| Exam Board | WJEC |
|---|---|
| Module | Further Unit 2 (Further Unit 2) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret regression line parameters |
| Difficulty | Moderate -0.3 Part (a) is a straightforward calculation of regression line coefficients using standard formulas with given summary statistics—pure routine application. Part (b) requires interpretation of extrapolation reliability by comparing how far x=70 is from each dataset's range, which involves some judgment but is a standard concept in A-level statistics. Overall slightly easier than average due to minimal problem-solving required. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line |
| Answer | Marks | Guidance |
|---|---|---|
| 7(a) | \(b = \frac{96.60984}{88.42142}\) | M1 |
| \(b = 1.09(26 \ldots)\) | A1 | Accept 1.1 |
| \(a = \frac{2738.656}{30} - 1.09(26 \ldots) \times \frac{2850.836}{30}\) | M1 | FT their '\(b\)' for M1 |
| \(a = -12.5(39...)\) | A1 | FT their '\(b\)', following A0. Answer correct to 3sf |
| \(y = -12.5 + 1.09x\) | A1 | A1 FT 'their' gradient and intercept provided at least one M1 awarded. |
| 7(b) | Africa because 70 is out of the data set for Asia. The data points for Africa are closer to a straight line than those for the Arab World. | E1 E1 |
| Total [7] |
7(a) | $b = \frac{96.60984}{88.42142}$ | M1 |
| $b = 1.09(26 \ldots)$ | A1 | Accept 1.1
| $a = \frac{2738.656}{30} - 1.09(26 \ldots) \times \frac{2850.836}{30}$ | M1 | FT their '$b$' for M1
| $a = -12.5(39...)$ | A1 | FT their '$b$', following A0. Answer correct to 3sf
| $y = -12.5 + 1.09x$ | A1 | A1 FT 'their' gradient and intercept provided at least one M1 awarded.
7(b) | Africa because 70 is out of the data set for Asia. The data points for Africa are closer to a straight line than those for the Arab World. | E1 E1 |
| **Total [7]** |7. Data from a large dataset shows the percentage of children enrolled in secondary education and the percentage of the adult population who are literate. The following graphs show data from 30 randomly selected regions from each of the Arab World, Africa and Asia. In each case, the least squares regression line of '\% Literacy' on '\% Enrolled in Secondary Education' is shown.\\
\includegraphics[max width=\textwidth, alt={}, center]{77fd7ad7-f5a3-4947-afc6-e5ef45bef7a8-6_682_1200_584_395}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Africa}
\includegraphics[alt={},max width=\textwidth]{77fd7ad7-f5a3-4947-afc6-e5ef45bef7a8-6_623_1191_1548_397}
\end{center}
\end{figure}
\includegraphics[max width=\textwidth, alt={}, center]{77fd7ad7-f5a3-4947-afc6-e5ef45bef7a8-7_665_1200_331_434}
\begin{enumerate}[label=(\alph*)]
\item Calculate the equation of the least squares regression line of '\% Literacy' ( $y$ ) on '\% Enrolled in Secondary Education' ( $x$ ) for Asia, given the following summary statistics.
$$\begin{array} { l l l }
\sum x = 2850.836 & \sum y = 2738.656 & S _ { x x } = 88.42142 \\
S _ { y y } = 204.733 & S _ { x y } = 96.60984 & n = 30
\end{array}$$
\item The Arab World, Africa and Asia each contain a region where $70 \%$ are enrolled in secondary education. The three regression lines are used to estimate the corresponding \% Literacy. Which of these estimates is likely to be the most reliable? Clearly explain your reasoning.
\section*{END OF PAPER}
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 2 2022 Q7 [7]}}