| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Convert regression equation between coded and original |
| Difficulty | Standard +0.3 This is a standard S1 regression question requiring routine application of formulas to find the regression line with coded variables, then converting back to original variables. The coding transformation is straightforward (linear shifts), and all calculations follow directly from given summary statistics. Slightly easier than average due to clear structure and standard technique. |
| Spec | 5.09a Dependent/independent variables5.09c Calculate regression line5.09d Linear coding: effect on regression5.09e Use regression: for estimation in context |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(S_y = 11600 - \frac{100 \times 23}{8} = 11312.5\) | M1 | |
| \(S_{xx} = 215000 - \frac{100^2}{8} = 213750\) | M1 | |
| \(b = \frac{11312.5}{213750} = 0.0529240\) | M1 A1 | |
| \(a = \frac{23}{8} - (0.0529240 \times \frac{100}{8}) = 2.21345\) | M1 A1 | |
| \(y = 2.21 + 0.0529x\) | A1 | |
| (b) \(n - 20 = 2.21345 + 0.0529240(v - 700)\) | M1 | |
| \(n = 14.8 + 0.0529v\) | A1 | |
| (c) \(n = 14.83 + 0.05292 \times 900 = 32.8 \therefore 33\) | M1 A1 | (11 marks) |
(a) $S_y = 11600 - \frac{100 \times 23}{8} = 11312.5$ | M1 |
$S_{xx} = 215000 - \frac{100^2}{8} = 213750$ | M1 |
$b = \frac{11312.5}{213750} = 0.0529240$ | M1 A1 |
$a = \frac{23}{8} - (0.0529240 \times \frac{100}{8}) = 2.21345$ | M1 A1 |
$y = 2.21 + 0.0529x$ | A1 |
(b) $n - 20 = 2.21345 + 0.0529240(v - 700)$ | M1 |
$n = 14.8 + 0.0529v$ | A1 |
(c) $n = 14.83 + 0.05292 \times 900 = 32.8 \therefore 33$ | M1 A1 | (11 marks)
---\begin{enumerate}
\item An engineer tested a new material under extreme conditions in a wind tunnel. He recorded the number of microfractures, $n$, that formed and the wind speed, $v$ metres per second, for 8 different values of $v$ with all other conditions remaining constant. He then coded the data using $x = v - 700$ and $y = n - 20$ and calculated the following summary statistics.
\end{enumerate}
$$\Sigma x = 100 , \quad \Sigma y = 23 , \quad \Sigma x ^ { 2 } = 215000 , \quad \Sigma x y = 11600 .$$
(a) Find an equation of the regression line of $y$ on $x$.\\
(b) Hence, find an equation of the regression line of $n$ on $v$.\\
(c) Use your regression line to estimate the number of microfractures that would be formed if the material was tested in a wind speed of 900 metres per second with all other conditions remaining constant.\\
(2 marks)\\
\hfill \mbox{\textit{Edexcel S1 Q4 [11]}}