| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from raw data table |
| Difficulty | Moderate -0.8 This is a straightforward application of standard S1 regression formulas with all summations provided. Students simply substitute into memorized formulas for regression line and correlation coefficient, then draw a line and make a basic comment. No problem-solving or interpretation challenges beyond routine textbook exercises. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.09b Least squares regression: concepts5.09c Calculate regression line |
| \(n\) | 1 | 2 | 3 | 4 | 5 | 6 |
| \(p ( \% )\) | 35.2 | 37.1 | 40.6 | 39.0 | 43.4 | 44.8 |
| Answer | Marks |
|---|---|
| Scatter diagram with line \(p = 33.5 + 1.87n\) | B4 |
| Answer | Marks |
|---|---|
| \(S_{yy} = 873 - \frac{21 \times 240.1}{6} = 32.65\) | M1 |
| \(S_{nn} = 91 - \frac{21^2}{6} = 17.5\) | M1 |
| \(b = \frac{32.65}{17.5} = 1.8657\) | M1 A1 |
| \(a = \frac{240.1}{6} - 1.8657 \times \frac{21}{6} = 33.4867\) | M1 A1 |
| \(p = 33.5 + 1.87n\) | A1 |
| line on graph above | B2 |
| Answer | Marks |
|---|---|
| \(S_{pp} = 9675.41 - \frac{240.1^2}{6} = 67.4083\) | M1 |
| \(r = \frac{\sqrt{17.5 \times 67.4083}}{32.65} = 0.9506\) | M1 A1 |
| \(r\) strongly +ve supporting linear model | B1 |
| (17) | |
| Total | (75) |
**Part (a)**
**Scatter diagram with line** $p = 33.5 + 1.87n$ | B4 |
**Part (b)**
$S_{yy} = 873 - \frac{21 \times 240.1}{6} = 32.65$ | M1 |
$S_{nn} = 91 - \frac{21^2}{6} = 17.5$ | M1 |
$b = \frac{32.65}{17.5} = 1.8657$ | M1 A1 |
$a = \frac{240.1}{6} - 1.8657 \times \frac{21}{6} = 33.4867$ | M1 A1 |
$p = 33.5 + 1.87n$ | A1 |
line on graph above | B2 |
**Part (c)**
$S_{pp} = 9675.41 - \frac{240.1^2}{6} = 67.4083$ | M1 |
$r = \frac{\sqrt{17.5 \times 67.4083}}{32.65} = 0.9506$ | M1 A1 |
$r$ strongly +ve supporting linear model | B1 |
| (17) |
**Total** | (75) |6. A school introduced a new programme of support lessons in 1994 with a view to improving grades in GCSE English. The table below shows the number of years since 1994, n, and the corresponding percentage of students achieving A to C grades in GCSE English, $p$, for each year.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
$n$ & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$p ( \% )$ & 35.2 & 37.1 & 40.6 & 39.0 & 43.4 & 44.8 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Represent these data on a scatter diagram.
You may use the following values.
$$\Sigma n = 21 , \quad \Sigma p = 240.1 , \quad \Sigma n ^ { 2 } = 91 , \quad \Sigma p ^ { 2 } = 9675.41 , \quad \Sigma n p = 873 .$$
\item Find an equation of the regression line of $p$ on $n$ and draw it on your graph.
\item Calculate the product moment correlation coefficient for these data and comment on the suitability of a linear model for the relationship between $n$ and $p$ during this period.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q6 [17]}}