| Exam Board | Edexcel |
|---|---|
| Module | FS2 (Further Statistics 2) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret residual plots |
| Difficulty | Standard +0.3 This is a standard residual plot interpretation question from Further Statistics 2. Students need to recognize that residuals must sum to zero (making sketch I infeasible) and identify patterns suggesting non-linearity. While it requires understanding of regression diagnostics, the visual patterns are clear and the reasoning straightforward for students who have covered this topic. Slightly easier than average due to its direct application of taught principles. |
| Spec | 5.09e Use regression: for estimation in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Is feasible as a residual plot but probably a non-linear relationship | B1 | For stating possibly non-linear (allow a suitable sketch) |
| Since the residuals are not randomly scattered about zero | B1 | For a suitable comment (e.g. follow a systematic pattern) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Impossible as a residual plot | B1 | For stating not feasible as a residual plot |
| Since the residuals do not sum to zero | B1 | For a correct reason |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Is feasible as a residual plot and probably a linear relationship | B1 | For stating probably a linear relationship |
| Since the points are randomly scattered about zero | B1 | For a suitable supporting reason |
# Question 3:
## Part I:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Is feasible as a residual plot but probably a non-linear relationship | B1 | For stating possibly non-linear (allow a suitable sketch) |
| Since the residuals are not randomly scattered about zero | B1 | For a suitable comment (e.g. follow a systematic pattern) |
## Part II:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Impossible as a residual plot | B1 | For stating not feasible as a residual plot |
| Since the residuals do not sum to zero | B1 | For a correct reason |
## Part III:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Is feasible as a residual plot and probably a linear relationship | B1 | For stating probably a linear relationship |
| Since the points are randomly scattered about zero | B1 | For a suitable supporting reason |
---3 Below are 3 sketches from some students of the residuals from their linear regressions of $y$ on $x$.\\
\includegraphics[max width=\textwidth, alt={}, center]{54bf68ab-7934-432a-890f-20093082ab07-06_252_704_342_660}\\
\includegraphics[max width=\textwidth, alt={}, center]{54bf68ab-7934-432a-890f-20093082ab07-06_266_718_625_660}\\
\includegraphics[max width=\textwidth, alt={}, center]{54bf68ab-7934-432a-890f-20093082ab07-06_248_599_936_660}
\section*{III}
III
For each sketch you should state, giving your reason,\\
(i) whether or not the sketch is feasible\\
and if it is feasible\\
(ii) whether or not the sketch suggests a linear or a non-linear relationship between $y$ and $x$.
\hfill \mbox{\textit{Edexcel FS2 2020 Q3 [6]}}