| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Relate two regression lines |
| Difficulty | Standard +0.3 This is a straightforward S1 regression question requiring standard formula application. Students must use the regression gradient formula to find Σxy, then apply standard formulas for the second regression line and correlation coefficient. While it involves multiple steps and careful algebraic manipulation, all techniques are routine textbook exercises with no conceptual challenges or novel problem-solving required. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(S_w = 810.104\), \(S_{xy} = 0.8 \times 810.104 = 648.0832\) | B1 M1 | |
| \(\sum xy = S_{xy} + (\sum x + \sum y)/10 = 1835.2\) | M1 A1 | |
| (b) \(S_{xx} = 862.075\) and \(y - 11.36 = \frac{648.0832}{862.075}(x - 10.45)\) | M1 A1 A1 | |
| \(y = 0.752x + 3.50\) | M1 A1 | |
| (c) \(r = \sqrt{0.776 \times 0.8} = 0.776\) | M1 A1 A1 | |
| (d) Moderate positive correlation | B1 | Total: 13 marks |
(a) $S_w = 810.104$, $S_{xy} = 0.8 \times 810.104 = 648.0832$ | B1 M1 |
$\sum xy = S_{xy} + (\sum x + \sum y)/10 = 1835.2$ | M1 A1 |
(b) $S_{xx} = 862.075$ and $y - 11.36 = \frac{648.0832}{862.075}(x - 10.45)$ | M1 A1 A1 |
$y = 0.752x + 3.50$ | M1 A1 |
(c) $r = \sqrt{0.776 \times 0.8} = 0.776$ | M1 A1 A1 |
(d) Moderate positive correlation | B1 | **Total: 13 marks**Two variables $x$ and $y$ are such that, for a sample of ten pairs of values,
$$\sum x = 104.5, \quad \sum y = 113.6, \quad \sum x^2 = 1954.1, \quad \sum y^2 = 2100.6.$$
The regression line of $x$ on $y$ has gradient 0.8. Find
\begin{enumerate}[label=(\alph*)]
\item $\sum xy$, [4 marks]
\item the equation of the regression line of $y$ on $x$, [5 marks]
\item the product moment correlation coefficient between $y$ and $x$. [3 marks]
\item Describe the kind of correlation indicated by your answer to (c). [1 mark]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q6 [13]}}