| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2014 |
| Session | November |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from raw data table |
| Difficulty | Standard +0.3 This is a standard linear regression question requiring routine calculations of regression line, correlation coefficient, and a hypothesis test lookup. All techniques are textbook procedures with no novel problem-solving required. Part (iv) adds mild complexity by requiring understanding of critical values for correlation tests, but this is still a standard application. Slightly easier than average due to straightforward computational nature. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.09a Dependent/independent variables5.09c Calculate regression line |
| \(x\) | 4 | 6 | 6 | 8 | 2 | 7 | 12 | 14 | 9 | 5 |
| \(y\) | 2 | 4 | 6 | 8 | 6 | 10 | 9 | 8 | 6 | 5 |
A random sample of 10 pairs of values of $x$ and $y$ is given in the following table.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
$x$ & 4 & 6 & 6 & 8 & 2 & 7 & 12 & 14 & 9 & 5 \\
\hline
$y$ & 2 & 4 & 6 & 8 & 6 & 10 & 9 & 8 & 6 & 5 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item Find the equation of the regression line of $y$ on $x$. [4]
\item Find the product moment correlation coefficient for the sample. [2]
\item Find the estimated value of $y$ when $x = 10$, and comment on the reliability of this estimate. [2]
\item Another sample of $N$ pairs of data from the same population has the same product moment correlation coefficient as the first sample given. A test, at the 1% significance level, on this second sample indicates that there is sufficient evidence to conclude that there is positive correlation. Find the set of possible values of $N$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE FP2 2014 Q9 [11]}}