| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate regression line equation |
| Difficulty | Moderate -0.3 This is a standard S1 correlation and regression question requiring direct application of formulae for PMCC and regression line equations. Parts (a) and (b) are routine calculations with given summary statistics. Parts (c) and (d) test understanding of linear transformations of variables, which is slightly more conceptual but still follows standard procedures. The question is slightly easier than average because it's entirely formulaic with no interpretation challenges or novel problem-solving required. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09c Calculate regression line |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(S_{xx} = 4201\), \(S_{yy} = 3588.2\), \(S_{xy} = 3460\), \(r = 0.891\) | M1 A1 A1 | |
| (b) \(y - 8.7 = \frac{3460}{4201}(x - 10)\) → \(y = 0.824x + 0.464\) | M1 M1 A1 A1 | |
| (c) \(q - 50 = 0.824(p - 30) + 0.464\) → \(q = 0.824p + 25.8\) | M1 A1 A1 | |
| (d) When \(p = 46\), \(q \approx 63.6\) | M1 A1 | Assumed these values of \(p\) and \(q\) are within or close to the range from which the data was collected |
(a) $S_{xx} = 4201$, $S_{yy} = 3588.2$, $S_{xy} = 3460$, $r = 0.891$ | M1 A1 A1 |
(b) $y - 8.7 = \frac{3460}{4201}(x - 10)$ → $y = 0.824x + 0.464$ | M1 M1 A1 A1 |
(c) $q - 50 = 0.824(p - 30) + 0.464$ → $q = 0.824p + 25.8$ | M1 A1 A1 |
(d) When $p = 46$, $q \approx 63.6$ | M1 A1 | Assumed these values of $p$ and $q$ are within or close to the range from which the data was collected | B1 | Total: 13 marks
---Twenty pairs of observations are made of two variables $x$ and $y$, which are believed to be related. It is found that
$$\sum x = 200, \quad \sum y = 174, \quad \sum x^2 = 6201, \quad \sum y^2 = 5102, \quad \sum xy = 5200.$$
Find
\begin{enumerate}[label=(\alph*)]
\item the product-moment correlation coefficient between $x$ and $y$, [3 marks]
\item the equation of the regression line of $y$ on $x$. [4 marks]
\end{enumerate}
Given that $p = x + 30$ and $q = y + 50$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the equation of the regression line of $q$ on $p$, in the form $q = mp + c$. [3 marks]
\item Estimate the value of $q$ when $p = 46$, stating any assumptions you make. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [13]}}