| Exam Board | WJEC |
|---|---|
| Module | Further Unit 2 (Further Unit 2) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from summary statistics |
| Difficulty | Moderate -0.3 This is a standard A-level statistics regression question requiring straightforward application of formulas for gradient (b = S_xy/S_xx) and intercept (a = ȳ - bx̄), followed by identifying common misuses of regression (extrapolation and wrong direction). All values are provided, requiring only substitution and basic arithmetic. Part (b) tests understanding of regression concepts rather than calculation. Slightly easier than average due to being purely procedural with no problem-solving required. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09e Use regression: for estimation in context |
| Answer | Marks | Guidance |
|---|---|---|
| \(b = \frac{49.4511}{3.48}\) | M1 | |
| \(b = 14.2(0977 \ldots)\) | A1 | |
| \(a = \frac{898}{14} - 14.2(0977 \ldots) \times \frac{46.2}{14}\) | M1 | |
| \(= 17.2(5061\ldots)\) | A1 | |
| \(y = 17.3 + 14.2x\) | B1 | B1 FT 'their' gradient and intercept. |
| Answer | Marks |
|---|---|
| The regression line \(x\) on \(y\) would be more appropriate. OR would not be able to rearrange this equation to find \(x\) from \(y\). | E1 |
| Gives a value outside the range. OR 90 is outside the range. | E1 |
| [7] |
## 7(a)
$b = \frac{49.4511}{3.48}$ | M1 |
$b = 14.2(0977 \ldots)$ | A1 |
$a = \frac{898}{14} - 14.2(0977 \ldots) \times \frac{46.2}{14}$ | M1 |
$= 17.2(5061\ldots)$ | A1 |
$y = 17.3 + 14.2x$ | B1 | B1 FT 'their' gradient and intercept.
## 7(b)
The regression line $x$ on $y$ would be more appropriate. OR would not be able to rearrange this equation to find $x$ from $y$. | E1 |
Gives a value outside the range. OR 90 is outside the range. | E1 |
| [7] |A university professor conducted some research into factors that affect job satisfaction. The four factors considered were Interesting work, Good wages, Job security and Appreciation of work done.
The professor interviewed workers at 14 different companies and asked them to rate their companies on each of the factors. The workers' ratings were averaged to give each company a score out of 5 on each factor.
Each company was also given a score out of 100 for Job satisfaction.
The following graph shows the part of the research concerning Job Satisfaction versus Interesting work.
\includegraphics{figure_2}
\begin{enumerate}[label=(\alph*)]
\item Calculate the equation of the least squares regression line of Job satisfaction ($y$) on Interesting work ($x$), given the following summary statistics. [5]
$\sum x = 46 \cdot 2$, \quad $\sum y = 898$, \quad $S_{xx} = 3 \cdot 48$
$S_{xy} = 49 \cdot 45$, \quad $S_{yy} = 1437 \cdot 714$, \quad $n = 14$
\item Give two reasons why it would be inappropriate for the professor to use this equation to calculate the score for Interesting work from a Job satisfaction score of 90. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 2 2018 Q7 [7]}}