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<h4>Activity</h4>
<p><img alt="Video still of oranges being weighed" class="img-fluid atto_image_button_text-bottom" height="257" src="https://k12.openstax.org/contents/raise/resources/194c305a630b817ca0d798dd41543916ef17aeed" width="449"></p>
<!--BEGIN ADD DESMOS INTERATIVE-->
<!--START QUESTION # 1-->
<p>Here is the data table for orange weights from a previous lesson. Use this information to answer the questions.</p>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col"> number of oranges </th>
<th scope="col"> weight in kilograms </th>
</tr>
</thead>
<tbody>
<tr>
<td>3 </td>
<td>1.027 </td>
</tr>
<tr>
<td>4 </td>
<td>1.162 </td>
</tr>
<tr>
<td>5 </td>
<td>1.502 </td>
</tr>
<tr>
<td>6 </td>
<td>1.617 </td>
</tr>
<tr>
<td>7 </td>
<td>1.761 </td>
</tr>
<tr>
<td>8 </td>
<td>2.115 </td>
</tr>
<tr>
<td>9 </td>
<td>2.233 </td>
</tr>
<tr>
<td>10 </td>
<td>2.569 </td>
</tr>
</tbody>
</table>
<br>
<ol class="os-raise-noindent">
<li>Use the graphing tool or technology outside the course. Create the scatter plot and calculate the best fit line using the Desmos tool below.</li>
</ol>
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
<!--END ADD DESMOS INTERATIVE-->
<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">
<!--QUESTION IS OUTSIDE OF INTERACTION DUE TO DESMOS-->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
<p>After you have finished graphing, 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>The equation of the best fit line is \(y=0.216x+0.345\).</p>
</div>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5e68f8af-4e26-41c1-bbaa-d6e25e532834" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>2. What level of accuracy makes sense for the slope and intercept values? 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:</p>
<p>Rounding the values to the thousandths place makes sense because that would be to an accuracy of 1 gram, which is what the original data used.</p>
</div>
</div>
<!--Interaction End -->
<p><br>
</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1b74daa2-8def-4550-924c-85728f73d755" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>3. What does the linear model estimate for how much the weight increases for of each additional box of oranges?</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:</p>
<p>0.216 kg for each orange</p>
</div>
</div>
<!--Interaction End -->
<p><br>
</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="84c408f2-bbf1-4927-acce-9729e48f4ca0" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>4. Compare the weight of the actual box with 3 oranges in it to the estimated weight of the box with 3 oranges in it. 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:</p>
<p>The actual weight is 1.027 kg, and the estimated weight is 0.993 kg. Therefore, the actual weight is 0.034 kg greater than the estimate.</p>
</div>
</div>
<!--Interaction End -->
<p><br>
</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b075ff00-0de9-405e-8c25-9eee7937f800" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>5. How many oranges are in the box when the linear model estimates the weight best? 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:</p>
<p>6 oranges are in the box when the estimate is best. The difference between the estimated weight and the actual weight is only 0.023 kg, while the other points are farther from the line.</p>
</div>
</div>
<!--Interaction End -->
<p><br>
</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="3f6567c2-7c44-4aac-8d97-03819592e95d" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>6. How many oranges are in the box when the linear model estimates the weight least well? 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:</p>
<p>7 oranges are in the box when the estimate is worst. The difference between the estimated weight and the actual weight is 0.095, which is the most of any of the values.</p>
</div>
</div>
<!--Interaction End -->
<!--Text Entry Interaction Start -->
<p>Use the following information to answer questions 7 and 8.</p>
<blockquote>
<p>The difference between the actual value and the value estimated by a linear model is called the residual.</p>
<ul>
<li>If the actual value is greater than the estimated value, the residual is positive. </li>
<li>If the actual value is less than the estimated value, the residual is negative.</li>
</ul>
</blockquote>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d5223b0d-a10a-4686-b683-54c37fc4f09b" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>7. For the orange weight data set, what is the residual for the line of best fit when there are 3 oranges?</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:</p>
<p>The residual is \(0.034 (1.027−0.993=0.034)\).</p>
</div>
</div>
<!--Interaction End -->
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="f6acf1fe-8cbc-4401-a081-94841a0a4114" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>8. On the same axes as the scatter plot, plot this residual at the point where \(x=3\) and \(y\) has the value of the residual.</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:</p>
<p>The point is (8,0.043).</p>
</div>
</div>
<!--Interaction End -->
<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">
<p>9. Find the residuals for each of the other points in the scatter plot and graph them.</p>
<p><img alt="Blank coordinate plane with grid. Horizontal axis from 0 to 11 by 1's. Vertical axis from negative 0 point 5 to 0 point 5, by 0 point 1's. " src="https://k12.openstax.org/contents/raise/resources/ad8dea61f8ed8a9bdf59dc47c6446b93ba30332c"></p>
</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><img alt="Discrete graph." src="https://k12.openstax.org/contents/raise/resources/b7243f82e7125491bd9a2a9ae3f52a9c03fd5bef"></p>
</div>
<p><br>
</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="19431a0c-d318-421b-8db8-c96268d51acc" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>10. Which point on the scatter plot has the residual closest to zero? What does this mean about the weight of the box with that many oranges in it?</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: Your answer may vary, but here is a sample.</p>
<p>6 oranges. It means the estimated weight of the box with 6 oranges in it is closest to the actual value.</p>
</div>
</div>
<!--Interaction End -->
<p><br>
</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1d6da696-8670-4c8c-a194-e087595cbfbf" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>11. How can you use the residuals to decide how well a line fits the data?</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: Your answer may vary, but here is a sample.</p>
<p>A line will result in more accurate estimates when the residuals are closer to zero.</p>
</div>
</div>
<!--Interaction End -->
<h4>Video: Finding Residuals</h4>
<p>Watch the following video to learn more about finding residuals.</p>
<p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="controls" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/23c4c5a71e02040cd50b142cc3fd9585b214bcaf">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/016997b431f1c5c96171aab3df5ced18ce0cc8f2" srclang="en_us">
https://k12.openstax.org/contents/raise/resources/23c4c5a71e02040cd50b142cc3fd9585b214bcaf
</video></div>
</div>
</p>