SPS SPS FM Statistics 2022 February — Question 4

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2022
SessionFebruary
TopicLinear regression
TypeExplain least squares concept

  1. (a) Using the scatter diagram below, explain what is meant by least squares in the context of a regression line of \(y\) on \(x\).
    \includegraphics[max width=\textwidth, alt={}, center]{5a60e87d-7a09-4ef5-96ca-8f33030c8747-08_481_889_276_219}
    (b) A set of bivariate data \(( t , u )\) is summarised as follows.
$$\begin{array} { l l l } n = 5 & \sum t = 35 & \sum u = 54
\sum t ^ { 2 } = 285 & \sum u ^ { 2 } = 758 & \sum t u = 460 \end{array}$$
  1. Calculate the equation of the regression line of \(u\) on \(t\).
  2. The variables \(t\) and \(u\) are now scaled using the following scaling. $$v = 2 t , w = u + 4$$ Find the equation of the regression line of \(w\) on \(v\), giving your equation in the form $$w = \mathrm { f } ( v ) .$$ [BLANK PAGE]