| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 17 |
| 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 straightforward linear regression question with coding/decoding. Part (a) requires simple arithmetic to find means from coded data. Part (b) is direct variance calculation from summary statistics. Part (c) involves standard regression formula application then transforming back to original variables. Part (d) is substitution. All steps are routine textbook procedures with no conceptual challenges, making it slightly easier than average. |
| Spec | 5.02c Linear coding: effects on mean and variance5.09c Calculate regression line |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\sum t = \sum x + 80 = 122.4\) and Mean time \(= 122.4 ÷ 8 = 15.3\) s | M1 A1 | |
| \(\sum p = \sum y + 1200 = 1760\) and Mean price \(= £1760 ÷ 8 = £220\) | M1 A1 | |
| (b) \(\text{Var}(T) = \text{Var}(X + 10) = \text{Var}(X) = 314.5 ÷ 8 - 5.3^2 = 11.2\) | M1 A1 A1 | |
| (c) \(y\) on \(x\): \(y - 70 = \frac{8(1592) - 424 \times 560}{8(3145) - 424^2}(x - 5.3)\) | M1 M1 A1 A1 | |
| \(y = -15.3x + 151.2\) and \(p - 150 = -15.3(t - 10) + 151.2\) | A1 M1 A1 | |
| \(p = -15.3t + 454\) | M1 A1 | |
| (d) £281 | A1 | 17 marks |
(a) $\sum t = \sum x + 80 = 122.4$ and Mean time $= 122.4 ÷ 8 = 15.3$ s | M1 A1 |
$\sum p = \sum y + 1200 = 1760$ and Mean price $= £1760 ÷ 8 = £220$ | M1 A1 |
(b) $\text{Var}(T) = \text{Var}(X + 10) = \text{Var}(X) = 314.5 ÷ 8 - 5.3^2 = 11.2$ | M1 A1 A1 |
(c) $y$ on $x$: $y - 70 = \frac{8(1592) - 424 \times 560}{8(3145) - 424^2}(x - 5.3)$ | M1 M1 A1 A1 |
$y = -15.3x + 151.2$ and $p - 150 = -15.3(t - 10) + 151.2$ | A1 M1 A1 |
$p = -15.3t + 454$ | M1 A1 |
(d) £281 | A1 | 17 marks6. In a survey for a computer magazine, the times $t$ seconds taken by eight laser printers to print a page of text were compared with the prices $\pounds p$ of the printers. The data were coded using the equations $x = t - 10$ and $y = p - 150$, and it was found that
$$\sum x = 42 \cdot 4 , \quad \sum x ^ { 2 } = 314 \cdot 5 , \quad \sum y = 560 , \quad \sum y ^ { 2 } = 60600 , \quad \sum x y = 1592 .$$
\begin{enumerate}[label=(\alph*)]
\item Find the mean time and the mean price for the eight printers.
\item Find the variance of the times.
\item Find the equation of the regression line of $p$ on $t$.
\item Estimate the price of a printer which takes 11.3 seconds to print the page.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q6 [17]}}