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<h2 class="hd hd-2 unit-title">Linear regression</h2>
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<h2 class="hd hd-2 unit-title">Class 26 reading questions: linear regression</h2>
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<p><b class="bf">1.</b> True or false: Linear regression can be used to fit a parabola to data. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_c26-rq11_2_1">
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<p><b class="bf">2.</b> In the least squares model [mathjaxinline]y = ax + b[/mathjaxinline] the variable [mathjaxinline]x[/mathjaxinline] is called </p>
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<p>
<b class="bf">3.</b>
<b class="bfseries">Lollipop Kids</b>
</p>
<p>
Consider the sample space of children under 13 in the United States. The random variable [mathjaxinline]X[/mathjaxinline] represents the age of a child. The random variable [mathjaxinline]Y[/mathjaxinline] represents the number of lollipops possessed by the child. By catching and releasing three children, we record the following sample data of the form [mathjaxinline](x,y)[/mathjaxinline]. </p>
<table id="a0000000002" class="equation" width="100%" cellspacing="0" cellpadding="7" style="table-layout:auto">
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<td class="equation" style="width:80%; border:none">[mathjax]\{ (1,2),(2,3),(3,3)\}[/mathjax]</td>
<td class="eqnnum" style="width:20%; border:none">&#160;</td>
</tr>
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<p><b class="bf">(a)</b> Calculate the sample means for the [mathjaxinline]x[/mathjaxinline] data and the [mathjaxinline]y[/mathjaxinline]. </p>
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Mean for [mathjaxinline]y[/mathjaxinline]: <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_c26-rq13_3_1" class=" capa_inputtype textline">
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<p><b class="bf">(b)</b> Using least squares determine the best-fit line in the [mathjaxinline]xy[/mathjaxinline]-plane </p>
<table id="a0000000003" class="equation" width="100%" cellspacing="0" cellpadding="7" style="table-layout:auto">
<tr>
<td class="equation" style="width:80%; border:none">[mathjax]y = \hat{a} x + \hat{b}.[/mathjax]</td>
<td class="eqnnum" style="width:20%; border:none">&#160;</td>
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Give [mathjaxinline]\hat{a}[/mathjaxinline]. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_c26-rq13_4_1" class=" capa_inputtype textline">
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Problem 4
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<b class="bf">4.</b>
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We use simple linear regression to predict the skill level of NBA players' sons from the skill level of their fathers. According to the prediction how will the sons compare with their fathers? On average they are: </p>
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