enter a new data value in the table.<br>
<br>
After you have finished entering all of the data in Desmos, click on the ZoomFit button magifying glass (located to the left of the table). This will adjust the graphing window so the points in the scatter plot are visible.</li>
</ol>
<ol class="os-raise-noindent" start="3">
<li>Click in the entry box #2 below the table from Question 1 and enter the command \(corr(x_1,y_1)\). (You can just type \(x_1\) and \(y_1\). The subscripts will appear automatically.)</li>
</ol>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="5af27a6b-ab60-4aec-8cf0-f4973441a476" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"><!--Q#4-->
<div class="os-raise-ib-pset-problem" data-content-id="46a10ee5-fdca-4332-93cb-65ae53f5ff39" data-problem-comparator="text" data-problem-type="input" data-solution="-0.948">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li> A number between -1 and 1 will appear after an equal sign in the bottom right-hand corner of the same box. What is the number rounded to the thousandths place? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -0.948</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -0.948.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Q#5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d6637486-14f7-4bef-8a6f-a329be61f285" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li> What does this number tell you about the strength of the linear relationship? </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>These data have a strong negative linear relationship. This means that as the \(x\)-values increase, the \(y\)-values decrease.</p>
</div>
</div>
<!--Interaction End -->
<br>