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.
| \(v\) | \(1000\) | \(5000\) | \(8000\) | \(10\,000\) | \(20\,000\) | \(30\,000\) | \(40\,000\) | \(50\,000\) | \(60\,000\) |
|---|
| \(f\) | \(15\) | \(163\) | \(10\) | \(278\) | \(389\) | \(456\) | \(492\) | \(541\) | \(560\) |
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.[2]
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 \(v\).[1]
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.[5]
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.[2]
Explain why in the 'method of least squares', the distances which are used in finding the least squares regression line are squared.[1]
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.
What can you deduce about the data points of this male influencer?[1]