| Exam Board | OCR MEI |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | January |
| Marks | 19 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from raw data table |
| Difficulty | Moderate -0.3 This is a straightforward application of standard linear regression formulas with all summary statistics provided. Students need only substitute values into the formulae for gradient and intercept, then use the line equation for predictions. The residual calculation is also routine. While it requires careful arithmetic and understanding of when extrapolation is unreliable, it involves no problem-solving or novel insight—just methodical application of S2 techniques. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09e Use regression: for estimation in context |
| \(a\) | 0 | 300 | 600 | 900 | 1200 | 1500 | 1800 |
| \(t\) | 635 | 704 | 776 | 836 | 923 | 1008 | 1105 |
1 A pilot records the take-off distance for his light aircraft on runways at various altitudes. The data are shown in the table below, where $a$ metres is the altitude and $t$ metres is the take-off distance. Also shown are summary statistics for these data.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | }
\hline
$a$ & 0 & 300 & 600 & 900 & 1200 & 1500 & 1800 \\
\hline
$t$ & 635 & 704 & 776 & 836 & 923 & 1008 & 1105 \\
\hline
\end{tabular}
\end{center}
$$n = 7 \quad \Sigma a = 6300 \quad \Sigma t = 5987 \quad \Sigma a ^ { 2 } = 8190000 \quad \Sigma t ^ { 2 } = 5288931 \quad \Sigma a t = 6037800$$
\begin{enumerate}[label=(\roman*)]
\item Draw a scatter diagram to illustrate these data.
\item State which of the two variables $a$ and $t$ is the independent variable and which is the dependent variable. Briefly explain your answer.
\item Calculate the equation of the regression line of $t$ on $a$.
\item Use the equation of the regression line to calculate estimates of the take-off distance for altitudes\\
(A) 800 metres,\\
(B) 2500 metres.
Comment on the reliability of each of these estimates.
\item Calculate the value of the residual for the data point where $a = 1200$ and $t = 923$, and comment on its sign.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S2 2010 Q1 [19]}}