- (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.
$$\begin{array} { l l l }
n = 5 & \sum t = 35 & \sum u = 54
\sum t ^ { 2 } = 285 & \sum u ^ { 2 } = 758 & \sum t u = 460
\end{array}$$
- Calculate the equation of the regression line of \(u\) on \(t\).
- 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
$$w = \mathrm { f } ( v ) .$$
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