| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2022 |
| Session | February |
| Marks | 7 |
| Topic | Linear regression |
| Type | Explain least squares concept |
| Difficulty | Moderate -0.8 This question tests basic understanding of least squares concept and routine regression calculations. Part (a) requires explaining a standard definition with a diagram provided. Parts (b)(i) and (b)(ii) involve straightforward application of regression formulas and linear transformations—standard Further Maths Statistics content with no novel problem-solving required. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09d Linear coding: effect on regression |
\begin{enumerate}
\item (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.
\end{enumerate}
$$\begin{array} { l l l }
n = 5 & \sum t = 35 & \sum u = 54 \\
\sum t ^ { 2 } = 285 & \sum u ^ { 2 } = 758 & \sum t u = 460
\end{array}$$
(i) Calculate the equation of the regression line of $u$ on $t$.\\
(ii) 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
$$w = \mathrm { f } ( v ) .$$
\\
\hfill \mbox{\textit{SPS SPS FM Statistics 2022 Q4 [7]}}