Using the scatter diagram in the Printed Answer Booklet, explain what is meant by least squares in the context of a regression line of \(y\) on \(x\).
A set of bivariate data \(( t , u )\) is summarised as follows.
\(n = 5 \quad \sum t = 35 \quad \sum u = 54\)
\(\sum t ^ { 2 } = 285 \quad \sum u ^ { 2 } = 758 \quad \sum \mathrm { tu } = 460\)
Calculate the equation of the regression line of \(u\) on \(t\).
The variables \(t\) and \(u\) are now scaled using the following scaling.
\(\mathrm { v } = 2 \mathrm { t } , \mathrm { w } = \mathrm { u } + 4\)
Find the equation of the regression line of \(w\) on \(v\), giving your equation in the form \(w = f ( v )\).