| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from summary statistics |
| Difficulty | Moderate -0.8 This is a straightforward application of standard regression formulas (b = S_vc/S_vv, a = ȳ - bx̄) with simple arithmetic, followed by routine interpretation and substitution. All steps are mechanical with no problem-solving or conceptual challenge beyond basic recall of the regression line method. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09d Linear coding: effect on regression |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(b = \frac{594.05}{85.44} = 6.953\) | M1 | |
| \(a = 104.4 - (6.953 \times 4.92) = 70.192\) | M1 | |
| \(c = 70.2 + 6.95y\) | M1 A1 | |
| (b) \(a\) = no. of sign-ups without an advert | B1 | |
| \(b\) = no. of extra sign-ups per million viewers of advert | B1 | |
| (c) \(70.192 + (6.953 \times 3.7) = 95.92 \therefore 96\) | M1 A1 | |
| (d) e.g. type of programme; length of advert | B2 | (10 marks total) |
(a) $b = \frac{594.05}{85.44} = 6.953$ | M1 |
$a = 104.4 - (6.953 \times 4.92) = 70.192$ | M1 |
$c = 70.2 + 6.95y$ | M1 A1 |
(b) $a$ = no. of sign-ups without an advert | B1 |
$b$ = no. of extra sign-ups per million viewers of advert | B1 |
(c) $70.192 + (6.953 \times 3.7) = 95.92 \therefore 96$ | M1 A1 |
(d) e.g. type of programme; length of advert | B2 | (10 marks total)4. An internet service provider runs a series of television adverts at weekly intervals. To investigate the effectiveness of the adverts the company recorded the viewing figures in millions, $v$, for the programme in which the advert was shown, and the number of new customers, $c$, who signed up for their service the next day.
The results are summarised as follows.
$$\bar { v } = 4.92 , \quad \bar { c } = 104.4 , \quad S _ { v c } = 594.05 , \quad S _ { v v } = 85.44 .$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the equation of the regression line of $c$ on $v$ in the form $c = a + b v$.
\item Give an interpretation of the constants $a$ and $b$ in this context.
\item Estimate the number of customers that will sign up with the company the day after an advert is shown during a programme watched by 3.7 million viewers.
\item State two other factors besides viewing figures that will affect the success of an advert in gaining new customers for the company.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q4 [10]}}