| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2018 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Find unknown values from regression |
| Difficulty | Standard +0.8 This question requires understanding that the regression line passes through (x̄, ȳ), setting up equations with the unknown p, solving simultaneously, then computing correlation coefficient and performing a hypothesis test. It combines multiple statistical concepts (regression properties, correlation, hypothesis testing) with algebraic manipulation, making it moderately challenging but still within standard Further Maths scope. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.09c Calculate regression line |
| \(x\) | 4 | 5 | 7 | 8 | 10 | 14 |
| \(y\) | 5 | 8 | \(p\) | 7 | \(p\) | 9 |
The regression line of $y$ on $x$, obtained from a random sample of 6 pairs of values of $x$ and $y$, has equation
$$y = 0.25 x + k$$
where $k$ is a constant. The values from the sample are shown in the following table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
$x$ & 4 & 5 & 7 & 8 & 10 & 14 \\
\hline
$y$ & 5 & 8 & $p$ & 7 & $p$ & 9 \\
\hline
\end{tabular}
\end{center}
(i) Find the value of $p$ and the value of $k$.\\
(ii) Find the product moment correlation coefficient for the data.\\
(iii) Test, at the $5 \%$ significance level, whether there is evidence of positive correlation between the variables.\\
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.\\
\hfill \mbox{\textit{CAIE FP2 2018 Q11 OR}}