| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Comment on reliability/validity of prediction |
| Difficulty | Standard +0.3 Parts (a) and (b) are standard calculations using given summary statistics and formulae from the formula book. Parts (c) and (d) require understanding of regression assumptions (interpolation vs extrapolation, linearity, residuals) but are conceptual recall rather than problem-solving. Slightly above average due to the interpretation component, but still routine for Further Maths Statistics students. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09c Calculate regression line |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | 0.8392… |
| [1] | 1.1 | Awrt 0.839 |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | y = –1.180 + 4.0781x | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Both coeffs, awrt –1.18 and 4.08 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | Value of PMCC suggests that there is strong | |
| correlation, or 0.75 shown close to mean 0.399 | B1 | |
| [1] | 3.5a | E.g. “r high so points lie close to |
| Answer | Marks |
|---|---|
| No wrong extras | Not “0.75 is close to mean”, |
| Answer | Marks | Guidance |
|---|---|---|
| (d) | Whether x = 0.75 is within the data range | B1 |
| [1] | 3.5b | E.g. “maximum and minimum |
| Answer | Marks |
|---|---|
| No wrong extras | Or clear reference to |
Question 1:
1 | (a) | 0.8392… | B1
[1] | 1.1 | Awrt 0.839 | S = 1.7449…, S = 41.2…,
xx yy
S = 7.116…
xy
(b) | y = –1.180 + 4.0781x | B1
B1
[2] | 1.1
1.1 | Both coeffs, awrt –1.18 and 4.08
Letters correct, needs 1 correct
coefficient
(c) | Value of PMCC suggests that there is strong
correlation, or 0.75 shown close to mean 0.399 | B1
[1] | 3.5a | E.g. “r high so points lie close to
line”. “r is high” alone is enough.
No wrong extras | Not “0.75 is close to mean”,
unless properly justified, e.g.
SD (= 0.264) calculated
(d) | Whether x = 0.75 is within the data range | B1
[1] | 3.5b | E.g. “maximum and minimum
values of x”; not “all data points”.
No wrong extras | Or clear reference to
interpolation. NB: 95% CI
for x is (–0.156, 0.954)1 A set of bivariate data ( $X , Y$ ) is summarised as follows.\\
$n = 25 , \sum x = 9.975 , \sum y = 11.175 , \sum x ^ { 2 } = 5.725 , \sum y ^ { 2 } = 46.200 , \sum x y = 11.575$
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of Pearson's product-moment correlation coefficient.
\item Calculate the equation of the regression line of $y$ on $x$.
It is desired to know whether the regression line of $y$ on $x$ will provide a reliable estimate of $y$ when $x = 0.75$.
\item State one reason for believing that the estimate will be reliable.
\item State what further information is needed in order to determine whether the estimate is reliable.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2019 Q1 [5]}}