| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2018 |
| Session | September |
| Marks | 4 |
| Topic | Bivariate data |
| Type | Use regression line for prediction |
| Difficulty | Moderate -0.8 This is a straightforward question on basic regression concepts requiring only recall and simple reasoning. Part (i) asks for standard terminology identification, part (ii) requires explaining a definition with a diagram provided, and part (iii) involves elementary unit conversion logic. No calculations or problem-solving required—well below average difficulty for A-level. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09a Dependent/independent variables5.09b Least squares regression: concepts |
| Controlled variable | Correlation coefficient |
| Dependent variable | Independent variable |
| Response variable | Regression coefficient |
| Answer | Marks | Guidance |
|---|---|---|
| Controlled variable, independent variable | B1 | Any extras or omissions: B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Draw vertical line from point to regression line; state the Least Squares Regression Line minimises sum of squares of these lengths | B1, E1 [2] | Allow this mark from horizontal lines |
| Answer | Marks | Guidance |
|---|---|---|
| Both coefficients divided by 2.54 | B1 [1] | oe |
## (i)
Controlled variable, independent variable | B1 | Any extras or omissions: B0
## (ii)
Draw vertical line from point to regression line; state the Least Squares Regression Line minimises sum of squares of these lengths | B1, E1 [2] | Allow this mark from horizontal lines
## (iii)
Both coefficients divided by 2.54 | B1 [1] | oe
---1 An experiment involves releasing a coin on a sloping plane so that it slides down the slope and then slides along a horizontal plane at the bottom of the slope before coming to rest. The angle $\theta ^ { \circ }$ of the sloping plane is varied, and for each value of $\theta$, the distance $d \mathrm {~cm}$ the coin slides on the horizontal plane is recorded. A scatter diagram to illustrate the results of the experiment is shown below, together with the least squares regression line of $d$ on $\theta$.\\
\includegraphics[max width=\textwidth, alt={}, center]{28c6a0d9-09a6-4743-af0e-fe2e43e256c9-2_639_972_561_548}\\
(i) State which two of the following correctly describe the variable $\theta$.
\begin{center}
\begin{tabular}{ l l }
Controlled variable & Correlation coefficient \\
Dependent variable & Independent variable \\
Response variable & Regression coefficient \\
\end{tabular}
\end{center}
The least squares regression line of $d$ on $\theta$ has equation $d = 1.96 + 0.11 \theta$.\\
(ii) Use the diagram in the Printed Answer Booklet to explain the term "least squares".\\
(iii) State what difference, if any, it would make to the equation of the regression line if $d$ were measured in inches rather than centimetres. ( 1 inch $\approx 2.54 \mathrm {~cm}$ ).
\hfill \mbox{\textit{OCR Further Statistics 2018 Q1 [4]}}