<p>A female social media influencer is analysing the performance of her past videos posted online. She wants to understand the relationship between the number of video views, \(v\), and the number of followers gained, \(f\), from her past video posts. The data from her earliest \(9\) videos is given in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">\(v\)</th><th style="text-align: center; --cell-justify: center">\(1000\)</th><th style="text-align: center; --cell-justify: center">\(5000\)</th><th style="text-align: center; --cell-justify: center">\(8000\)</th><th style="text-align: center; --cell-justify: center">\(10\,000\)</th><th style="text-align: center; --cell-justify: center">\(20\,000\)</th><th style="text-align: center; --cell-justify: center">\(30\,000\)</th><th style="text-align: center; --cell-justify: center">\(40\,000\)</th><th style="text-align: center; --cell-justify: center">\(50\,000\)</th><th style="text-align: left; --cell-justify: flex-start">\(60\,000\)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(f\)</td><td style="text-align: center; --cell-justify: center">\(15\)</td><td style="text-align: center; --cell-justify: center">\(163\)</td><td style="text-align: center; --cell-justify: center">\(10\)</td><td style="text-align: center; --cell-justify: center">\(278\)</td><td style="text-align: center; --cell-justify: center">\(389\)</td><td style="text-align: center; --cell-justify: center">\(456\)</td><td style="text-align: center; --cell-justify: center">\(492\)</td><td style="text-align: center; --cell-justify: center">\(541\)</td><td style="text-align: left; --cell-justify: flex-start">\(560\)</td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Due to a technical issue, one of the \(9\) videos had no audio which affected the number of followers gained. Draw a scatter diagram of these \(9\) data points and circle the data point that likely represents the video with no audio.<span class="inline-marks">[2]</span></div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1783577986572-u718gsxdb5p.png" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>The female social media influencer decides to <strong>exclude</strong> the data point that represents the video with no audio from her analysis. For parts <strong>(b)</strong>, <strong>(c)</strong> and <strong>(d)</strong> of this question, you should <strong>exclude</strong> this data point.</p>
<ol class="abc-list" start="2"><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Use your scatter diagram to explain with reasons the conclusion that the influencer should reach regarding the relationship between \(f\) and \(v\).<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">By referring to the scatter diagram and calculating the relevant product moment correlation coefficients, determine whether the relationship between \(f\) and \(v\) is modelled better by \(f = a + bv\) or \(f = a + b \ln v\), where&nbsp;\(a\) and \(b\) are constants.<br>Explain how you decide which model is better and state the equation of the least squares regression line in this case, giving your answer to \(3\) decimal places.<span class="inline-marks">[5]</span></div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">Use the appropriate least squares regression line in <strong>(c)</strong> to estimate the number of followers gained when the number of video views is \(100\,000\). Comment on the reliability of this estimate.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-e" data-list-item-path="item-e"><div class="list-item-paragraph">Explain why in the 'method of least squares', the distances which are used in finding the least squares regression line are squared.<span class="inline-marks">[1]</span></div></li></ol>
<p>A male social media influencer also decides to analyse the performance of his past videos posted online and found that the sum of the squares of the distances which are used in finding the least squares regression line is zero.</p>
<ol class="abc-list" start="6"><li data-list-item-id="item-f" data-list-item-path="item-f"><div class="list-item-paragraph">What can you deduce about the data points of this male influencer?<span class="inline-marks">[1]</span></div></li></ol>

A female social media influencer is analysing the performance of her past videos posted online. She wants to understand the relationship between the number of video views, \(v\), and the number of followers gained, \(f\), from her past video posts. The data from her earliest \(9\) videos is given in the table below.

Due to a technical issue, one of the \(9\) videos had no audio which affected the number of followers gained. Draw a scatter diagram of these \(9\) data points and circle the data point that likely represents the video with no audio.

The female social media influencer decides to **exclude** the data point that represents the video with no audio from her analysis. For parts **(b)**, **(c)** and **(d)** of this question, you should **exclude** this data point.

Use your scatter diagram to explain with reasons the conclusion that the influencer should reach regarding the relationship between \(f\) and \(v\).

By referring to the scatter diagram and calculating the relevant product moment correlation coefficients, determine whether the relationship between \(f\) and \(v\) is modelled better by \(f = a + bv\) or \(f = a + b \ln v\), where \(a\) and \(b\) are constants.
Explain how you decide which model is better and state the equation of the least squares regression line in this case, giving your answer to \(3\) decimal places.

Use the appropriate least squares regression line in **(c)** to estimate the number of followers gained when the number of video views is \(100\,000\). Comment on the reliability of this estimate.

Explain why in the 'method of least squares', the distances which are used in finding the least squares regression line are squared.

A male social media influencer also decides to analyse the performance of his past videos posted online and found that the sum of the squares of the distances which are used in finding the least squares regression line is zero.

2024 ACJC P2 Q10

2024 ACJC P2 Q10