| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Moderate -0.3 Parts (a) and (b) are standard formula applications for correlation and regression that any Further Maths student should know. Parts (c) and (d) require understanding of reliability concepts (interpolation vs extrapolation, correlation strength) but are straightforward interpretative questions. This is slightly easier than average due to being mostly computational with minimal conceptual challenge. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09c Calculate regression line |
A set of bivariate data $(X, Y)$ is summarised as follows.
$n = 25$, $\Sigma x = 9.975$, $\Sigma y = 11.175$, $\Sigma x^2 = 5.725$, $\Sigma y^2 = 46.200$, $\Sigma xy = 11.575$
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of Pearson's product-moment correlation coefficient. [1]
\item Calculate the equation of the regression line of $y$ on $x$. [2]
\end{enumerate}
It is desired to know whether the regression line of $y$ on $x$ will provide a reliable estimate of $y$ when $x = 0.75$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item State one reason for believing that the estimate will be reliable. [1]
\item State what further information is needed in order to determine whether the estimate is reliable. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2021 Q1 [5]}}