| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret regression line parameters |
| Difficulty | Easy -1.2 This is a straightforward interpretation question requiring only basic understanding of regression line parameters: recognizing negative correlation from a negative gradient, stating units (cm/day), simple arithmetic (3 × -1.1), and commenting on extrapolation. All parts are direct recall or one-step calculations with no problem-solving required. |
| Spec | 2.02c Scatter diagrams and regression lines5.09a Dependent/independent variables |
| Answer | Marks | Guidance |
|---|---|---|
| 1(a) Negative (since gradient of regression line is negative) | B1 | AO 1.2 |
| 1(b) cm/day (o.e. e.g. cm day\(^{-1}\)) | B1 | AO 2.2a |
| 1(c) \(3x[\pm]1.1 = \text{decrease of } 3.3 \text{ [cm]}\) | M1, A1 | AO 3.4, 1.1b |
| 1(d) 19 is (well) outside the range [1, 10] or involves extrapolation (o.e.) so (possibly) unreliable/inaccurate (o.e.) | B1 | AO 2.4 |
**1(a)** Negative (since gradient of regression line is negative) | B1 | AO 1.2
**1(b)** cm/day (o.e. e.g. cm day$^{-1}$) | B1 | AO 2.2a
**1(c)** $3x[\pm]1.1 = \text{decrease of } 3.3 \text{ [cm]}$ | M1, A1 | AO 3.4, 1.1b | Answers may be written within the question. B1 for stating "negative". Allow a correct interpretation e.g. as $t$ increases then $p$ decreases (o.e.) [ignore any values]. B0 for contradictory statements e.g. "negative correlation since as $t$ increases $p$ increases". M1 for attempt at a calculation (allow use of $t = x$ and $t = x + 3$ followed by subtraction that should lead to 3.3). A1 for correct description must include word "decrease" (o.e.) and value "3.3". Just seeing: $22 - 1.1 \times 3 = 18.7$ is M0A0 BUT going on to subtract 18.7 from 22 scores M1. Reaching 3.3 and stating "decrease" or "reduced" (o.e.) will score A1 too. An answer of $-3.3$ without a word describing decrease (o.e.), will just score M1A0.
**1(d)** 19 is (well) outside the range [1, 10] or involves extrapolation (o.e.) so (possibly) unreliable/inaccurate (o.e.) | B1 | AO 2.4 | B1 for stating "unreliable" (o.e.) **and** giving a suitable reason based on idea of extrapolation. Must have both statement about reliability and suitable reason e.g. $t = 19$ is too big or (Model is based on) $t$ between 1 and 10 (only) [since this is $t = 19$ is too big]. Allow e.g. (model) "may not work" because of "extrapolation". Just saying "no" since "extrapolation" is B0 but "unreliable"(o.e.) since "extrapolation" is B1.
**Total: 5 marks**
---\begin{enumerate}
\item The relationship between two variables $p$ and $t$ is modelled by the regression line with equation
\end{enumerate}
$$p = 22 - 1.1 t$$
The model is based on observations of the independent variable, $t$, between 1 and 10\\
(a) Describe the correlation between $p$ and $t$ implied by this model.
Given that $p$ is measured in centimetres and $t$ is measured in days,\\
(b) state the units of the gradient of the regression line.
Using the model,\\
(c) calculate the change in $p$ over a 3-day period.
Tisam uses this model to estimate the value of $p$ when $t = 19$\\
(d) Comment, giving a reason, on the reliability of this estimate.
\hfill \mbox{\textit{Edexcel AS Paper 2 2022 Q1 [5]}}