| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Topic | Linear regression |
| Type | Calculate y on x from summary statistics |
| Difficulty | Moderate -0.3 This is a straightforward application of standard linear regression formulas from summary statistics. Students need to substitute given values into memorized formulas for regression line and correlation coefficient, then interpret. While it requires careful arithmetic and understanding of extrapolation reliability, it involves no problem-solving or novel insight—just routine procedural work slightly below average difficulty due to being purely formulaic. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09c Calculate regression line5.09e Use regression: for estimation in context |
**Question 2(i)**
$$\frac{1350.2 - \frac{24.6 \times 404}{8}}{105.56 - \frac{24.6^2}{8}}$$
**M1**
$= 3.60(6886178)$ **A1**
$$y - \frac{404}{8} = 3.61\left(x - \frac{24.6}{8}\right) \text{ or } a = \frac{404}{8} - 3.61 \times \frac{24.6}{8}$$
**M1** Using their 3.61, allow sign errors
$y = 39.4 + 3.61x$ **A1**
**Question 2(ii)**
Attempt at use of correct formula **M1**
Get $0.965$ **A1** (0.964914428)
**Question 2(iii)(a)**
$44.8$ **B1** Accept 45; **FT** *their* $y$ on $x$
**Question 2(iii)(b)**
Reliable as within range of used values (interpolation) **B1**
Close to linearity **B1** Accept strong correlation2 A teacher is monitoring the progress of students. The length of time, $x$ hours, spent revising in a given week is compared to the score, $y$, achieved in an assessment at the end of the week. The scatter diagram for a random sample of 8 students is shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{35d24778-1203-4d5d-be4b-bb375344fe09-2_866_967_715_589}
The data are summarised as $\Sigma x = 24.6 , \Sigma y = 404 , \Sigma x ^ { 2 } = 105.56 , \Sigma y ^ { 2 } = 20820$ and $\Sigma x y = 1350.2$.\\
(i) Find the equation of the least squares regression line of $y$ on $x$.\\
(ii) Calculate the product moment correlation coefficient for the data.\\
(iii) A ninth student, Jane, revises for 1.5 hours.
\begin{enumerate}[label=(\alph*)]
\item Estimate her score in the assessment.
\item Comment on the reliability of this estimate.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2018 Q2 [9]}}