| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate PMCC from summary statistics |
| Difficulty | Moderate -0.3 This is a straightforward application of standard linear regression formulas from A-level statistics. Part (i) requires interpretation of correlation (1 mark, routine). Part (ii) involves calculating means and using the regression line formula with given summaries (6 marks, mechanical calculation). Part (iii) uses the relationship between regression coefficients and correlation (2 marks, formula recall). While it's Further Maths content, the question requires only direct application of memorized formulas with no problem-solving or insight, making it slightly easier than average overall. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09c Calculate regression line |
A set of $20$ pairs of bivariate data $(x, y)$ is summarised by
$$\Sigma x = 200, \quad \Sigma x^2 = 2125, \quad \Sigma y = 240, \quad \Sigma y^2 = 8245.$$
The product moment correlation coefficient is $-0.992$.
\begin{enumerate}[label=(\roman*)]
\item What does the value of the product moment correlation coefficient indicate about a scatter diagram of the data points? [1]
\item Find the equation of the regression line of $y$ on $x$. [6]
\item The equation of the regression line of $x$ on $y$ is $x = a' + b'y$. Find the value of $b'$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE FP2 2010 Q9 [9]}}