| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate PMCC from summary statistics |
| Difficulty | Moderate -0.8 This is a straightforward S1 question testing standard linear regression calculations with given summary statistics. Parts (a) and (b) are basic interpretation requiring minimal calculation, while (c) and (d) involve routine application of regression formulas (calculating gradient b = S_ch/S_cc and intercept a). All necessary summary statistics are provided, eliminating any computational burden. This is easier than average as it's purely procedural with no problem-solving or conceptual challenges. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc5.08c Pearson: measure of straight-line fit5.08d Hypothesis test: Pearson correlation5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line5.09d Linear coding: effect on regression |
3. Martin is investigating the relationship between a person's daily caffeine consumption, $c$ milligrams, and the amount of sleep they get, $h$ hours, per night. He collected this information from 20 people and the results are summarised below.
$$\begin{array} { c c }
\sum c = 3660 \quad \sum h = 126 \quad \sum c ^ { 2 } = 973228 \\
\sum c h = 20023.4 \quad S _ { c c } = 303448 \quad S _ { c h } = - 3034.6
\end{array}$$
Martin calculates the product moment correlation coefficient for these data and obtains - 0.833
\begin{enumerate}[label=(\alph*)]
\item Give a reason why this value supports a linear relationship between $c$ and $h$
The amount of sleep per night is the response variable.
\item Explain what you understand by the term 'response variable'.
Martin says that for each additional 100 mg of caffeine consumed, the expected number of hours of sleep decreases by 1
\item Determine, by calculation, whether or not the data support this statement.
\item Use the data to calculate an estimate for the expected number of hours of sleep per night when no caffeine is consumed.\\
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\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2018 Q3 [8]}}