| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | January |
| Marks | 7 |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Moderate -0.3 This is a standard A-level statistics question testing routine application of correlation and regression formulas. Parts (a)-(c) require direct substitution into standard formulas (PMCC and regression line), while part (d) tests basic interpretation of the gradient. No problem-solving insight is needed, though it requires careful arithmetic with the given summary statistics. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09a Dependent/independent variables5.09c Calculate regression line |
A large field of wheat is split into 8 plots of equal area. Each plot is treated with a different amount of fertiliser, $f$ grams/m². The yield of wheat, $w$ tonnes, from each plot is recorded. The results are summarised below.
$$\sum f = 28 \quad \sum w = 303 \quad \sum w^2 = 13447 \quad S_{ff} = 42 \quad S_{fw} = 269.5$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the product moment correlation coefficient between $f$ and $w$ [2]
\item Interpret the value of your product moment correlation coefficient. [1]
\item Find the equation of the regression line of $w$ on $f$ in the form $w = a + bf$ [3]
\item Using your equation, estimate the decrease in yield when the amount of fertiliser decreases by 0.5 grams/m² [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q3 [7]}}