| Exam Board | WJEC |
|---|---|
| Module | Further Unit 2 (Further Unit 2) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret correlation strength/direction |
| Difficulty | Moderate -0.8 This is a straightforward statistics question requiring interpretation of correlation coefficients (2 marks of basic description) and standard regression calculations using given summary statistics with the formulas b = S_xy/S_xx and a = ȳ - bx̄. The prediction in part (c) is simple substitution. All techniques are routine A-level statistics with no problem-solving or novel insight required, making it easier than average. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09a Dependent/independent variables5.09c Calculate regression line |
| Variable | Entry standards | Student satisfaction | Graduate prospects | Research quality |
| Entry standards | 1 | |||
| Student satisfaction | -0.030 | 1 | ||
| Graduate prospects | 0.772 | 0.236 | 1 | |
| Research quality | 0.866 | 0.066 | 0.827 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) The evidence suggests that good graduate prospects are associated with: strong research quality or high entry standards. | B1, B1 | AO2, AO2 |
| (b) Gradient = \(\frac{122.72}{1.0542} = 116.4(105)\) | M1, A1 | AO2, AO1 |
| Intercept = \(\frac{2522}{7} - 116.4105 \times \frac{22.24}{7} = -9.5(67)\) | M1, A1 | AO2, AO1 |
| \(y = 116.4(105)x - 9.5(67)\) | B1 | AO1 |
| (c) \(116.4 \times 3 - 9.6 = 339.6\) | M1, A1 | AO3, AO1 |
**(a)** The evidence suggests that good graduate prospects are associated with: strong research quality or high entry standards. | B1, B1 | AO2, AO2 | Or The evidence suggests that good graduate prospects are not associated with student satisfaction
**(b)** Gradient = $\frac{122.72}{1.0542} = 116.4(105)$ | M1, A1 | AO2, AO1
Intercept = $\frac{2522}{7} - 116.4105 \times \frac{22.24}{7} = -9.5(67)$ | M1, A1 | AO2, AO1 | Allow for using 116.4 giving -9.5(337)
$y = 116.4(105)x - 9.5(67)$ | B1 | AO1 | FT 'their' gradient and intercept
**(c)** $116.4 \times 3 - 9.6 = 339.6$ | M1, A1 | AO3, AO1 | [9] | Accept 358.7(988...) if using exact values throughout
---A year 12 student wishes to study at a Welsh university. For a randomly chosen year between 2000 and 2017 she collected data for seven universities in Wales from the Complete University Guide website. The data are for the variables:
• 'Entry standards' – the average UCAS tariff score of new undergraduate students;
• 'Student satisfaction' – a measure of student views of the teaching quality at the university taken from the National Student Survey (maximum 5);
• 'Graduate prospects' – a measure of the employability of a university's first degree graduates (maximum 100);
• 'Research quality' – a measure of the quality of the research undertaken in the university (maximum 4).
\begin{enumerate}[label=(\alph*)]
\item Pearson's product-moment correlation coefficients, for each pairing of the four variables, are shown in the table below. Discuss the correlation between graduate prospects and the other three variables. [2]
\begin{tabular}{|l|c|c|c|c|}
\hline
Variable & Entry standards & Student satisfaction & Graduate prospects & Research quality \\
\hline
Entry standards & 1 & & & \\
\hline
Student satisfaction & -0.030 & 1 & & \\
\hline
Graduate prospects & 0.772 & 0.236 & 1 & \\
\hline
Research quality & 0.866 & 0.066 & 0.827 & 1 \\
\hline
\end{tabular}
\item Calculate the equation of the least squares regression line to predict 'Entry standards'(y) from 'Research quality'(x), given the summary statistics:
$$\sum x = 22.24, \sum y = 2522, S_{xx} = 1.0542, S_{xy} = 20193.5, S_{yy} = 122.72.$$ [5]
\item The data for one of the Welsh universities are missing. This university has a research quality of 3.00. Use your equation to predict the entry standard for this university. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 2 Q4 [9]}}