| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret regression line parameters |
| Difficulty | Easy -1.2 This is a straightforward statistics question requiring interpretation of a regression line and basic substitution. Part (a) asks for a simple description of correlation from a diagram, part (b)(i) requires standard interpretation of gradient/intercept in context (routine A-level stats), and part (b)(ii) involves substituting x=20 into the given equation plus a comment on extrapolation reliability. All techniques are basic recall with no problem-solving or mathematical complexity beyond arithmetic. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09e Use regression: for estimation in context |
A baker is aware that the pH of his sourdough, $y$, and the hydration, $x$, affect the taste and texture of the final product. The hydration is measured in ml of water per 100 g of flour (ml/100 g). The baker researches how the pH of his sourdough changes as the hydration changes.
The results of his research are shown in the diagram below.
\includegraphics{figure_5}
\begin{enumerate}[label=(\alph*)]
\item Describe the relationship between pH and hydration. [2]
\item The equation of the regression line for $y$ on $x$ is
$$y = 5.4 - 0.02x.$$
\begin{enumerate}[label=(\roman*)]
\item Interpret the gradient and intercept of the regression line in this context.
\item Estimate the pH of the sourdough when the hydration is 20 ml/100 g.
Comment on the reliability of this estimate. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2018 Q05 [6]}}